From a3b9c8f07eb8fee0612dcdf218410a97cfcd0440 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 18 Mar 2024 19:02:30 +0000 Subject: [PATCH 001/140] add draft design content for superspreading and chains episodes --- config.yaml | 11 +- episodes/fig/SEE-dist.png | Bin 0 -> 35883 bytes .../SEE-individual-reproductive-number.png | Bin 0 -> 149897 bytes episodes/fig/SEE-params.png | Bin 0 -> 41828 bytes episodes/superspreading-estimate.Rmd | 430 ++++++++++++++++++ 5 files changed, 436 insertions(+), 5 deletions(-) create mode 100644 episodes/fig/SEE-dist.png create mode 100644 episodes/fig/SEE-individual-reproductive-number.png create mode 100644 episodes/fig/SEE-params.png create mode 100644 episodes/superspreading-estimate.Rmd diff --git a/config.yaml b/config.yaml index b554de4f..20e39703 100644 --- a/config.yaml +++ b/config.yaml @@ -14,7 +14,7 @@ carpentry: 'incubator' title: 'Real-time analysis and forecasting for outbreak analytics with R' # Date the lesson was created (YYYY-MM-DD, this is empty by default) -created: +created: # Comma-separated list of keywords for the lesson keywords: 'forecasts, epidemic models, interventions' @@ -62,21 +62,22 @@ episodes: #- quantify-transmissibility.Rmd - create-forecast.Rmd - severity-static.Rmd +- superspreading-estimate.Rmd # Information for Learners -learners: +learners: # Information for Instructors -instructors: +instructors: # Learner Profiles -profiles: +profiles: # Customisation --------------------------------------------- # # This space below is where custom yaml items (e.g. pinning # sandpaper and varnish versions) should live + varnish: epiverse-trace/varnish@epiversetheme -# this is carpentries/sandpaper#533 in our fork so we can keep it up to date with main sandpaper: epiverse-trace/sandpaper@patch-renv-github-bug diff --git a/episodes/fig/SEE-dist.png b/episodes/fig/SEE-dist.png new file mode 100644 index 0000000000000000000000000000000000000000..c42cc6e0e1eb67fe81d26bf4c202146519342e75 GIT binary 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you reconstruct transmission chains? + +:::::::::::::::::::::::::::::::::::::::::::::::: + +::::::::::::::::::::::::::::::::::::: objectives + +- Quantify transmission heterogeneity +- Estimate overdispersion from early outbreak data +- Estimate R0 +- Estimate k +- Estimate the proportion of superspreading events + +- Create a Short term forecast using branching process +- Create simulation of interventions + +:::::::::::::::::::::::::::::::::::::::::::::::: + +::::::::::::::::::::::::::::::::::::: prereq + +## Prerequisites + +List (and hyperlink) the lessons/packages which need to be covered before this lesson + +::::::::::::::::::::::::::::::::: + +## my questions + +- does the count of 0-1 secondary cases also biased by delays or interventions when secondary cases measured? [DISCUSSION: potential callout] + +- is size equal to dispersion parameter? or inverse-dispersion? [MISCONCEPTION: review in wiki] + +- what is the difference between superspreading and epichains? is creating projects is the key feature that differenciates them? + +## pre material not to overlap + +- https://www.epirhandbook.com/en/transmission-chains.html +- if needed to redirect https://lshtm.zoom.us/j/7845692710 + +## Introduction + +Effort to control + +## summarized order of topics to show + +### episode 01: estimate superspreading from parameters + +new reference: + +- transmission heterogeneity + + individual reproductive number (+1 -> gather content from lloyds-smith paper) + + effect of heterogeneity + + difficulty of establishment + + ease to control + + mass vs targeted interventions + + tree reconstruction + + resource: [key questions Cori et al paper](https://royalsocietypublishing.org/doi/10.1098/rstb.2016.0371) + +- distributions for transmission heterogeneity + + offspring distribution + + negative binomial + + mean, size or (inverse-)dispersion + + variance + + [extra: poisson, mean/variance ratio, overdispersion] + + [37-nbinom-dispersion.R](https://github.com/avallecam/epicatador/blob/main/37-nbinom-dispersion.R) + + resource: + +- reuse offspring distributions from historical outbreaks + + use epiparameter + +- summ01: estimate probability of large outbreak + + number of imported cases + + how "large" is defined? + + resource: + + resource: + + refer to external on the internal machinery - branching process: + +- summ02: estimate proportion of cases that cause proportion of transmissions + + [figure 1B](https://www.nature.com/articles/nature04153/figures/1) + + [Figure 1C](https://www.nature.com/articles/nature04153/figures/1) + + pareto rule + +### episode 02: estimate parameters from data + +- summ03: estimate R0 and k from data + + read linelist + contact data + + question: isolate primary (index) and secondary transmission (not in code example)? + + get vector of secondary cases per id + + fit distributions to data using {fitdistrplus} + + assess fit performance w/ model comparison AIC, BIC + + resource: + + resource: [appliedepi](https://community.appliedepi.org/t/estimating-the-degree-of-super-spreading-from-transmission-chain-data/103/2) + + resource: [Figure 1A](https://www.nature.com/articles/nature04153/figures/1) + + refer to external link: networks are heterogeneous + * how to get input data from linelist+contacts? + +### episode 03: simulate transmission tree from parameters + +- example: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7158960/ (suggested by adam) +- example (of how many of simulated outbreaks can be controleed): https://www.thelancet.com/article/S2214-109X(20)30074-7/fulltext (ringbp tailor offspreing distribution) +- new zealand: https://pubmed.ncbi.nlm.nih.gov/33311501/ (suggested by adam) + +- good example: simulation of uncontrolled outbreaks + +- branching process + + To assess the effect of individual variation on disease outbreaks, we analyse a branching process model with negative binomial offspring distribution + +- estimate tree parameters using branching process + + estimate size + + estimate length + +- summ04: projecting cases + + aim: interoperability example? + * epiparameter + * epichains + + resource + +- questions: how case projection from epichains differ from epinow2? + +## issues to fill + +- why to estimate R and k for index cases on README? +- create internal data to express more clearly the index and secondary infector-infectee data? + +epichains +- reduce lenght of first lines of text within chunks? I can not read the full line when mouse is inside. example + +## summatives + +### reuse epiparameter + +Load packages + +```{r} +# Get libraries +library(epiparameter) +library(superspreading) +library(tidyverse) +``` + +Reuse distributions + +```{r} +epidist_db( + epi_dist = "offspring distribution" + ) %>% + list_distributions() %>% + select(disease,prob_distribution) +``` + + +```{r} +# Load parameters +sars <- epidist_db( + disease = "SARS", + epi_dist = "offspring_distribution", + single_epidist=T + ) +sars_params <- get_parameters(sars) +sars_params +``` + +### 01 estimate probability of large outbreak + + + +```{r} +# how to estimate the probability of a large outbreak? + +# Estimate probability of large outbreak +# with 5 independent imported cases +probability_epidemic( + R = sars_params[["mean"]], + k = sars_params[["dispersion"]], + num_init_infect = 5 +) +``` + + +### 02 estimate proportion of cases that cause proportion of transmissions + + + +```{r} +# proportion of cases that +# generate 80% of transmission +proportion_transmission( + R = sars_params[["mean"]], + k = sars_params[["dispersion"]], + percent_transmission=0.8, +) +``` + +analogy 80-20 pareto rule + +question: is there a way to visualize this in the figure of axis: +- expected proportion of transmission and proportion of infectious cases (ranked)? (recreate Fig 1B) +- proportion of transmission due to most infectious 20% of cases and dispersion parameter k? (recreate Fig 1C) + +### get linelist and contact data + +Load packages + +```{r} +# we use {fitdistrplus} to fit the models +library(fitdistrplus) +library(outbreaks) +library(epicontacts) +library(ggplot2) +``` + +wrangle data + +```{r} +## make epicontact object +epi <- make_epicontacts( + mers_korea_2015$linelist, + mers_korea_2015$contacts + ) + +## extract ids in contact *and* linelist using "which" argument +ids <- get_id(epi, which = "all") + +## iterate counting function over these ids +non_index_cases <- sapply( + ids, + function(id) sum(id == epi$contacts$from, + na.rm = TRUE) + ) + +## plot the distribution +qplot( + non_index_cases, + geom = "histogram", + binwidth = 1, + xlab = "Individual reproduction number", + ylab = "Number of individuals" +) +``` + + +### 03 fit distribution to data + +- question: does this needs to isolate index and secondary case transmission? + +```{r} +param_non_index <- fitdist( + data = non_index_cases, + distr = "nbinom" +) +param_non_index +# rename size and mu to k and R +names(param_non_index$estimate) <- + c("k_dispersion_size", "R_reproduction_number_mean") +# param_non_index$estimate +param_non_index +``` + + +## concepts + +### overdispersion + +- for occurrences of associated discrete events we can use Poisson or negative binomial discrete distributions. +- in a Poisson distribution, mean is equal to variance. +- when variance is higher than the mean, this is called over-dispersion. +- in biological applications, over-dispersion occurs and so a negative binomial may be worth considering as an alternative to Poisson distribution. + +- in epidemiology, negative binomial have being used to model disease transmission for infectious diseases where the likely number of onward infections may vary considerably from individual to individual and from setting to setting + +- In a sequence of independent Bernoulli trials, in each trial the probability of success is $p$ and of failure is $1-p$. We observe this sequence until a predefined number $r$ of successes occurs. Then the random number of observed failures follows the negative binomial distribution. +- some authors refer to $\alpha = \frac{1}{r}$ and express variance in terms of $\alpha$: $variance = m + \alpha m^2$ where mean $ m = \frac{r(1-p)}{p}$ +- depending on the author, either the parameter or its the reciprocal of $r$, $\alpha$, is refereed to as the "dispersion parameter". + +- From Lloyd-Smith, in a more general formulation, we let $v$ be gamma-distributed with mean $R_{o}$ and dispersion parameter $k$, yielding $Z$~negative binomial($R_{o}, k$). The negative binomial model includes the conventional Poisson ($k \rightarrow \inf$) as an special case. It has variance $R_{o}(1 + R_{o}/k)$, so smaller values of $k$ indicate (greater variance, thus) greater heterogeneity. + +- To sync up with Lloyd-Smith and R base function for negative binomial, $k = r = {size} = {inversedispersion}$ + +- negative binomial distribution is specially useful for discrete data over an unbounded positive range whose sample variance exceeds the sample mean. In such terms, the observations are overdispersed with respect to a Poisson distribution, for which the mean is equal to the variance. +- The additional parameter of the negative binomial distribution ($r$) can be used to adjust the variance independently of the mean. + +### how parameters look for a overdispersed distribution + +- from normal to dispersed distributions + - mean + - dispersion parameter + + explore this with https://ben18785.shinyapps.io/distribution-zoo/ + + discrete univariate + +### example using negative binomial: + +- mean +- inverse-dispersion +- range + +explore wikipedia page + + + + +### example using lognormal: + + +![Normal (left) and log-normal (right) distributions, both with parameters μ=0 and σ=1. The normal distribution's measures of central tendency (mean, median, mode) are all equal, while the log-normal distribution's measures are different due to the log-normal distribution's skew.](fig/SEE-dist.png) + + +![Several log-normal distributions with (left) the parameter $\sigma=1$ fixed and (right) the parameter $\mu=1$ fixed. We can see that both the central tendency and dispersion of a log-normal distribution depend on $\mu$ and $\sigma$.](fig/SEE-params.png) + +- our context: the offspring distribution + + the x value is the: + + number of secondary cases + + individual reproductive number + +- tricky relationship: + + inverse proportionality between dispersion and heterogeneity + + small dispersion, greater probability density across the x axis, thus grater heterogeneity + + large dispersion, less probability density across the x axis, thus less heterogeneity + +- focus on the cumulative probability distribution of the most infectious cases + + if there is a 0.2 proportion of (the most infectious) cases contributing to the 0.8 proportion of transmission, this is a highly heterogeneous distribution. (e.g. SARS) + + if there is a 0.2 proportion of (the most infectious) cases contributing to the 0.4 of transmission, this is a less heterogeneous distribution (compared to the above one, e.g. pneumonic plague). + + +![](fig/SEE-individual-reproductive-number.png) + +https://www.nature.com/articles/nature04153 + + +### ‘individual reproductive number’, ν, + +- interpretation: is the concept, not yet a distribution +- as a random variable representing the expected number of secondary cases caused by a particular infected individual. + +- Values for ν are drawn from a continuous probability distribution with + - population mean R0 + + that encodes all variation in infectious histories of individuals + - dispersion parameter k + + smaller values of k indicate greater heterogeneity + + larger values of k indicate less heterogeneity + +### offspring distribution + +- Stochastic effects in transmission are modelled using a Poisson process, so that the number of secondary infections caused by each case, Z, is described by an ‘offspring distribution’ Pr(Z = k) where Z∼Poisson(ν). + +- interpretation: it describes properly as a distribution the ‘individual reproductive number’ + +the offspring distribution, + +- can be characterized by a statistical distribution + - negative binomial, usually +- with distribution parameters given by + - R0 as the mean and + + average number of (secondary) cases produced by a single individual in an entirely susceptible population + - k as the dispersion parameter, + +degree of heterogeneity in transmission by single individuals + + +### superspreading events (SSEs) + +- are important realizations from the right-hand tail of a distribution of ν +- define an SSE as any infected individual who infects more than Z(n) others, where Z(n) is the nth percentile of the Poisson(R) distribution. +- A 99th-percentile SSE is then any case causing more infections than would occur in 99% of infectious histories in a homogeneous population +- interpretation: + + [EVALUATE TO UPDATE] + + [NOTE: POTENTIAL MISCONCEPTION] the area under the curve of the offspring distribution using a e.g. 99 percentile, representing the amount or frequency of SSE + +### branching process + +- probability generating function (pgf) of the offspring distribution + + +## Ideas + +understanding offspring distribution overdispersion is superspreading! + +individual variation of transmission informs the frequency of superspreading events (SSE) + +- heterogeneity at the individual level of transmission reduce chance of an emerging outbreak + +- but it can also make it hard to control when there is a lot of SSE + +with estimated parameter we then can reconstruct tranmission chains to forecast and simulate interventions + +## Ideas from https://royalsocietypublishing.org/doi/10.1098/rstb.2016.0371 + +Heterogeneity is the number of secondary cases generated by each infected individual + +Heterogeneity affects epidemic establishment and the ease of control + ++ Greater heterogeneity reduces the chance of an outbreak emerging from single case [NOTE: DIFICULT INTUITION] [EXAMPLE: lots of individual with individual reproduction number around 1 or below] + ++ However, this heterogeneity can make an established outbreak hard to control using mass interventions, as a single uncontrolled case can generate a large number of secondary cases. [INTERPRETATION: if the outbreak gets established, then it is hard to control assuming homogeneity of transmission] + +Conversely, heterogeneity in transmission may provide opportunities for targeting interventions if the individuals who contribute more to transmission (due to biological, environmental or behavuoral factors) share socia-demographic or geographical characteristics that can be defined [INTERPRETATION: ones identified, this can help targetted interventions to this population] + +Reconstruction of transmission trees (whom infected whom) can provide an understanding of who contributes more to transmission. This can be done qith detailed case investigations and/or genetic data. [EXAMPLE: case data paired with contact data to visualize and find the patterns] + +## links + +https://en.wikipedia.org/wiki/Negative_binomial_distribution + +https://community.appliedepi.org/t/estimating-the-degree-of-super-spreading-from-transmission-chain-data/103/2 + +[you familiar site: stats for epi] + +https://stats.oarc.ucla.edu/r/dae/negative-binomial-regression/ + +## packages + +https://epiverse-trace.github.io/epichains/ + +https://epiverse-trace.github.io/superspreading/ + +https://epiverse-trace.github.io/simulist/ + +::::::::::::::::::::::::::::::::::::: keypoints + +- Use `{superspreading}` to + +:::::::::::::::::::::::::::::::::::::::::::::::: + From 382e667c2545a8621dfbe05520d90b4f1cfde871 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sat, 30 Mar 2024 17:02:30 +0000 Subject: [PATCH 002/140] add episode on simulate --- config.yaml | 1 + 1 file changed, 1 insertion(+) diff --git a/config.yaml b/config.yaml index 20e39703..c2325c69 100644 --- a/config.yaml +++ b/config.yaml @@ -63,6 +63,7 @@ episodes: - create-forecast.Rmd - severity-static.Rmd - superspreading-estimate.Rmd +- superspreading-simulate.Rmd # Information for Learners learners: From 673fa2e72798e6c46d939c1da6fd8516be7da784 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sat, 30 Mar 2024 17:05:02 +0000 Subject: [PATCH 003/140] add empty lesson template --- episodes/superspreading-simulate.Rmd | 28 ++++++++++++++++++++++++++++ 1 file changed, 28 insertions(+) create mode 100644 episodes/superspreading-simulate.Rmd diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd new file mode 100644 index 00000000..e063d4c8 --- /dev/null +++ b/episodes/superspreading-simulate.Rmd @@ -0,0 +1,28 @@ +--- +title: 'superspreading-simulate' +teaching: 10 +exercises: 2 +--- + +:::::::::::::::::::::::::::::::::::::: questions + +- How do ? + +:::::::::::::::::::::::::::::::::::::::::::::::: + +::::::::::::::::::::::::::::::::::::: objectives + +- Explain + +:::::::::::::::::::::::::::::::::::::::::::::::: + +## Introduction + +This is a + +::::::::::::::::::::::::::::::::::::: keypoints + +- Use + +:::::::::::::::::::::::::::::::::::::::::::::::: + From c2ef8463332641a67a268f943d57e7858b054e79 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 1 Apr 2024 12:20:11 +0100 Subject: [PATCH 004/140] add packages and testimonial --- episodes/superspreading-estimate.Rmd | 389 +-------------------------- episodes/superspreading-simulate.Rmd | 2 +- 2 files changed, 7 insertions(+), 384 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 79c4c213..98ca6b54 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -33,397 +33,20 @@ List (and hyperlink) the lessons/packages which need to be covered before this l ::::::::::::::::::::::::::::::::: -## my questions - -- does the count of 0-1 secondary cases also biased by delays or interventions when secondary cases measured? [DISCUSSION: potential callout] - -- is size equal to dispersion parameter? or inverse-dispersion? [MISCONCEPTION: review in wiki] - -- what is the difference between superspreading and epichains? is creating projects is the key feature that differenciates them? - -## pre material not to overlap - -- https://www.epirhandbook.com/en/transmission-chains.html -- if needed to redirect https://lshtm.zoom.us/j/7845692710 - ## Introduction -Effort to control - -## summarized order of topics to show - -### episode 01: estimate superspreading from parameters - -new reference: - -- transmission heterogeneity - + individual reproductive number (+1 -> gather content from lloyds-smith paper) - + effect of heterogeneity - + difficulty of establishment - + ease to control - + mass vs targeted interventions - + tree reconstruction - + resource: [key questions Cori et al paper](https://royalsocietypublishing.org/doi/10.1098/rstb.2016.0371) - -- distributions for transmission heterogeneity - + offspring distribution - + negative binomial - + mean, size or (inverse-)dispersion - + variance - + [extra: poisson, mean/variance ratio, overdispersion] - + [37-nbinom-dispersion.R](https://github.com/avallecam/epicatador/blob/main/37-nbinom-dispersion.R) - + resource: - -- reuse offspring distributions from historical outbreaks - + use epiparameter - -- summ01: estimate probability of large outbreak - + number of imported cases - + how "large" is defined? - + resource: - + resource: - + refer to external on the internal machinery - branching process: - -- summ02: estimate proportion of cases that cause proportion of transmissions - + [figure 1B](https://www.nature.com/articles/nature04153/figures/1) - + [Figure 1C](https://www.nature.com/articles/nature04153/figures/1) - + pareto rule - -### episode 02: estimate parameters from data - -- summ03: estimate R0 and k from data - + read linelist + contact data - + question: isolate primary (index) and secondary transmission (not in code example)? - + get vector of secondary cases per id - + fit distributions to data using {fitdistrplus} - + assess fit performance w/ model comparison AIC, BIC - + resource: - + resource: [appliedepi](https://community.appliedepi.org/t/estimating-the-degree-of-super-spreading-from-transmission-chain-data/103/2) - + resource: [Figure 1A](https://www.nature.com/articles/nature04153/figures/1) - + refer to external link: networks are heterogeneous - * how to get input data from linelist+contacts? - -### episode 03: simulate transmission tree from parameters - -- example: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7158960/ (suggested by adam) -- example (of how many of simulated outbreaks can be controleed): https://www.thelancet.com/article/S2214-109X(20)30074-7/fulltext (ringbp tailor offspreing distribution) -- new zealand: https://pubmed.ncbi.nlm.nih.gov/33311501/ (suggested by adam) - -- good example: simulation of uncontrolled outbreaks - -- branching process - + To assess the effect of individual variation on disease outbreaks, we analyse a branching process model with negative binomial offspring distribution - -- estimate tree parameters using branching process - + estimate size - + estimate length - -- summ04: projecting cases - + aim: interoperability example? - * epiparameter - * epichains - + resource - -- questions: how case projection from epichains differ from epinow2? - -## issues to fill - -- why to estimate R and k for index cases on README? -- create internal data to express more clearly the index and secondary infector-infectee data? - -epichains -- reduce lenght of first lines of text within chunks? I can not read the full line when mouse is inside. example - -## summatives - -### reuse epiparameter - -Load packages - -```{r} -# Get libraries -library(epiparameter) -library(superspreading) -library(tidyverse) -``` - -Reuse distributions - -```{r} -epidist_db( - epi_dist = "offspring distribution" - ) %>% - list_distributions() %>% - select(disease,prob_distribution) -``` - - -```{r} -# Load parameters -sars <- epidist_db( - disease = "SARS", - epi_dist = "offspring_distribution", - single_epidist=T - ) -sars_params <- get_parameters(sars) -sars_params -``` - -### 01 estimate probability of large outbreak - - - -```{r} -# how to estimate the probability of a large outbreak? - -# Estimate probability of large outbreak -# with 5 independent imported cases -probability_epidemic( - R = sars_params[["mean"]], - k = sars_params[["dispersion"]], - num_init_infect = 5 -) -``` - - -### 02 estimate proportion of cases that cause proportion of transmissions - - - -```{r} -# proportion of cases that -# generate 80% of transmission -proportion_transmission( - R = sars_params[["mean"]], - k = sars_params[["dispersion"]], - percent_transmission=0.8, -) -``` - -analogy 80-20 pareto rule - -question: is there a way to visualize this in the figure of axis: -- expected proportion of transmission and proportion of infectious cases (ranked)? (recreate Fig 1B) -- proportion of transmission due to most infectious 20% of cases and dispersion parameter k? (recreate Fig 1C) - -### get linelist and contact data - -Load packages - -```{r} -# we use {fitdistrplus} to fit the models -library(fitdistrplus) -library(outbreaks) -library(epicontacts) -library(ggplot2) -``` - -wrangle data - -```{r} -## make epicontact object -epi <- make_epicontacts( - mers_korea_2015$linelist, - mers_korea_2015$contacts - ) - -## extract ids in contact *and* linelist using "which" argument -ids <- get_id(epi, which = "all") - -## iterate counting function over these ids -non_index_cases <- sapply( - ids, - function(id) sum(id == epi$contacts$from, - na.rm = TRUE) - ) - -## plot the distribution -qplot( - non_index_cases, - geom = "histogram", - binwidth = 1, - xlab = "Individual reproduction number", - ylab = "Number of individuals" -) -``` - - -### 03 fit distribution to data - -- question: does this needs to isolate index and secondary case transmission? - -```{r} -param_non_index <- fitdist( - data = non_index_cases, - distr = "nbinom" -) -param_non_index -# rename size and mu to k and R -names(param_non_index$estimate) <- - c("k_dispersion_size", "R_reproduction_number_mean") -# param_non_index$estimate -param_non_index -``` - - -## concepts - -### overdispersion - -- for occurrences of associated discrete events we can use Poisson or negative binomial discrete distributions. -- in a Poisson distribution, mean is equal to variance. -- when variance is higher than the mean, this is called over-dispersion. -- in biological applications, over-dispersion occurs and so a negative binomial may be worth considering as an alternative to Poisson distribution. - -- in epidemiology, negative binomial have being used to model disease transmission for infectious diseases where the likely number of onward infections may vary considerably from individual to individual and from setting to setting - -- In a sequence of independent Bernoulli trials, in each trial the probability of success is $p$ and of failure is $1-p$. We observe this sequence until a predefined number $r$ of successes occurs. Then the random number of observed failures follows the negative binomial distribution. -- some authors refer to $\alpha = \frac{1}{r}$ and express variance in terms of $\alpha$: $variance = m + \alpha m^2$ where mean $ m = \frac{r(1-p)}{p}$ -- depending on the author, either the parameter or its the reciprocal of $r$, $\alpha$, is refereed to as the "dispersion parameter". - -- From Lloyd-Smith, in a more general formulation, we let $v$ be gamma-distributed with mean $R_{o}$ and dispersion parameter $k$, yielding $Z$~negative binomial($R_{o}, k$). The negative binomial model includes the conventional Poisson ($k \rightarrow \inf$) as an special case. It has variance $R_{o}(1 + R_{o}/k)$, so smaller values of $k$ indicate (greater variance, thus) greater heterogeneity. - -- To sync up with Lloyd-Smith and R base function for negative binomial, $k = r = {size} = {inversedispersion}$ - -- negative binomial distribution is specially useful for discrete data over an unbounded positive range whose sample variance exceeds the sample mean. In such terms, the observations are overdispersed with respect to a Poisson distribution, for which the mean is equal to the variance. -- The additional parameter of the negative binomial distribution ($r$) can be used to adjust the variance independently of the mean. - -### how parameters look for a overdispersed distribution - -- from normal to dispersed distributions - - mean - - dispersion parameter - + explore this with https://ben18785.shinyapps.io/distribution-zoo/ - + discrete univariate - -### example using negative binomial: - -- mean -- inverse-dispersion -- range - -explore wikipedia page - - - - -### example using lognormal: - - -![Normal (left) and log-normal (right) distributions, both with parameters μ=0 and σ=1. The normal distribution's measures of central tendency (mean, median, mode) are all equal, while the log-normal distribution's measures are different due to the log-normal distribution's skew.](fig/SEE-dist.png) - - -![Several log-normal distributions with (left) the parameter $\sigma=1$ fixed and (right) the parameter $\mu=1$ fixed. We can see that both the central tendency and dispersion of a log-normal distribution depend on $\mu$ and $\sigma$.](fig/SEE-params.png) - -- our context: the offspring distribution - + the x value is the: - + number of secondary cases - + individual reproductive number - -- tricky relationship: - + inverse proportionality between dispersion and heterogeneity - + small dispersion, greater probability density across the x axis, thus grater heterogeneity - + large dispersion, less probability density across the x axis, thus less heterogeneity - -- focus on the cumulative probability distribution of the most infectious cases - + if there is a 0.2 proportion of (the most infectious) cases contributing to the 0.8 proportion of transmission, this is a highly heterogeneous distribution. (e.g. SARS) - + if there is a 0.2 proportion of (the most infectious) cases contributing to the 0.4 of transmission, this is a less heterogeneous distribution (compared to the above one, e.g. pneumonic plague). - - -![](fig/SEE-individual-reproductive-number.png) - -https://www.nature.com/articles/nature04153 - - -### ‘individual reproductive number’, ν, - -- interpretation: is the concept, not yet a distribution -- as a random variable representing the expected number of secondary cases caused by a particular infected individual. - -- Values for ν are drawn from a continuous probability distribution with - - population mean R0 - + that encodes all variation in infectious histories of individuals - - dispersion parameter k - + smaller values of k indicate greater heterogeneity - + larger values of k indicate less heterogeneity - -### offspring distribution - -- Stochastic effects in transmission are modelled using a Poisson process, so that the number of secondary infections caused by each case, Z, is described by an ‘offspring distribution’ Pr(Z = k) where Z∼Poisson(ν). - -- interpretation: it describes properly as a distribution the ‘individual reproductive number’ - -the offspring distribution, - -- can be characterized by a statistical distribution - - negative binomial, usually -- with distribution parameters given by - - R0 as the mean and - + average number of (secondary) cases produced by a single individual in an entirely susceptible population - - k as the dispersion parameter, - +degree of heterogeneity in transmission by single individuals - - -### superspreading events (SSEs) - -- are important realizations from the right-hand tail of a distribution of ν -- define an SSE as any infected individual who infects more than Z(n) others, where Z(n) is the nth percentile of the Poisson(R) distribution. -- A 99th-percentile SSE is then any case causing more infections than would occur in 99% of infectious histories in a homogeneous population -- interpretation: - + [EVALUATE TO UPDATE] - + [NOTE: POTENTIAL MISCONCEPTION] the area under the curve of the offspring distribution using a e.g. 99 percentile, representing the amount or frequency of SSE - -### branching process - -- probability generating function (pgf) of the offspring distribution - - -## Ideas - -understanding offspring distribution overdispersion is superspreading! - -individual variation of transmission informs the frequency of superspreading events (SSE) - -- heterogeneity at the individual level of transmission reduce chance of an emerging outbreak - -- but it can also make it hard to control when there is a lot of SSE - -with estimated parameter we then can reconstruct tranmission chains to forecast and simulate interventions - -## Ideas from https://royalsocietypublishing.org/doi/10.1098/rstb.2016.0371 - -Heterogeneity is the number of secondary cases generated by each infected individual - -Heterogeneity affects epidemic establishment and the ease of control - -+ Greater heterogeneity reduces the chance of an outbreak emerging from single case [NOTE: DIFICULT INTUITION] [EXAMPLE: lots of individual with individual reproduction number around 1 or below] - -+ However, this heterogeneity can make an established outbreak hard to control using mass interventions, as a single uncontrolled case can generate a large number of secondary cases. [INTERPRETATION: if the outbreak gets established, then it is hard to control assuming homogeneity of transmission] - -Conversely, heterogeneity in transmission may provide opportunities for targeting interventions if the individuals who contribute more to transmission (due to biological, environmental or behavuoral factors) share socia-demographic or geographical characteristics that can be defined [INTERPRETATION: ones identified, this can help targetted interventions to this population] - -Reconstruction of transmission trees (whom infected whom) can provide an understanding of who contributes more to transmission. This can be done qith detailed case investigations and/or genetic data. [EXAMPLE: case data paired with contact data to visualize and find the patterns] - -## links - -https://en.wikipedia.org/wiki/Negative_binomial_distribution - -https://community.appliedepi.org/t/estimating-the-degree-of-super-spreading-from-transmission-chain-data/103/2 - -[you familiar site: stats for epi] - -https://stats.oarc.ucla.edu/r/dae/negative-binomial-regression/ - -## packages +::::::::::::::::::::::::::::: testimonial -https://epiverse-trace.github.io/epichains/ +### Going viral -https://epiverse-trace.github.io/superspreading/ + -https://epiverse-trace.github.io/simulist/ +::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::: keypoints +- Use `{epicontacts}` +- Use `{fitdistplus}` - Use `{superspreading}` to :::::::::::::::::::::::::::::::::::::::::::::::: diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index e063d4c8..92849b1a 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -22,7 +22,7 @@ This is a ::::::::::::::::::::::::::::::::::::: keypoints -- Use +- Use `{epichains}` :::::::::::::::::::::::::::::::::::::::::::::::: From a660b273fb5577a01e12a2594907d98e35af21f4 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 2 Apr 2024 00:14:20 +0100 Subject: [PATCH 005/140] add summative code to episode --- episodes/superspreading-estimate.Rmd | 400 ++++++++++++++++++++++++++- episodes/superspreading-simulate.Rmd | 312 ++++++++++++++++++++- 2 files changed, 696 insertions(+), 16 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 98ca6b54..4dad3fc0 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -1,27 +1,23 @@ --- -title: 'Estimate superspreading' +title: 'Account for superspreading' teaching: 10 exercises: 2 --- :::::::::::::::::::::::::::::::::::::: questions -- What is the estimated amount of superespreading events? - What is the level of individual variation of transmission? -- can you reconstruct transmission chains? +- How to estimate de amount of superspreading events? +- How to account for superspreading in decision-making for contact tracing? :::::::::::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::: objectives -- Quantify transmission heterogeneity -- Estimate overdispersion from early outbreak data -- Estimate R0 -- Estimate k -- Estimate the proportion of superspreading events - -- Create a Short term forecast using branching process -- Create simulation of interventions +- Evaluate for transmission heterogeneity. +- Create the offspring distribution from outbreak data using `{epicontacts}`. +- Estimate the dispersion parameter from the offspring distribution using `{fitdistrplus}`. +- Estimate the proportion of transmission accounting for superspreading events using `{superspreading}`. :::::::::::::::::::::::::::::::::::::::::::::::: @@ -29,12 +25,392 @@ exercises: 2 ## Prerequisites -List (and hyperlink) the lessons/packages which need to be covered before this lesson +Learners should familiarise themselves with following concept dependencies before working through this tutorial: + +**Statistics**: probability distributions. + +**Epidemic theory**: Reproduction number. ::::::::::::::::::::::::::::::::: ## Introduction + + + + + + +## questions + +- What is the offspring distribution? +- How to assess for heterogeneity in transmission? +- How to estimate the mean reproduction number and dispersion parameter from an offspring distribution? +- The definition of a 99th-percentile SSE (not directly cover by the package) + + +## The offspring distribution + +```{r} +library(outbreaks) +library(epicontacts) +library(tidyverse) + +## make epicontact object +epi <- make_epicontacts( + linelist = mers_korea_2015$linelist, + contacts = mers_korea_2015$contacts +) + +# visualise contact tree +epicontacts::vis_epicontacts(epi) + +# no infector-infectee pairs are replicated +epi %>% + pluck("contacts") %>% + group_by(from,to) %>% + filter(n()>1) + +# count secondary cases per infectee +infector_secondary <- epi %>% + pluck("contacts") %>% + count(from, name = "secondary_cases") + +epi_secondary <- + epi %>% + # extract ids in contact *and* linelist using "which" argument + get_id(which = "all") %>% + enframe(name = NULL, value = "from") %>% + # join count secondary cases per infectee + left_join(infector_secondary) %>% + # infectee with missing secondary cases are replaced with zero + replace_na( + replace = list(secondary_cases = 0) + ) + +# count of secondary cases per individual +epi_secondary + +# arrange in descendant order of secondary cases +epi_secondary %>% + arrange(desc(secondary_cases)) + +## plot the distribution +epi_secondary %>% + ggplot(aes(secondary_cases)) + + geom_histogram(binwidth = 1) + + labs( + xlab = "Individual reproduction number", + ylab = "Number of individuals" + ) +``` + +## Estimate the dispersion parameter + +fit distribution to data +provide maximum likelihood estimates + +the estimated value of k +suggest that +SSE are an expected feature of the +individual level variation in infectiousness + +```{r} +library(fitdistrplus) + +conflicted::conflict_scout() +conflicted::conflict_prefer( + name = "filter", + winner = "dplyr" +) +conflicted::conflict_prefer( + name = "lag", + winner = "dplyr" +) +conflicted::conflict_prefer( + name = "select", + winner = "dplyr" +) +conflicted::conflict_scout() + +## fit distribution +offspring_fit <- epi_secondary %>% + pull(secondary_cases) %>% + fitdist(distr = "nbinom") + +offspring_fit + +## extract the "size" parameter +mid <- offspring_fit$estimate[["size"]] + +## calculate the 95% confidence intervals using the standard error estimate and +## the 0.025 and 0.975 quantiles of the normal distribution. +lower <- mid + offspring_fit$sd[["size"]]*qnorm(0.025) +upper <- mid + offspring_fit$sd[["size"]]*qnorm(0.975) + +round(mid, 4) +round(lower, 4) +round(upper, 4) +``` + +We can see that the +dispersion parameter is estimated as +0.020 (95% CI 0.006 - 0.035). + +As this value is significantly lower +than one, we can conclude that +the degree of super-spreading is high. + +This is in line with visual inspection +of the histogram made above. + +```{r} +# calculate density fit +fit_density <- + tibble(quantile = 0:40) %>% + mutate( + density = dnbinom( + x = quantile, + mu=offspring_fit$estimate[["mu"]], + size=mid + ) + ) + +# plot offspring distribution with density fit +ggplot() + + geom_histogram( + data = epi_secondary, + mapping = aes( + x = secondary_cases, + y = after_stat(density) + ), + binwidth = 1) + + geom_point( + data = fit_density, + mapping = aes(x = quantile, y = density), + alpha = 0.3, color = "red" + ) + + labs( + xlab = "Individual reproduction number", + ylab = "Number of individuals" + ) +``` + +## Interpret the dispersion parameter + + + + + +In a Negative Binomial distribution, the relationship between mean (Ro), dispersion (k), variance and heterogeneity is given by: + +$$ \uparrow heterogeneity = \uparrow variance = R_{o}(1+\frac{R_{o}}{\downarrow k})$$ + +The Poisson distribution is an special case of the Negative Binomial. When k approximates infinity $k \rightarrow \infty$ the variance equals the mean because $\frac{R_{o}}{\infty}=0$ + + +:::::::::::::::::::::::: callout + +### Use epiparameter + +```{r} +library(epiparameter) + +epidist_db( + epi_dist = "offspring distribution" +) %>% + list_distributions() %>% + select(disease,prob_distribution) + +# Load parameters +sars <- epidist_db( + disease = "SARS", + epi_dist = "offspring_distribution", + single_epidist=T +) +sars_params <- get_parameters(sars) +sars_params +``` + +:::::::::::::::::::::::: + +:::::::::::::::::::::::: callout + +### Select the best model + +Using Information criteria for the best fit. Read further in vignette using helper functions + + + +::::::::::::::::::::::::: + +::::::::::::::::::::::::: spoiler + +### Define SSE + +code this up lloyds definition + +:::::::::::::::::::::::: + + +## Proportion of transmission + +#### Proportion of cases resposible of 80% of infection + +show from figure (not available in vignette) + +```{r} +# estimate prop cases cause transmission ---------------------------------- + +## text --------------------------------- + +# proportion of cases that +# generate 80% of transmission +proportion_transmission( + R = sars_params[["mean"]], + k = sars_params[["dispersion"]], + percent_transmission=0.8, +) + +## assessment --------------------------------- + +# proportion of cases that +# generate 80% of transmission +proportion_transmission( + R = offspring_fit$estimate["mu"], + k = offspring_fit$estimate["size"], + percent_transmission=0.8, +) + +## assessment -------------------------------------------------------------- + +#' estimate for ebola + +``` + + +## Backward and forward contact tracing + +### Proportion of events in a given cluster size + +the proportion of new cases that originated within a transmission event of a given size. What proportion of all transmission events were part of secondary case clusters from a set of initial cases + +useful to inform backwards contact tracing efforts + +Given the observed number of new cases, cluster of cases, what proportion of them came from same index case + +cluster is the transmission from primary to secondary case + +Given a set of cases, what proportion of them (transmission events) where part of secondary case clusters (from the same primary case) + +prevent superspreading events + +```{r} +# estimate prop cluster size ---------------------------------------------- + +## text -------------------------- + +#' Given a set of cases, +#' what proportion of them +#' (transmission events) +#' where part of +#' secondary case clusters +#' (from the same primary case) +#' +#' useful for +#' backward contact traicing + +proportion_cluster_size( + R = offspring_fit$estimate["mu"], + k = offspring_fit$estimate["size"], + cluster_size = 10 +) + +``` + +## Superspreading in decision making + +- How to estimate the probability of large outbreak? +- How to estimate the proportion of cases responsible of the 80% of transmission? + +Early understanding of disease epidemic potential from R0 and dispersion + +ease of control with either mass or targeted interventions + +**Probability of a large epidemic** + +The more heterogeneity, less probability to stablish. + +But the higher the number of introductions, the higher the likelihood + +:::::::::::::::::::: challenge + +```{r} +## assessment ------------------------------------- + +# Estimate probability of large outbreak +# with 5 independent imported cases +probability_epidemic( + R = offspring_fit$estimate["mu"], + k = offspring_fit$estimate["size"], + num_init_infect = 5 +) + + +## assessment -------------------------------------------------------------- + +#' get ebola params +``` + +::::::::::::::::::: + +**Probability of extintion** + +more heterogeneity, more difficult to go extinct. + + + +**Probability to contain** + +not exceed 100 cases + +```{r} +# estimate prob to contain ------------------------------------------------ + + +## text ---------------------------------- + +probability_contain( + R = offspring_fit$estimate["mu"], + k = offspring_fit$estimate["size"], + num_init_infect = 1, + case_threshold = 100 +) +``` + + +### Go to vignette + +Given initial conditions or a range of plausible scenarios or R and k, you can use + +Look at them in the {superspreading} vignette + + + +## Challenges + +::::::::::::::::::::::::::: challenge + +use mers to estimate ... + +::::::::::::::::::::::::::: + +:::::::::::::::::::::::::: challenge + +inform backward contact tracing strategy + +::::::::::::::::::::::::: + ::::::::::::::::::::::::::::: testimonial ### Going viral diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 92849b1a..ec0ce63c 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -1,24 +1,328 @@ --- -title: 'superspreading-simulate' +title: 'Simulate transmission chains' teaching: 10 exercises: 2 --- :::::::::::::::::::::::::::::::::::::: questions -- How do ? +- How to simulate transmission chains? :::::::::::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::: objectives -- Explain +- Create a short term projection using branching process with `{epichains}`. :::::::::::::::::::::::::::::::::::::::::::::::: +::::::::::::::::::::::::::::::::::::: prereq + +## Prerequisites + +Learners should familiarise themselves with following concept dependencies before working through this tutorial: + +**Statistics**: probability distributions. + +**Epidemic theory**: Reproduction number. + +::::::::::::::::::::::::::::::::: + +## questions + ## Introduction -This is a + + + + + + +```{r} +library(epichains) +``` + + +## Get the offspring distribution + +from MERS estimates in estimate episode + +```{r} +mers_offspring <- + c( + mean = 0.60, + dispersion = 0.02 + ) + +mers_offspring +``` + +instead of the offspring distribution +we can also define a poisson process +using the lambda distribution parameter +lambda = rate = mean + + +## Get generation time + +```{r} +library(epiparameter) + +serial_inverval <- epidist_db( + disease = "mers", + epi_dist = "serial", + single_epidist = T +) + +serial_inverval +``` + +Similar to the `{cfr}` interface for `{epiparameter}` + +```r +function(x) generate(x = serial_inverval,times = x) +``` + +## Simulate a single chain + +```{r} +simulate_chains( + # simulation controls + index_cases = 5, + statistic = "size", + # offspring + offspring_dist = rnbinom, + mu = mers_offspring["mean"], + size = mers_offspring["dispersion"], + # generation + generation_time = function(x) generate(x = serial_inverval,times = x) +) %>% + as_tibble() +``` + +the output dataframe collects +infectees as observation unit +each infectee has a sim_id +the infector sim_id of each infectee is in infector_id +infectee got infected in generation and time +as part of the simulation_n chain + +## Simulate multiple chains + +```{r} +# Set seed for random number generator +set.seed(33) +# Number of simulation runs +number_chains <- 1e3 +# Number of initial cases +initial_cases <- 1 + +``` + + +```{r} +simulated_chains_list <- + map( + .x = seq_len(number_chains), + .f = function(sim) { + simulate_chains( + # simulation controls + index_cases = initial_cases, + statistic = "size", + # offspring + offspring_dist = rnbinom, + mu = mers_offspring["mean"], + size = mers_offspring["dispersion"], + # generation + generation_time = function(x) generate(x = serial_inverval,times = x) + ) %>% + mutate(simulation_n = sim) + } + ) + +sim_chains_bind <- bind_rows(simulated_chains_list) + +sim_chains_bind +``` + +```{r,echo=FALSE} +#### get simulated chain with more infections -------------------------------- + +chain_to_observe <- sim_chains_bind %>% + as_tibble() %>% + count(simulation_n,sort = TRUE) %>% + filter(n == max(n)) %>% + pull(simulation_n) +``` + +get simulated chain `r chain_to_observe` with more infections + +get epichain summary + +```{r} +#### get epichain summary ---------------------------------------------------- + +simulated_chains_list %>% + pluck(chain_to_observe) +``` + +the `NA` includes the infector of the index case, for that reason (known) cases + +infectee-infector data frame + +```{r} +#### infector-infectee data frame -------------------------------------------- + +simulated_chains_list %>% + pluck(chain_to_observe) %>% + as.data.frame() +``` + + +## Visualize multiple chains + +```{r} +# daily aggregate of cases +simulated_chains_day <- + sim_chains_bind %>% + as_tibble() %>% + mutate(simulation_n = as_factor(simulation_n)) %>% + # Daily number of cases for each simulation + mutate(day = ceiling(time)) %>% + count(simulation_n, day, name = "cases") %>% + # Cumulative number of cases for each simulation + group_by(simulation_n) %>% + mutate(cases_cumsum = cumsum(cases)) %>% + ungroup() + +# Summarise the chain length and size +sim_chains_max <- + simulated_chains_day %>% + group_by(simulation_n) %>% + summarise( + # length + day_max = max(day), + # size + cases_total = max(cases_cumsum) + ) %>% + ungroup() + +# Visualize transmission chains by cumulative cases +ggplot() + + geom_line( + data = simulated_chains_day, + mapping = aes( + x = day, + y = cases_cumsum, + group = simulation_n, + color = simulation_n + ), + show.legend = FALSE + ) + + geom_point( + data = sim_chains_max, + mapping = aes( + x = day_max, + y = cases_total, + group = simulation_n, + color = simulation_n + ), + show.legend = FALSE + ) + + # xlim(0,150) + + # ylim(0,300) + + NULL + +# Visualize transmission chains by daily cases +ggplot() + + geom_line( + data = simulated_chains_day, + mapping = aes( + x = day, + y = cases, + group = simulation_n, + color = simulation_n + ), + show.legend = FALSE + ) +``` + + +## Challenges + +:::::::::::::::::::::::::: challenge + +Evaluate for ebola with know data from previous outbreaks + +```{r} +epidist_db( + disease = "ebola", + epi_dist = "offspring", + single_epidist = T +) + +epidist_db( + disease = "ebola", + epi_dist = "serial interval", + single_epidist = T +) +``` + + +::::::::::::::::::::::::: + +:::::::::::::::::::::::::: challenge + +from paper +Christian Althaus + + +data from Fayre et al on ebola + +```{r} +# Number of individuals in the trees +n <- 152 +# Number of secondary cases for all individuals +c1 <- c(1,2,2,5,14,1,4,4,1,3,3,8,2,1,1,4,9,9,1,1,17, + 2,1,1,1,4,3,3,4,2,5,1,2,2,1,9,1,3,1,2,1,1,2) +c0 <- c(c1,rep(0,n-length(c1))) + +c0 %>% + enframe() %>% + ggplot(aes(value)) + + geom_histogram() +``` + + +::::::::::: hint + +... + +::::::::::: + +::::::::::: solution + +remarkable even with R0 less than 1 +with potentially explosive outbreaks + +the observed variation in individual infectiousness in Ebola +means that although the probability of extinction is high, +new index cases also have the potential for explosive +regrowth of the epidemic. + +::::::::::: + +::::::::::::::::::::::::::::: + +::::::::::::::::::::::::: testimonial + +you can use early linelist data as seed cases to make short term projection of cases + +take a look to vignette + + + +::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::: keypoints From 9151313a49f14c942802e33e9a0503ee6e8dbe6c Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 2 Apr 2024 18:57:09 +0100 Subject: [PATCH 006/140] add draft content to episodes --- episodes/superspreading-estimate.Rmd | 179 ++++++++++++++++++++++++++- episodes/superspreading-simulate.Rmd | 16 +++ 2 files changed, 193 insertions(+), 2 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 4dad3fc0..34ca625d 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -41,16 +41,74 @@ Learners should familiarise themselves with following concept dependencies befor -## questions +## questions {to remove} - What is the offspring distribution? - How to assess for heterogeneity in transmission? - How to estimate the mean reproduction number and dispersion parameter from an offspring distribution? - The definition of a 99th-percentile SSE (not directly cover by the package) +## Transmission heterogeneity + +individual reproductive number + +distributions for transmission heterogeneity + +Heterogeneity is in the variance of the number of secondary cases generated by each infected individual + +## The individual reproduction number + +- interpretation: is the concept, not yet a distribution +- as a random variable representing the expected number of secondary cases caused by a particular infected individual. + +- Values for ν are drawn from a continuous probability distribution with + - population mean R0 + + that encodes all variation in infectious histories of individuals + - dispersion parameter k + + smaller values of k indicate greater heterogeneity + + larger values of k indicate less heterogeneity ## The offspring distribution +- Stochastic effects in transmission are modelled using a Poisson process, so that the number of secondary infections caused by each case, Z, is described by an ‘offspring distribution’ Pr(Z = k) where Z∼Poisson(ν). + +- interpretation: it describes properly as a distribution the ‘individual reproductive number’ + +the offspring distribution, + +- can be characterized by a statistical distribution + - negative binomial, usually +- with distribution parameters given by + - R0 as the mean and + + average number of (secondary) cases produced by a single individual in an entirely susceptible population + - k as the dispersion parameter, + +degree of heterogeneity in transmission by single individuals + +negative binomial + +mean, size or (inverse-)dispersion + +variance + +heterogeneity + +mean/variance ratio + +read linelist + contact data + +secondary transmission distribution + +get vector of secondary cases per id + +[appliedepi](https://community.appliedepi.org/t/estimating-the-degree-of-super-spreading-from-transmission-chain-data/103/2) + +[Figure 1A](https://www.nature.com/articles/nature04153/figures/1) + +- our context: the offspring distribution + + the x value is the: + + number of secondary cases + + individual reproductive number + ```{r} library(outbreaks) library(epicontacts) @@ -107,7 +165,7 @@ epi_secondary %>% ## Estimate the dispersion parameter -fit distribution to data +fit distribution to data using {fitdistrplus} provide maximum likelihood estimates the estimated value of k @@ -115,6 +173,8 @@ suggest that SSE are an expected feature of the individual level variation in infectiousness + + ```{r} library(fitdistrplus) @@ -200,8 +260,78 @@ ggplot() + +- for occurrences of associated discrete events we can use Poisson or negative binomial discrete distributions. +- in a Poisson distribution, mean is equal to variance. +- when variance is higher than the mean, this is called over-dispersion. +- in biological applications, over-dispersion occurs and so a negative binomial may be worth considering as an alternative to Poisson distribution. + +- in epidemiology, negative binomial have being used to model disease transmission for infectious diseases where the likely number of onward infections may vary considerably from individual to individual and from setting to setting + +- In a sequence of independent Bernoulli trials, in each trial the probability of success is $p$ and of failure is $1-p$. We observe this sequence until a predefined number $r$ of successes occurs. Then the random number of observed failures follows the negative binomial distribution. +- some authors refer to $\alpha = \frac{1}{r}$ and express variance in terms of $\alpha$: $variance = m + \alpha m^2$ where mean $ m = \frac{r(1-p)}{p}$ +- depending on the author, either the parameter or its the reciprocal of $r$, $\alpha$, is refereed to as the "dispersion parameter". + +- From Lloyd-Smith, in a more general formulation, we let $v$ be gamma-distributed with mean $R_{o}$ and dispersion parameter $k$, yielding $Z$~negative binomial($R_{o}, k$). The negative binomial model includes the conventional Poisson ($k \rightarrow \inf$) as an special case. It has variance $R_{o}(1 + R_{o}/k)$, so smaller values of $k$ indicate (greater variance, thus) greater heterogeneity. + +- To sync up with Lloyd-Smith and R base function for negative binomial, $k = r = {size} = {inverse-dispersion}$ + +- negative binomial distribution is specially useful for discrete data over an unbounded positive range whose sample variance exceeds the sample mean. In such terms, the observations are overdispersed with respect to a Poisson distribution, for which the mean is equal to the variance. +- The additional parameter of the negative binomial distribution ($r$) can be used to adjust the variance independently of the mean. + +the "dispersion" parameter +refers to the "size" for base R +or +refer to the "k" parameter for Lloyd-Smith +of the negative binomial distribution + +k is inversely-proportional +to variance (i.e, to heterogeneity) +- high k -> get low variance (low heterogeneity) +- low k -> get high variance (high heterogeneity) + +when k approches infinity, +the negative binomial approaches poisson + +negative binomial +two parameters: +- mean (or R0, in offspring distribution) +- size (or k, named also dispersion) + +variance = +mean(1 + mean/k) + +higher k, +(higher inverse-dispersion), +lower variance, +(variance closer to mean) +lower heterogeneity + +lower k +(lower the inverse-dispersion), +higher the variance, +(variance further from mean) +higher heterogeneity + +useful when variance is higher than mean +for discrete data +when observations exceed a positive range +whose sample variance exceeds the +sample mean. +thus, the observations are overdispersed +with respect to a Poisson distribution + +a Poisson distribution can be defined as +an special case of Negative Binomial +when k approaches infinity +or +variance gets closer to mean +or +when mean/variance ratio gets closer to 1 + + + In a Negative Binomial distribution, the relationship between mean (Ro), dispersion (k), variance and heterogeneity is given by: $$ \uparrow heterogeneity = \uparrow variance = R_{o}(1+\frac{R_{o}}{\downarrow k})$$ @@ -238,6 +368,8 @@ sars_params ### Select the best model +assess fit performance w/ model comparison AIC, BIC + Using Information criteria for the best fit. Read further in vignette using helper functions @@ -252,13 +384,52 @@ code this up lloyds definition :::::::::::::::::::::::: +## Superspreading events (SSEs) + +- are important realizations from the right-hand tail of a distribution of ν +- define an SSE as any infected individual who infects more than Z(n) others, where Z(n) is the nth percentile of the Poisson(R) distribution. +- A 99th-percentile SSE is then any case causing more infections than would occur in 99% of infectious histories in a homogeneous population + +## Effect of heterogeneity + +Heterogeneity affects epidemic establishment and the ease of control + +understanding offspring distribution overdispersion is superspreading! + +individual variation of transmission informs the frequency of superspreading events (SSE) + +- heterogeneity at the individual level of transmission reduce chance of an emerging outbreak + +- but it can also make it hard to control when there is a lot of SSE + ++ difficulty of establishment ++ ease to control ++ mass vs targeted interventions + ++ Greater heterogeneity reduces the chance of an outbreak emerging from single case [NOTE: DIFICULT INTUITION] [EXAMPLE: lots of individual with individual reproduction number around 1 or below] + ++ However, this heterogeneity can make an established outbreak hard to control using mass interventions, as a single uncontrolled case can generate a large number of secondary cases. [INTERPRETATION: if the outbreak gets established, then it is hard to control assuming homogeneity of transmission] + +Conversely, heterogeneity in transmission may provide opportunities for targeting interventions if the individuals who contribute more to transmission (due to biological, environmental or behavuoral factors) share socia-demographic or geographical characteristics that can be defined [INTERPRETATION: ones identified, this can help targetted interventions to this population] + + ## Proportion of transmission #### Proportion of cases resposible of 80% of infection ++ [figure 1B](https://www.nature.com/articles/nature04153/figures/1) ++ [Figure 1C](https://www.nature.com/articles/nature04153/figures/1) ++ pareto rule + show from figure (not available in vignette) +- focus on the cumulative probability distribution of the most infectious cases + + if there is a 0.2 proportion of (the most infectious) cases contributing to the 0.8 proportion of transmission, this is a highly heterogeneous distribution. (e.g. SARS) + + if there is a 0.6 proportion of (the most infectious) cases contributing to the 0.8 of transmission, this is a less heterogeneous distribution (compared to the above one, e.g. pneumonic plague) + +![](fig/SEE-individual-reproductive-number.png) + ```{r} # estimate prop cases cause transmission ---------------------------------- @@ -291,6 +462,10 @@ proportion_transmission( ## Backward and forward contact tracing +Reconstruction of transmission trees (whom infected whom) can provide an understanding of who contributes more to transmission. This can be done qith detailed case investigations and/or genetic data. [EXAMPLE: case data paired with contact data to visualize and find the patterns] + + + ### Proportion of events in a given cluster size the proportion of new cases that originated within a transmission event of a given size. What proportion of all transmission events were part of secondary case clusters from a set of initial cases diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index ec0ce63c..c99d9016 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -42,6 +42,22 @@ Learners should familiarise themselves with following concept dependencies befor library(epichains) ``` +## Simulation of uncontrolled outbreaks + +simulation of uncontrolled outbreaks + +- branching process + + To assess the effect of individual variation on disease outbreaks, we analyse a branching process model with negative binomial offspring distribution + +- estimate tree parameters using branching process + + estimate size + + estimate length + +with estimated parameter we then can reconstruct tranmission chains to forecast and simulate interventions + +### branching process + +- probability generating function (pgf) of the offspring distribution ## Get the offspring distribution From 47d3c7e767a8359e47c15cf1abbb931af8b9233e Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 2 Apr 2024 20:55:04 +0100 Subject: [PATCH 007/140] fix code output in build lesson --- episodes/superspreading-estimate.Rmd | 48 +++++++++++++++++++++++----- episodes/superspreading-simulate.Rmd | 5 ++- 2 files changed, 44 insertions(+), 9 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 34ca625d..277891bf 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -4,17 +4,21 @@ teaching: 10 exercises: 2 --- +```{r setup, echo= FALSE, message = FALSE, warning = FALSE} +library(webshot) +webshot::install_phantomjs(force = TRUE) +``` + + :::::::::::::::::::::::::::::::::::::: questions -- What is the level of individual variation of transmission? -- How to estimate de amount of superspreading events? -- How to account for superspreading in decision-making for contact tracing? +- How to evaluate for transmission heterogeneity from contact tracing data? +- How to account for transmission heterogeneity in decision-making? :::::::::::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::: objectives -- Evaluate for transmission heterogeneity. - Create the offspring distribution from outbreak data using `{epicontacts}`. - Estimate the dispersion parameter from the offspring distribution using `{fitdistrplus}`. - Estimate the proportion of transmission accounting for superspreading events using `{superspreading}`. @@ -41,6 +45,15 @@ Learners should familiarise themselves with following concept dependencies befor +```{r,message=FALSE,warning=FALSE} +library(outbreaks) +library(epicontacts) +library(fitdistrplus) +library(superspreading) +library(tidyverse) +``` + + ## questions {to remove} - What is the offspring distribution? @@ -110,19 +123,38 @@ get vector of secondary cases per id + individual reproductive number ```{r} -library(outbreaks) -library(epicontacts) -library(tidyverse) - ## make epicontact object epi <- make_epicontacts( linelist = mers_korea_2015$linelist, contacts = mers_korea_2015$contacts ) +``` +```{r,eval=FALSE} # visualise contact tree epicontacts::vis_epicontacts(epi) +``` + +```{r,echo=FALSE} +# visualise contact tree +network <- + epicontacts::vis_epicontacts(epi) %>% + visNetwork::visPhysics(solver = "barnesHut") + +fname <- "network.html" +visNetwork::visSave(network,fname) + +webshot::webshot( + fname, + delay = 5, + zoom = 10#, + # vwidth=900,vheight=900 + ) +``` + + +```{r} # no infector-infectee pairs are replicated epi %>% pluck("contacts") %>% diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index c99d9016..f78f456a 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -38,8 +38,11 @@ Learners should familiarise themselves with following concept dependencies befor -```{r} +We are going to use `{purrr}` + +```{r,message=FALSE,warning=FALSE} library(epichains) +library(tidyverse) ``` ## Simulation of uncontrolled outbreaks From 520d5382c73e28c8b943b3e4061ec2ea69eac46a Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 2 Apr 2024 20:57:17 +0100 Subject: [PATCH 008/140] add episode specific packages --- renv/profiles/lesson-requirements/renv.lock | 212 ++++++++++++++++++++ 1 file changed, 212 insertions(+) diff --git a/renv/profiles/lesson-requirements/renv.lock b/renv/profiles/lesson-requirements/renv.lock index 77d08829..017591d6 100644 --- a/renv/profiles/lesson-requirements/renv.lock +++ b/renv/profiles/lesson-requirements/renv.lock @@ -289,6 +289,23 @@ ], "Hash": "40415719b5a479b87949f3aa0aee737c" }, + "bpmodels": { + "Package": "bpmodels", + "Version": "0.3.1", + "Source": "GitHub", + "RemoteType": "github", + "RemoteHost": "api.github.com", + "RemoteRepo": "bpmodels", + "RemoteUsername": "epiverse-trace", + "RemotePkgRef": "epiverse-trace/bpmodels", + "RemoteRef": "HEAD", + "RemoteSha": "07c054090f2b07367855b73a0cc2c43e24bc32d3", + "Requirements": [ + "R", + "checkmate" + ], + "Hash": "4374941c8a9cf7a8991072466918c3b2" + }, "broom": { "Package": "broom", "Version": "1.0.5", @@ -513,6 +530,19 @@ ], "Hash": "e8a1e41acf02548751f45c718d55aa6a" }, + "crosstalk": { + "Package": "crosstalk", + "Version": "1.2.1", + "Source": "Repository", + "Repository": "CRAN", + "Requirements": [ + "R6", + "htmltools", + "jsonlite", + "lazyeval" + ], + "Hash": "ab12c7b080a57475248a30f4db6298c0" + }, "curl": { "Package": "curl", "Version": "5.2.0", @@ -676,6 +706,42 @@ ], "Hash": "bb0eec2fe32e88d9e2836c2f73ea2077" }, + "epichains": { + "Package": "epichains", + "Version": "0.0.0.9999", + "Source": "GitHub", + "RemoteType": "github", + "RemoteHost": "api.github.com", + "RemoteRepo": "epichains", + "RemoteUsername": "epiverse-trace", + "RemotePkgRef": "epiverse-trace/epichains", + "RemoteRef": "HEAD", + "RemoteSha": "7b5b80b7b8531fba18e827636a45b0d064e73c76", + "Requirements": [ + "R", + "checkmate", + "stats", + "utils" + ], + "Hash": "e4d58df3ff7111aa1c89356cad126c3b" + }, + "epicontacts": { + "Package": "epicontacts", + "Version": "1.1.3", + "Source": "Repository", + "Repository": "CRAN", + "Requirements": [ + "R", + "colorspace", + "dplyr", + "grDevices", + "igraph", + "methods", + "threejs", + "visNetwork" + ], + "Hash": "ce65f8ac65b26b2a6c17497a4cd5d3a0" + }, "epiparameter": { "Package": "epiparameter", "Version": "0.0.0.9000", @@ -747,6 +813,21 @@ ], "Hash": "66fa5a16464666772f4929f8f5b2fc71" }, + "fitdistrplus": { + "Package": "fitdistrplus", + "Version": "1.1-11", + "Source": "Repository", + "Repository": "CRAN", + "Requirements": [ + "MASS", + "R", + "grDevices", + "methods", + "stats", + "survival" + ], + "Hash": "f40ef9686e85681a1ccbf33d9236aeb9" + }, "fontawesome": { "Package": "fontawesome", "Version": "0.5.2", @@ -1080,6 +1161,21 @@ ], "Hash": "2d7b3857980e0e0d0a1fd6f11928ab0f" }, + "htmlwidgets": { + "Package": "htmlwidgets", + "Version": "1.6.4", + "Source": "Repository", + "Repository": "CRAN", + "Requirements": [ + "grDevices", + "htmltools", + "jsonlite", + "knitr", + "rmarkdown", + "yaml" + ], + "Hash": "04291cc45198225444a397606810ac37" + }, "httr": { "Package": "httr", "Version": "1.4.7", @@ -1106,6 +1202,29 @@ ], "Hash": "99df65cfef20e525ed38c3d2577f7190" }, + "igraph": { + "Package": "igraph", + "Version": "2.0.3", + "Source": "Repository", + "Repository": "CRAN", + "Requirements": [ + "Matrix", + "R", + "cli", + "cpp11", + "grDevices", + "graphics", + "lifecycle", + "magrittr", + "methods", + "pkgconfig", + "rlang", + "stats", + "utils", + "vctrs" + ], + "Hash": "c3b7d801d722e26e4cd888e042bf9af5" + }, "incidence2": { "Package": "incidence2", "Version": "2.2.3", @@ -1215,6 +1334,16 @@ ], "Hash": "7c5e89f04e72d6611c77451f6331a091" }, + "lazyeval": { + "Package": "lazyeval", + "Version": "0.2.2", + "Source": "Repository", + "Repository": "CRAN", + "Requirements": [ + "R" + ], + "Hash": "d908914ae53b04d4c0c0fd72ecc35370" + }, "lifecycle": { "Package": "lifecycle", "Version": "1.0.4", @@ -1902,6 +2031,42 @@ ], "Hash": "960e2ae9e09656611e0b8214ad543207" }, + "superspreading": { + "Package": "superspreading", + "Version": "0.2.0.9000", + "Source": "GitHub", + "Remotes": "epiverse-trace/epiparameter, epiverse-trace/bpmodels", + "RemoteType": "github", + "RemoteHost": "api.github.com", + "RemoteRepo": "superspreading", + "RemoteUsername": "epiverse-trace", + "RemotePkgRef": "epiverse-trace/superspreading", + "RemoteRef": "HEAD", + "RemoteSha": "4549ff929acb90aee04dc3b66a7fb30503affbc5", + "Requirements": [ + "bpmodels", + "checkmate", + "rlang", + "stats" + ], + "Hash": "b6902d57c67ae90e59f588c01319aea7" + }, + "survival": { + "Package": "survival", + "Version": "3.5-7", + "Source": "Repository", + "Repository": "CRAN", + "Requirements": [ + "Matrix", + "R", + "graphics", + "methods", + "splines", + "stats", + "utils" + ], + "Hash": "b8e943d262c3da0b0febd3e04517c197" + }, "sys": { "Package": "sys", "Version": "3.4.2", @@ -1932,6 +2097,22 @@ ], "Hash": "997aac9ad649e0ef3b97f96cddd5622b" }, + "threejs": { + "Package": "threejs", + "Version": "0.3.3", + "Source": "Repository", + "Repository": "CRAN", + "Requirements": [ + "R", + "base64enc", + "crosstalk", + "htmlwidgets", + "igraph", + "methods", + "stats" + ], + "Hash": "2ad32c3a8745e827977f394bc387e3b0" + }, "tibble": { "Package": "tibble", "Version": "3.2.1", @@ -2116,6 +2297,24 @@ ], "Hash": "c826c7c4241b6fc89ff55aaea3fa7491" }, + "visNetwork": { + "Package": "visNetwork", + "Version": "2.1.2", + "Source": "Repository", + "Repository": "CRAN", + "Requirements": [ + "R", + "grDevices", + "htmltools", + "htmlwidgets", + "jsonlite", + "magrittr", + "methods", + "stats", + "utils" + ], + "Hash": "3e48b097e8d9a91ecced2ed4817a678d" + }, "vroom": { "Package": "vroom", "Version": "1.6.5", @@ -2142,6 +2341,19 @@ ], "Hash": "390f9315bc0025be03012054103d227c" }, + "webshot": { + "Package": "webshot", + "Version": "0.5.5", + "Source": "Repository", + "Repository": "CRAN", + "Requirements": [ + "R", + "callr", + "jsonlite", + "magrittr" + ], + "Hash": "16858ee1aba97f902d24049d4a44ef16" + }, "withr": { "Package": "withr", "Version": "3.0.0", From a0c0743632065338ced8d8af113b65f57851ff63 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Wed, 3 Apr 2024 16:47:52 +0100 Subject: [PATCH 009/140] edit to pass lintr checks --- episodes/superspreading-estimate.Rmd | 96 ++++++++++++++-------------- episodes/superspreading-simulate.Rmd | 79 ++++++++++++----------- 2 files changed, 88 insertions(+), 87 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 277891bf..47407a22 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -125,7 +125,7 @@ get vector of secondary cases per id ```{r} ## make epicontact object epi <- make_epicontacts( - linelist = mers_korea_2015$linelist, + linelist = mers_korea_2015$linelist, contacts = mers_korea_2015$contacts ) ``` @@ -137,42 +137,41 @@ epicontacts::vis_epicontacts(epi) ```{r,echo=FALSE} # visualise contact tree -network <- +network <- epicontacts::vis_epicontacts(epi) %>% visNetwork::visPhysics(solver = "barnesHut") fname <- "network.html" -visNetwork::visSave(network,fname) +visNetwork::visSave(network, fname) webshot::webshot( fname, delay = 5, - zoom = 10#, - # vwidth=900,vheight=900 - ) + zoom = 10 +) ``` ```{r} # no infector-infectee pairs are replicated -epi %>% - pluck("contacts") %>% - group_by(from,to) %>% - filter(n()>1) +epi %>% + pluck("contacts") %>% + group_by(from, to) %>% + filter(n() > 1) # count secondary cases per infectee -infector_secondary <- epi %>% - pluck("contacts") %>% +infector_secondary <- epi %>% + pluck("contacts") %>% count(from, name = "secondary_cases") -epi_secondary <- - epi %>% +epi_secondary <- + epi %>% # extract ids in contact *and* linelist using "which" argument - get_id(which = "all") %>% - enframe(name = NULL, value = "from") %>% + get_id(which = "all") %>% + enframe(name = NULL, value = "from") %>% # join count secondary cases per infectee - left_join(infector_secondary) %>% + left_join(infector_secondary) %>% # infectee with missing secondary cases are replaced with zero replace_na( replace = list(secondary_cases = 0) @@ -182,11 +181,11 @@ epi_secondary <- epi_secondary # arrange in descendant order of secondary cases -epi_secondary %>% +epi_secondary %>% arrange(desc(secondary_cases)) ## plot the distribution -epi_secondary %>% +epi_secondary %>% ggplot(aes(secondary_cases)) + geom_histogram(binwidth = 1) + labs( @@ -226,8 +225,8 @@ conflicted::conflict_prefer( conflicted::conflict_scout() ## fit distribution -offspring_fit <- epi_secondary %>% - pull(secondary_cases) %>% +offspring_fit <- epi_secondary %>% + pull(secondary_cases) %>% fitdist(distr = "nbinom") offspring_fit @@ -237,8 +236,8 @@ mid <- offspring_fit$estimate[["size"]] ## calculate the 95% confidence intervals using the standard error estimate and ## the 0.025 and 0.975 quantiles of the normal distribution. -lower <- mid + offspring_fit$sd[["size"]]*qnorm(0.025) -upper <- mid + offspring_fit$sd[["size"]]*qnorm(0.975) +lower <- mid + offspring_fit$sd[["size"]] * qnorm(0.025) +upper <- mid + offspring_fit$sd[["size"]] * qnorm(0.975) round(mid, 4) round(lower, 4) @@ -258,13 +257,13 @@ of the histogram made above. ```{r} # calculate density fit -fit_density <- - tibble(quantile = 0:40) %>% +fit_density <- + tibble(quantile = 0:40) %>% mutate( density = dnbinom( x = quantile, - mu=offspring_fit$estimate[["mu"]], - size=mid + mu = offspring_fit$estimate[["mu"]], + size = mid ) ) @@ -272,16 +271,18 @@ fit_density <- ggplot() + geom_histogram( data = epi_secondary, - mapping = aes( - x = secondary_cases, - y = after_stat(density) - ), - binwidth = 1) + + mapping = + aes( + x = secondary_cases, + y = after_stat(density) + ), + binwidth = 1 + ) + geom_point( data = fit_density, mapping = aes(x = quantile, y = density), alpha = 0.3, color = "red" - ) + + ) + labs( xlab = "Individual reproduction number", ylab = "Number of individuals" @@ -380,15 +381,15 @@ library(epiparameter) epidist_db( epi_dist = "offspring distribution" -) %>% - list_distributions() %>% - select(disease,prob_distribution) +) %>% + list_distributions() %>% + select(disease, prob_distribution) # Load parameters sars <- epidist_db( disease = "SARS", epi_dist = "offspring_distribution", - single_epidist=T + single_epidist = TRUE ) sars_params <- get_parameters(sars) sars_params @@ -467,22 +468,22 @@ show from figure (not available in vignette) ## text --------------------------------- -# proportion of cases that +# proportion of cases that # generate 80% of transmission proportion_transmission( R = sars_params[["mean"]], k = sars_params[["dispersion"]], - percent_transmission=0.8, + percent_transmission = 0.8 ) ## assessment --------------------------------- -# proportion of cases that +# proportion of cases that # generate 80% of transmission proportion_transmission( R = offspring_fit$estimate["mu"], k = offspring_fit$estimate["size"], - percent_transmission=0.8, + percent_transmission = 0.8 ) ## assessment -------------------------------------------------------------- @@ -517,14 +518,13 @@ prevent superspreading events ## text -------------------------- -#' Given a set of cases, -#' what proportion of them -#' (transmission events) -#' where part of -#' secondary case clusters +#' Given a set of cases, +#' what proportion of them +#' (transmission events) +#' where part of +#' secondary case clusters #' (from the same primary case) -#' -#' useful for +#' useful for #' backward contact traicing proportion_cluster_size( diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index f78f456a..dcd22fcc 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -67,9 +67,9 @@ with estimated parameter we then can reconstruct tranmission chains to forecast from MERS estimates in estimate episode ```{r} -mers_offspring <- +mers_offspring <- c( - mean = 0.60, + mean = 0.60, dispersion = 0.02 ) @@ -90,7 +90,7 @@ library(epiparameter) serial_inverval <- epidist_db( disease = "mers", epi_dist = "serial", - single_epidist = T + single_epidist = TRUE ) serial_inverval @@ -114,8 +114,8 @@ simulate_chains( mu = mers_offspring["mean"], size = mers_offspring["dispersion"], # generation - generation_time = function(x) generate(x = serial_inverval,times = x) -) %>% + generation_time = function(x) generate(x = serial_inverval, times = x) +) %>% as_tibble() ``` @@ -132,7 +132,7 @@ as part of the simulation_n chain # Set seed for random number generator set.seed(33) # Number of simulation runs -number_chains <- 1e3 +number_chains <- 1e2 # Number of initial cases initial_cases <- 1 @@ -140,9 +140,9 @@ initial_cases <- 1 ```{r} -simulated_chains_list <- +simulated_chains_list <- map( - .x = seq_len(number_chains), + .x = seq_len(number_chains), .f = function(sim) { simulate_chains( # simulation controls @@ -153,8 +153,8 @@ simulated_chains_list <- mu = mers_offspring["mean"], size = mers_offspring["dispersion"], # generation - generation_time = function(x) generate(x = serial_inverval,times = x) - ) %>% + generation_time = function(x) generate(x = serial_inverval, times = x) + ) %>% mutate(simulation_n = sim) } ) @@ -167,10 +167,10 @@ sim_chains_bind ```{r,echo=FALSE} #### get simulated chain with more infections -------------------------------- -chain_to_observe <- sim_chains_bind %>% - as_tibble() %>% - count(simulation_n,sort = TRUE) %>% - filter(n == max(n)) %>% +chain_to_observe <- sim_chains_bind %>% + as_tibble() %>% + count(simulation_n, sort = TRUE) %>% + filter(n == max(n)) %>% pull(simulation_n) ``` @@ -181,7 +181,7 @@ get epichain summary ```{r} #### get epichain summary ---------------------------------------------------- -simulated_chains_list %>% +simulated_chains_list %>% pluck(chain_to_observe) ``` @@ -192,8 +192,8 @@ infectee-infector data frame ```{r} #### infector-infectee data frame -------------------------------------------- -simulated_chains_list %>% - pluck(chain_to_observe) %>% +simulated_chains_list %>% + pluck(chain_to_observe) %>% as.data.frame() ``` @@ -202,28 +202,28 @@ simulated_chains_list %>% ```{r} # daily aggregate of cases -simulated_chains_day <- - sim_chains_bind %>% - as_tibble() %>% - mutate(simulation_n = as_factor(simulation_n)) %>% +simulated_chains_day <- + sim_chains_bind %>% + as_tibble() %>% + mutate(simulation_n = as_factor(simulation_n)) %>% # Daily number of cases for each simulation mutate(day = ceiling(time)) %>% - count(simulation_n, day, name = "cases") %>% + count(simulation_n, day, name = "cases") %>% # Cumulative number of cases for each simulation - group_by(simulation_n) %>% - mutate(cases_cumsum = cumsum(cases)) %>% + group_by(simulation_n) %>% + mutate(cases_cumsum = cumsum(cases)) %>% ungroup() -# Summarise the chain length and size -sim_chains_max <- +# Summarise the chain length and size +sim_chains_max <- simulated_chains_day %>% - group_by(simulation_n) %>% + group_by(simulation_n) %>% summarise( # length day_max = max(day), # size cases_total = max(cases_cumsum) - ) %>% + ) %>% ungroup() # Visualize transmission chains by cumulative cases @@ -231,8 +231,8 @@ ggplot() + geom_line( data = simulated_chains_day, mapping = aes( - x = day, - y = cases_cumsum, + x = day, + y = cases_cumsum, group = simulation_n, color = simulation_n ), @@ -257,8 +257,8 @@ ggplot() + geom_line( data = simulated_chains_day, mapping = aes( - x = day, - y = cases, + x = day, + y = cases, group = simulation_n, color = simulation_n ), @@ -277,13 +277,13 @@ Evaluate for ebola with know data from previous outbreaks epidist_db( disease = "ebola", epi_dist = "offspring", - single_epidist = T + single_epidist = TRUE ) epidist_db( disease = "ebola", epi_dist = "serial interval", - single_epidist = T + single_epidist = TRUE ) ``` @@ -302,12 +302,13 @@ data from Fayre et al on ebola # Number of individuals in the trees n <- 152 # Number of secondary cases for all individuals -c1 <- c(1,2,2,5,14,1,4,4,1,3,3,8,2,1,1,4,9,9,1,1,17, - 2,1,1,1,4,3,3,4,2,5,1,2,2,1,9,1,3,1,2,1,1,2) -c0 <- c(c1,rep(0,n-length(c1))) +c1 <- c(1, 2, 2, 5, 14, 1, 4, 4, 1, 3, 3, 8, 2, 1, 1, + 4, 9, 9, 1, 1, 17, 2, 1, 1, 1, 4, 3, 3, 4, 2, + 5, 1, 2, 2, 1, 9, 1, 3, 1, 2, 1, 1, 2) +c0 <- c(c1, rep(0, n - length(c1))) -c0 %>% - enframe() %>% +c0 %>% + enframe() %>% ggplot(aes(value)) + geom_histogram() ``` From 6c5eb9107cb4c06684925ad7fafd7fb7444ff9a6 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Wed, 3 Apr 2024 17:35:31 +0100 Subject: [PATCH 010/140] add redirection to project cases --- episodes/superspreading-simulate.Rmd | 13 ++++++++++++- 1 file changed, 12 insertions(+), 1 deletion(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index dcd22fcc..1ac5ef94 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -132,7 +132,7 @@ as part of the simulation_n chain # Set seed for random number generator set.seed(33) # Number of simulation runs -number_chains <- 1e2 +number_chains <- 1000 # Number of initial cases initial_cases <- 1 @@ -251,7 +251,9 @@ ggplot() + # xlim(0,150) + # ylim(0,300) + NULL +``` +```{r,eval=FALSE} # Visualize transmission chains by daily cases ggplot() + geom_line( @@ -266,6 +268,15 @@ ggplot() + ) ``` +:::::::::::::::::::::: testimonial + +### Early spread projections + +In the initial phase of the epidemic you can use `{epichains}` to apply a branching process model to project the number of future cases. Validation analysis showed that this is a rapid and low detail model with forecast prediction intervals that are too certain ([Pearson et al., 2020](https://www.eurosurveillance.org/content/10.2807/1560-7917.ES.2020.25.18.2000543#validationofthemodel-1)). + +We invite you to read the vignette on [Projecting infectious disease incidence: a COVID-19 example](https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html)! + +:::::::::::::::::::::: ## Challenges From 916ce00e3210d8d9da5631246976a80d3d029679 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Wed, 3 Apr 2024 19:15:16 +0100 Subject: [PATCH 011/140] add text on contact tracing effords --- episodes/superspreading-estimate.Rmd | 25 ++++++++++++++----------- 1 file changed, 14 insertions(+), 11 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 47407a22..3e01896f 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -495,23 +495,20 @@ proportion_transmission( ## Backward and forward contact tracing -Reconstruction of transmission trees (whom infected whom) can provide an understanding of who contributes more to transmission. This can be done qith detailed case investigations and/or genetic data. [EXAMPLE: case data paired with contact data to visualize and find the patterns] +Reconstruction of transmission trees (whom infected whom) can provide an understanding of who contributes more to transmission. This can be done with detailed case investigations and/or genetic data ([Cori et al., 2017](https://royalsocietypublishing.org/doi/10.1098/rstb.2016.0371)) - - -### Proportion of events in a given cluster size +Contact tracing can be deployed in multiple strategies. Forward tracing targets downstream individuals who may be infected by index individual. Backward tracing targets the upstream primary case who infected the index case (or a setting or event at which the index case was infected) by retracing history of contact to the likely point of exposure up to the upper bound of the incubation period. -the proportion of new cases that originated within a transmission event of a given size. What proportion of all transmission events were part of secondary case clusters from a set of initial cases +In the presence of heterogeneous transmission, i.e., with an overdispersed offspring distribution, if this primary case is identified, a larger fraction of the transmission chain can be detected by forward tracing each of the contacts of this primary case [Endo et al., 2020](https://wellcomeopenresearch.org/articles/5-239/v3). -useful to inform backwards contact tracing efforts +![Schematic representation of contact tracing strategies. Black arrows indicate the directions of transmission, blue and Orange arrows, a successful or failed contact tracing, respectivelly. When there is evidence of individual-level transmission heterogeneity, often resulting in superspreading, backward contact tracing from the index case (blue circle) increase the probability to find the primary case (green circle) or clusters with a larger fraction of cases, potentially increasing the number of quarentined cases (yellow circles). [Claire Blackmore, 2021](https://www.paho.org/sites/default/files/backward_contact_tracing_v3_0.pdf)](fig/contact-tracing-strategies.png) -Given the observed number of new cases, cluster of cases, what proportion of them came from same index case +When there is evidence of individual-level variation (i.e. overdispersion), often resulting in so-called superspreading events, a large proportion of infections may be linked to a small proportion of original clusters. As a result, finding and targeting originating clusters in combination with reducing onwards infection may substantially enhance the effectiveness of tracing methods [Endo et al., 2020](https://wellcomeopenresearch.org/articles/5-239/v3). -cluster is the transmission from primary to secondary case -Given a set of cases, what proportion of them (transmission events) where part of secondary case clusters (from the same primary case) +### Proportion of events in a given cluster size -prevent superspreading events +By looking at the tail of the probability offspring distribution, we can identify the size of the cluster of secondary infections. The probability that a cluster of secondary infections caused by a primary case identified by backward tracing has a size of $X$ or larger ([Endo et al., 2020](https://wellcomeopenresearch.org/articles/5-239/v3)). ```{r} # estimate prop cluster size ---------------------------------------------- @@ -530,11 +527,17 @@ prevent superspreading events proportion_cluster_size( R = offspring_fit$estimate["mu"], k = offspring_fit$estimate["size"], - cluster_size = 10 + cluster_size = c(5, 10, 25) ) ``` +Even though we have an $R<1$, given a highly overdispersed offspring distribution ($k=0.02$) we have a 46.9% probability to find a cluster of 25 people or larger. + +The probability of a cluster size can also inform backwards contact tracing efforts. Among other factors, high cluster sizes could imply that a contac tracing approach may no longer likely result in successful containment due to increased proportion of contacts not identified by the process or achieving low case ascertainment ([Public Health England, 2020](https://www.gov.uk/government/publications/phe-when-to-stop-contact-tracing-developing-triggers-from-phe-systems-20-february-2020)). + +We can also use this number to prevent gathering of certain sized to reduce the epidemic by preventing potential superspreading events. Interventions can target to reduce the reproduction number in order to reduce the probability of having clusters of secondary cases. + ## Superspreading in decision making - How to estimate the probability of large outbreak? 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Monkeypox and smallpox viruses show intermediate variation, consistent across multiple data sets, and pneumonic plague transmission is slightly less variable + +![Expected proportion of all transmission due to a given proportion of infectious cases, where cases are ranked by infectiousness. For a homogeneous population (all ν = R0), this relation is linear. For five directly transmitted infections (based on specific k values), the line is concave owing to variation in ν.](fig/SEE-individual-reproductive-number-fig-b.png) + @@ -69,17 +75,10 @@ distributions for transmission heterogeneity Heterogeneity is in the variance of the number of secondary cases generated by each infected individual -## The individual reproduction number +individual variation of transmission informs the frequency of superspreading events (SSE) + -- interpretation: is the concept, not yet a distribution -- as a random variable representing the expected number of secondary cases caused by a particular infected individual. -- Values for ν are drawn from a continuous probability distribution with - - population mean R0 - + that encodes all variation in infectious histories of individuals - - dispersion parameter k - + smaller values of k indicate greater heterogeneity - + larger values of k indicate less heterogeneity ## The offspring distribution @@ -189,8 +188,70 @@ epi_secondary %>% ggplot(aes(secondary_cases)) + geom_histogram(binwidth = 1) + labs( - xlab = "Individual reproduction number", - ylab = "Number of individuals" + x = "Number of secondary cases", + y = "Frequency" + ) +``` + +## The individual reproduction number + +- interpretation: is the concept, not yet a distribution +- as a random variable representing the expected number of secondary cases caused by a particular infected individual. + +- Values for ν are drawn from a continuous probability distribution with + - population mean R0 + + that encodes all variation in infectious histories of individuals + - dispersion parameter k + + smaller values of k indicate greater heterogeneity + + larger values of k indicate less heterogeneity + +SSE are important realizations from the right-hand tail of a distribution of ν + +```{r,echo=FALSE,message=FALSE,warning=FALSE} +# Load parameters +mpox <- epidist_db( + disease = "SARS", + epi_dist = "offspring_distribution", + single_epidist = TRUE +) +mpox_params <- get_parameters(mpox) +# mpox_params + +# calculate density fit +fit_density <- + tibble(quantile = 0:40) %>% + mutate( + density = dnbinom( + x = quantile, + mu = mpox_params["mean"], + size = mpox_params["dispersion"] + ) + ) + +# plot offspring distribution with density fit +ggplot() + + geom_line( + data = fit_density, + mapping = + aes( + x = quantile, + y = density + ) + ) + + geom_vline( + aes(xintercept = mpox_params["mean"] + ), lty = 2 + ) + + annotate( + "text", label = "mean Ro", + x = mpox_params["mean"] + 5, + y = 0.5, + size = 8, + colour = "red" + ) + + labs( + x = "Individual reproductive number", + y = "Density" ) ``` @@ -289,6 +350,12 @@ ggplot() + ) ``` +::::::::::::::::::::::: challenge + +read ebola contact data and estimate R and dispersion? + +::::::::::::::::::::::: + ## Interpret the dispersion parameter @@ -376,7 +443,7 @@ The Poisson distribution is an special case of the Negative Binomial. When k app ### Use epiparameter -```{r} +```{r,message=FALSE,warning=FALSE} library(epiparameter) epidist_db( @@ -401,7 +468,7 @@ sars_params ### Select the best model -assess fit performance w/ model comparison AIC, BIC +Assess fit performance w/ model comparison AIC, BIC Using Information criteria for the best fit. Read further in vignette using helper functions @@ -409,65 +476,33 @@ Using Information criteria for the best fit. Read further in vignette using help ::::::::::::::::::::::::: -::::::::::::::::::::::::: spoiler - -### Define SSE - -code this up lloyds definition - -:::::::::::::::::::::::: - -## Superspreading events (SSEs) - -- are important realizations from the right-hand tail of a distribution of ν -- define an SSE as any infected individual who infects more than Z(n) others, where Z(n) is the nth percentile of the Poisson(R) distribution. -- A 99th-percentile SSE is then any case causing more infections than would occur in 99% of infectious histories in a homogeneous population +## Evidence for variation in individual reproductive number -## Effect of heterogeneity +Comparing our findings to the 20/80 rule proposed for sexually transmitted and vector-borne diseases, no general rule emerges but the core principle of heterogeneous transmission is certainly supported (Fig. 1c). -Heterogeneity affects epidemic establishment and the ease of control - -understanding offspring distribution overdispersion is superspreading! - -individual variation of transmission informs the frequency of superspreading events (SSE) - -- heterogeneity at the individual level of transmission reduce chance of an emerging outbreak - -- but it can also make it hard to control when there is a lot of SSE +- focus on the cumulative probability distribution of the most infectious cases + + if there is a 0.2 proportion of (the most infectious) cases contributing to the 0.8 proportion of transmission, this is a highly heterogeneous distribution. (e.g. SARS) + + if there is a 0.6 proportion of (the most infectious) cases contributing to the 0.8 of transmission, this is a less heterogeneous distribution (compared to the above one, e.g. pneumonic plague) -+ difficulty of establishment -+ ease to control -+ mass vs targeted interventions +![Proportion of transmission expected from the most infectious 20% of cases, for 10 outbreak or surveillance data sets (triangles). Dashed lines show proportions expected under the 20/80 rule (top) and homogeneity (bottom). Superscript ‘v’ indicates a partially vaccinated population.](fig/SEE-individual-reproductive-number-fig-c.png) -+ Greater heterogeneity reduces the chance of an outbreak emerging from single case [NOTE: DIFICULT INTUITION] [EXAMPLE: lots of individual with individual reproduction number around 1 or below] -+ However, this heterogeneity can make an established outbreak hard to control using mass interventions, as a single uncontrolled case can generate a large number of secondary cases. [INTERPRETATION: if the outbreak gets established, then it is hard to control assuming homogeneity of transmission] +::::::::::::::::::::::::::::: challenge -Conversely, heterogeneity in transmission may provide opportunities for targeting interventions if the individuals who contribute more to transmission (due to biological, environmental or behavuoral factors) share socia-demographic or geographical characteristics that can be defined [INTERPRETATION: ones identified, this can help targetted interventions to this population] +What is the proportion of cases that are responsible of the 80% of transmission? - +Compare between SARS, MERS, Ebola -## Proportion of transmission +::::::::::::::::::::: hint -#### Proportion of cases resposible of 80% of infection +Use `proportion_transmission()` -+ [figure 1B](https://www.nature.com/articles/nature04153/figures/1) -+ [Figure 1C](https://www.nature.com/articles/nature04153/figures/1) -+ pareto rule +::::::::::::::::::::: -show from figure (not available in vignette) - -- focus on the cumulative probability distribution of the most infectious cases - + if there is a 0.2 proportion of (the most infectious) cases contributing to the 0.8 proportion of transmission, this is a highly heterogeneous distribution. (e.g. SARS) - + if there is a 0.6 proportion of (the most infectious) cases contributing to the 0.8 of transmission, this is a less heterogeneous distribution (compared to the above one, e.g. pneumonic plague) - -![](fig/SEE-individual-reproductive-number.png) +::::::::::::::::::::: solution ```{r} -# estimate prop cases cause transmission ---------------------------------- - -## text --------------------------------- - +# estimate # proportion of cases that # generate 80% of transmission proportion_transmission( @@ -478,6 +513,7 @@ proportion_transmission( ## assessment --------------------------------- +# estimate # proportion of cases that # generate 80% of transmission proportion_transmission( @@ -492,6 +528,26 @@ proportion_transmission( ``` +::::::::::::::::::::: + +::::::::::::::::::::::::::::: + +::::::::::::::::::::::::: callout + +### Define Superspreading events + +Lloyds propose a general protocol for defining a superspreading event: + +- define an SSE as any infected individual who infects more than Z(n) others, where Z(n) is the nth percentile of the Poisson(R) distribution. +- A 99th-percentile SSE is then any case causing more infections than would occur in 99% of infectious histories in a homogeneous population + +```{r} +qpois(p = 0.99,lambda = offspring_fit$estimate["mu"]) +``` + +![Reported superspreading events (SSEs; diamonds) relative to estimated reproductive number R (squares) for twelve directly transmitted infections. Lines show 5–95 percentile range of Z∼Poisson(R), and crosses show the 99th-percentile proposed as threshold for SSEs. Stars represent SSEs caused by more than one source case. ‘Other’ diseases are: 1, Streptococcus group A; 2, Lassa fever; 3, Mycoplasma pneumonia; 4, pneumonic plague; 5, tuberculosis. R is not shown for ‘other’ diseases, and is off-scale for monkeypox.](fig/SEE-individual-reproductive-number-fig-d.png) + +:::::::::::::::::::::::: ## Backward and forward contact tracing @@ -506,7 +562,7 @@ In the presence of heterogeneous transmission, i.e., with an overdispersed offsp When there is evidence of individual-level variation (i.e. overdispersion), often resulting in so-called superspreading events, a large proportion of infections may be linked to a small proportion of original clusters. As a result, finding and targeting originating clusters in combination with reducing onwards infection may substantially enhance the effectiveness of tracing methods [Endo et al., 2020](https://wellcomeopenresearch.org/articles/5-239/v3). -### Proportion of events in a given cluster size +## Proportion of events in a given cluster size By looking at the tail of the probability offspring distribution, we can identify the size of the cluster of secondary infections. The probability that a cluster of secondary infections caused by a primary case identified by backward tracing has a size of $X$ or larger ([Endo et al., 2020](https://wellcomeopenresearch.org/articles/5-239/v3)). @@ -530,82 +586,83 @@ The probability of a cluster size can also inform backwards contact tracing effo We can also use this number to prevent gathering of certain sized to reduce the epidemic by preventing potential superspreading events. Interventions can target to reduce the reproduction number in order to reduce the probability of having clusters of secondary cases. -## Superspreading in decision making -- How to estimate the probability of large outbreak? -- How to estimate the proportion of cases responsible of the 80% of transmission? +::::::::::::::::::::::: challenge -Early understanding of disease epidemic potential from R0 and dispersion +reuse ebola parameters? interpret -ease of control with either mass or targeted interventions +::::::::::::::::::::::: -**Probability of a large epidemic** +## Superspreading in decision making -The more heterogeneity, less probability to stablish. +Transmission heterogeneity affects epidemic establishment and the ease of control ([Cori et al., 2017](https://royalsocietypublishing.org/doi/10.1098/rstb.2016.0371)). -But the higher the number of introductions, the higher the likelihood ++ Greater heterogeneity reduces the chance of an outbreak emerging from single case. Individuals with more extreme amount of secondary cases are rare. -:::::::::::::::::::: challenge ++ However, if the outbreak gets established, this heterogeneity can make an outbreak hard to control using *mass interventions* (which assumes transmission homogeneity), as a single uncontrolled case can generate a large number of secondary cases. -```{r} -## assessment ------------------------------------- ++ Conversely, heterogeneity in transmission may provide opportunities for *targeted interventions* if the individuals who contribute more to transmission (due to biological, environmental or behavioral factors) share socio-demographic or geographical characteristics that can be defined. -# Estimate probability of large outbreak -# with 5 independent imported cases -probability_epidemic( - R = offspring_fit$estimate["mu"], - k = offspring_fit$estimate["size"], - num_init_infect = 5 -) +We can have an early understanding of a disease epidemic potential from the mean reproduction number $R_{o}$ and dispersion $k$ of an offspring distribution to answer questions like: +- What is the probability of an pathogen to cause large outbreak? +- What is the probability of an outbreak to get extinct? +- What is the probability to contain the ongoing outbreak? -## assessment -------------------------------------------------------------- +::::::::::::::::::::::::::: testimonial -#' get ebola params -``` +### Epidemic Risk assessment accounting for superspreading -::::::::::::::::::: +These estimates vary non-linearly with respect to the mean reproduction number $R_{o}$ and dispersion $k$ of a given disease. -**Probability of extintion** +We invite you to read the `{superspreading}` vignette on [Epidemic risk](https://epiverse-trace.github.io/superspreading/articles/epidemic_risk.html)! -more heterogeneity, more difficult to go extinct. +::::::::::::::::::::::::::: +## Challenges +::::::::::::::::::::::::::: challenge -**Probability to contain** +use mers to estimate ... -not exceed 100 cases +::::::::::::::::::::::::::: -```{r} -# estimate prob to contain ------------------------------------------------ +:::::::::::::::::::: challenge +Calculate probabilities for Ebola using data from epiparameter -## text ---------------------------------- +:::::::::::::::::: hint +```{r} +# estimate probability to contain probability_contain( R = offspring_fit$estimate["mu"], k = offspring_fit$estimate["size"], num_init_infect = 1, case_threshold = 100 ) -``` +# Estimate probability of large outbreak +# with 5 independent imported cases +probability_epidemic( + R = offspring_fit$estimate["mu"], + k = offspring_fit$estimate["size"], + num_init_infect = 5 +) +``` -### Go to vignette - -Given initial conditions or a range of plausible scenarios or R and k, you can use - -Look at them in the {superspreading} vignette +:::::::::::::::::: - +:::::::::::::::::: solution -## Challenges +```{r} +#' get ebola params +``` -::::::::::::::::::::::::::: challenge +:::::::::::::::::: -use mers to estimate ... +::::::::::::::::::::::::::::::::::::: -::::::::::::::::::::::::::: :::::::::::::::::::::::::: challenge From 8655c9e29ada23ff26fc8a947a8fe3ed6ba56726 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Wed, 3 Apr 2024 21:50:42 +0100 Subject: [PATCH 015/140] add unit figures from SEE paper --- ...SEE-individual-reproductive-number-fig-b.png | Bin 0 -> 42785 bytes ...SEE-individual-reproductive-number-fig-c.png | Bin 0 -> 41607 bytes ...SEE-individual-reproductive-number-fig-d.png | Bin 0 -> 32479 bytes 3 files changed, 0 insertions(+), 0 deletions(-) create mode 100644 episodes/fig/SEE-individual-reproductive-number-fig-b.png create mode 100644 episodes/fig/SEE-individual-reproductive-number-fig-c.png create mode 100644 episodes/fig/SEE-individual-reproductive-number-fig-d.png diff --git a/episodes/fig/SEE-individual-reproductive-number-fig-b.png b/episodes/fig/SEE-individual-reproductive-number-fig-b.png new file mode 100644 index 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zCe-_Cu~}A!hd^1O=WK>_gpWO0mApWahbd{bxhb{1u*Unye$oWHOp%#PyFB0rA_sHm zThM1-sX&U$1ksxeSo_Ld_2_Z9WLxdWS5d$SAE9+n`~^Y^AYet<7_Ya90`9 zGr@1AaPBmvClueonGO>-LFCAHzMW!($)ev5zTflhowvQCI&mVs`!FEYOWR6Y<0;;| z?#HCL&$nL;O8d5%S?KDv2fs#^DdEF84af#$mDp!k)?V47@w2yY%j1brZ6kI)UZC8T z!=R#o5Ac>MBEG^SliSKrISRz6XptD^>4`mWv?~RK?7jG>xNG-X;ntWk0d;oD5vQiN zrCO2_-;wd|em%)d$8*vmc--jXW%Ml((GT0mL@ZB{?&g?zN_CaCYpE z9t-bYA-K-LuBQ5+>dyqk6WWp0FiiC^HGQxL@^@0&<@OBq1H3@pObitk<&nEO(_f*}Par3=e{bWZ=;ezVzddt2f+|Upu1*}~r%M}(1~h;;Jk&K|YZ@ Date: Wed, 3 Apr 2024 22:48:44 +0100 Subject: [PATCH 016/140] edit code issues in output --- episodes/superspreading-estimate.Rmd | 1 + episodes/superspreading-simulate.Rmd | 8 ++++++++ 2 files changed, 9 insertions(+) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index cb004b1d..da17acca 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -56,6 +56,7 @@ library(outbreaks) library(epicontacts) library(fitdistrplus) library(superspreading) +library(epiparameter) library(tidyverse) ``` diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 1ac5ef94..e0a10513 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -164,6 +164,13 @@ sim_chains_bind <- bind_rows(simulated_chains_list) sim_chains_bind ``` +```{r} +# view infectee number per simulation +sim_chains_bind %>% + as_tibble() %>% + count(simulation_n, sort = TRUE) +``` + ```{r,echo=FALSE} #### get simulated chain with more infections -------------------------------- @@ -248,6 +255,7 @@ ggplot() + ), show.legend = FALSE ) + + geom_hline(aes(yintercept = 100), lty = 2) + # xlim(0,150) + # ylim(0,300) + NULL From 1ee92e67a8241a4d44222b206be681180061e64f Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Wed, 3 Apr 2024 23:00:00 +0100 Subject: [PATCH 017/140] fix code to pass lintr --- episodes/superspreading-estimate.Rmd | 13 ++++++++----- 1 file changed, 8 insertions(+), 5 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index da17acca..65d0d60e 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -245,9 +245,9 @@ ggplot() + ) + annotate( "text", label = "mean Ro", - x = mpox_params["mean"] + 5, - y = 0.5, - size = 8, + x = mpox_params["mean"] + 5, + y = 0.5, + size = 8, colour = "red" ) + labs( @@ -543,7 +543,10 @@ Lloyds propose a general protocol for defining a superspreading event: - A 99th-percentile SSE is then any case causing more infections than would occur in 99% of infectious histories in a homogeneous population ```{r} -qpois(p = 0.99,lambda = offspring_fit$estimate["mu"]) +qpois( + p = 0.99, + lambda = offspring_fit$estimate["mu"] +) ``` ![Reported superspreading events (SSEs; diamonds) relative to estimated reproductive number R (squares) for twelve directly transmitted infections. Lines show 5–95 percentile range of Z∼Poisson(R), and crosses show the 99th-percentile proposed as threshold for SSEs. Stars represent SSEs caused by more than one source case. ‘Other’ diseases are: 1, Streptococcus group A; 2, Lassa fever; 3, Mycoplasma pneumonia; 4, pneumonic plague; 5, tuberculosis. R is not shown for ‘other’ diseases, and is off-scale for monkeypox.](fig/SEE-individual-reproductive-number-fig-d.png) @@ -635,7 +638,7 @@ Calculate probabilities for Ebola using data from epiparameter :::::::::::::::::: hint ```{r} -# estimate probability to contain +# estimate probability to contain probability_contain( R = offspring_fit$estimate["mu"], k = offspring_fit$estimate["size"], From 26a246040283771400b8e9428086458cd9fc3e61 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Wed, 3 Apr 2024 23:00:14 +0100 Subject: [PATCH 018/140] select a minimal chain --- episodes/superspreading-simulate.Rmd | 2 ++ 1 file changed, 2 insertions(+) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index e0a10513..0a0b6824 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -177,7 +177,9 @@ sim_chains_bind %>% chain_to_observe <- sim_chains_bind %>% as_tibble() %>% count(simulation_n, sort = TRUE) %>% + filter(n < 10) %>% filter(n == max(n)) %>% + slice_min(simulation_n) %>% pull(simulation_n) ``` From 989d8d59162e0db212f057d7a790659c61d0b773 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Wed, 3 Apr 2024 23:20:39 +0100 Subject: [PATCH 019/140] clean simluation output to three generations only --- episodes/superspreading-simulate.Rmd | 15 ++++++++++++++- 1 file changed, 14 insertions(+), 1 deletion(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 0a0b6824..9db036a1 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -174,12 +174,25 @@ sim_chains_bind %>% ```{r,echo=FALSE} #### get simulated chain with more infections -------------------------------- +chains_subgroup <- sim_chains_bind %>% + as_tibble() %>% + group_by(simulation_n) %>% + distinct(infector_id) %>% + count(simulation_n) %>% + filter(n < 5, n >= 3) %>% + pull(simulation_n) + chain_to_observe <- sim_chains_bind %>% as_tibble() %>% count(simulation_n, sort = TRUE) %>% + filter( + magrittr::is_in( + simulation_n, chains_subgroup + ) + ) %>% filter(n < 10) %>% filter(n == max(n)) %>% - slice_min(simulation_n) %>% + slice_min(simulation_n) %>% pull(simulation_n) ``` From 6c577fce5054796cb014d61d0d78035abbb3e50d Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Thu, 4 Apr 2024 11:52:10 +0100 Subject: [PATCH 020/140] add intro to estimate episode --- episodes/superspreading-estimate.Rmd | 30 +++++++++++++++++++--------- 1 file changed, 21 insertions(+), 9 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 65d0d60e..4c2892ec 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -41,22 +41,29 @@ Learners should familiarise themselves with following concept dependencies befor -Comparing results for eight directly transmitted infections reveals the differing degree of individual variation among diseases and outbreak settings +From epidemics like Smallpox or the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), we know that some people spread disease more than others. Since disease transmission is caused by many physiological and social factors, we usually use population averages to assess the disease potential to spread. However, individual differences in infectiousness increase the tendency towards superspreading events (SSEs) which can ignite explosive epidemics and affect the ease of control. -Like SARS, measles in highly vaccinated populations shows high variation in two surveillance data sets, with narrow confidence intervals excluding the conventional models (note that heterogeneous vaccination coverage is an important environmental factor contributing to this pattern). Monkeypox and smallpox viruses show intermediate variation, consistent across multiple data sets, and pneumonic plague transmission is slightly less variable - -![Expected proportion of all transmission due to a given proportion of infectious cases, where cases are ranked by infectiousness. For a homogeneous population (all ν = R0), this relation is linear. For five directly transmitted infections (based on specific k values), the line is concave owing to variation in ν.](fig/SEE-individual-reproductive-number-fig-b.png) +![**Chains of SARS-CoV-2 transmission in Hong Kong initiated by local or imported cases.** (**a**), Transmission network of a cluster of cases traced back to a collection of four bars across Hong Kong (n = 106). (**b**), Transmission network associated with a wedding without clear infector–infectee pairs but linked back to a preceding social gathering and local source (n = 22). (**c**), Transmission network associated with a temple cluster of undetermined source (n = 19). (**d**), All other clusters of SARS-CoV-2 infections where the source and transmission chain could be determined ([Adam et al., 2020](https://www.nature.com/articles/s41591-020-1092-0)).](fig/see-intro-superspreading.png) +The [basic reproduction number](../learners/reference.md#basic), $R_0$, is the average number of cases caused by one infectious individual in a entirely susceptible population. Population estimates of $R_0$ can obscure considerable individual variation in infectiousness, as highlighted during the global emergence of SARS-CoV-2 by numerous ‘superspreading events’ in which certain individuals infected unusually large numbers of secondary cases ([Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153)). + +![**Observed offspring distribution of SARS-CoV-2 transmission in Hong Kong.** N = 91 SARS-CoV-2 infectors, N = 153 terminal infectees and N = 46 sporadic local cases. Histogram bars indicate the proportion of onward transmission per amount of secondary cases. Line corresponds to a fitted negative binomial distribution ([Adam et al., 2020](https://www.nature.com/articles/s41591-020-1092-0)).](fig/see-intro-secondary-cases-fig-b.png){alt='R = 0.58 and k = 0.43.'} + +In this tutorial, we are going to estimate the individual variation in transmission and assess its heterogeneity, which often results in superspreading events. Also, we are going to use these estimates to account for superspreading in contact tracing interventions. + +We are going to use data from the `{outbreaks}` package, manage linelist and contacts data using `{epicontacts}`, and estimate distribution parameters with `{fitdistrplus}`. Lastly, we are going to use `{superspreading}` to account for it in decision-making. + +We’ll use the pipe `%>%` to connect some of their functions, so let’s also call to the `{tidyverse}` package: + ```{r,message=FALSE,warning=FALSE} library(outbreaks) library(epicontacts) library(fitdistrplus) library(superspreading) -library(epiparameter) library(tidyverse) ``` @@ -167,12 +174,14 @@ infector_secondary <- epi %>% epi_secondary <- epi %>% - # extract ids in contact *and* linelist using "which" argument + # extract ids in contact *and* linelist + # using "which" argument get_id(which = "all") %>% enframe(name = NULL, value = "from") %>% # join count secondary cases per infectee left_join(infector_secondary) %>% - # infectee with missing secondary cases are replaced with zero + # infectee with missing secondary cases + # are replaced with zero replace_na( replace = list(secondary_cases = 0) ) @@ -210,12 +219,12 @@ SSE are important realizations from the right-hand tail of a distribution of ν ```{r,echo=FALSE,message=FALSE,warning=FALSE} # Load parameters -mpox <- epidist_db( +mpox <- epiparameter::epidist_db( disease = "SARS", epi_dist = "offspring_distribution", single_epidist = TRUE ) -mpox_params <- get_parameters(mpox) +mpox_params <- epiparameter::get_parameters(mpox) # mpox_params # calculate density fit @@ -487,6 +496,9 @@ Comparing our findings to the 20/80 rule proposed for sexually transmitted and v ![Proportion of transmission expected from the most infectious 20% of cases, for 10 outbreak or surveillance data sets (triangles). Dashed lines show proportions expected under the 20/80 rule (top) and homogeneity (bottom). Superscript ‘v’ indicates a partially vaccinated population.](fig/SEE-individual-reproductive-number-fig-c.png) +The comparison of directly transmitted infections reveals the differing degree of individual variation among diseases and outbreak settings. Like SARS, measles in highly vaccinated populations shows high variation, with heterogeneous vaccination coverage as an important environmental factor contributing to this pattern. Monkeypox and smallpox viruses show intermediate variation, consistent across multiple data sets, and pneumonic plague transmission is slightly less variable. + +![Expected proportion of all transmission due to a given proportion of infectious cases, where cases are ranked by infectiousness. For a homogeneous population (all ν = R0), this relation is linear. For five directly transmitted infections (based on specific k values), the line is concave owing to variation in ν.](fig/SEE-individual-reproductive-number-fig-b.png) ::::::::::::::::::::::::::::: challenge From 15e303cc382ca3e4962f135f4baa8fb70cec5071 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Thu, 4 Apr 2024 13:18:41 +0100 Subject: [PATCH 021/140] clean entry content --- episodes/superspreading-estimate.Rmd | 192 +++++++++++---------------- 1 file changed, 79 insertions(+), 113 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 4c2892ec..379eb05e 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -67,85 +67,30 @@ library(superspreading) library(tidyverse) ``` +## The individual reprodution number -## questions {to remove} - -- What is the offspring distribution? -- How to assess for heterogeneity in transmission? -- How to estimate the mean reproduction number and dispersion parameter from an offspring distribution? -- The definition of a 99th-percentile SSE (not directly cover by the package) - -## Transmission heterogeneity - -individual reproductive number - -distributions for transmission heterogeneity - -Heterogeneity is in the variance of the number of secondary cases generated by each infected individual - -individual variation of transmission informs the frequency of superspreading events (SSE) - - - - -## The offspring distribution - -- Stochastic effects in transmission are modelled using a Poisson process, so that the number of secondary infections caused by each case, Z, is described by an ‘offspring distribution’ Pr(Z = k) where Z∼Poisson(ν). - -- interpretation: it describes properly as a distribution the ‘individual reproductive number’ - -the offspring distribution, - -- can be characterized by a statistical distribution - - negative binomial, usually -- with distribution parameters given by - - R0 as the mean and - + average number of (secondary) cases produced by a single individual in an entirely susceptible population - - k as the dispersion parameter, - +degree of heterogeneity in transmission by single individuals - -negative binomial - -mean, size or (inverse-)dispersion - -variance - -heterogeneity - -mean/variance ratio - -read linelist + contact data - -secondary transmission distribution - -get vector of secondary cases per id - -[appliedepi](https://community.appliedepi.org/t/estimating-the-degree-of-super-spreading-from-transmission-chain-data/103/2) - -[Figure 1A](https://www.nature.com/articles/nature04153/figures/1) +Reconstruction of transmission trees (whom infected whom) can provide an understanding of who contributes more to transmission. This can be done with detailed case investigations and/or genetic data ([Cori et al., 2017](https://royalsocietypublishing.org/doi/10.1098/rstb.2016.0371)) -- our context: the offspring distribution - + the x value is the: - + number of secondary cases - + individual reproductive number +Let's use the `mers_korea_2015` linelist and contact data from `{outbreaks}` with `{epicontacts}` to get the distribution of secondary cases ([Campbell, 2022](https://community.appliedepi.org/t/estimating-the-degree-of-super-spreading-from-transmission-chain-data/103/2)): ```{r} ## make epicontact object -epi <- make_epicontacts( - linelist = mers_korea_2015$linelist, - contacts = mers_korea_2015$contacts -) +epi_contacts <- + epicontacts::make_epicontacts( + linelist = mers_korea_2015$linelist, + contacts = mers_korea_2015$contacts + ) ``` ```{r,eval=FALSE} # visualise contact tree -epicontacts::vis_epicontacts(epi) +epicontacts::vis_epicontacts(epi_contacts) ``` ```{r,echo=FALSE} # visualise contact tree network <- - epicontacts::vis_epicontacts(epi) %>% + epicontacts::vis_epicontacts(epi_contacts) %>% visNetwork::visPhysics(solver = "barnesHut") fname <- "network.html" @@ -159,24 +104,43 @@ webshot::webshot( ) ``` +::::::::::::::::::::::::::: spoiler + +### Is contact data tidy? + +Contact data contains information of whom infected whom. We expect to have the infector (`from`) and the infectee (`to`) plus additional columns of variables related to their contact like location (`exposure`) and date of contact. + +Following [tidy data](https://tidyr.tidyverse.org/articles/tidy-data.html#tidy-data) principles, in contact data the observation unit is the **infector-infectee** pair. Although one infector can infect multiple infectees, from contact tracing investigations we may record infectees contacts with more than one infector. But we should expect to have unique infector-infectee pairs. + +We can check on replicates for infectees: ```{r} # no infector-infectee pairs are replicated -epi %>% +epi_contacts %>% pluck("contacts") %>% - group_by(from, to) %>% + group_by(to) %>% filter(n() > 1) +``` + +::::::::::::::::::::::::::: -# count secondary cases per infectee -infector_secondary <- epi %>% +When each infector-infectee row is unique, the number of entries per infector corresponds to the number of secondary cases. + +```{r} +# count secondary cases per infector +infector_secondary <- epi_contacts %>% pluck("contacts") %>% count(from, name = "secondary_cases") +``` +The number + +```{r,message=FALSE,warning=FALSE} epi_secondary <- - epi %>% + epi_contacts %>% # extract ids in contact *and* linelist # using "which" argument - get_id(which = "all") %>% + epicontacts::get_id(which = "all") %>% enframe(name = NULL, value = "from") %>% # join count secondary cases per infectee left_join(infector_secondary) %>% @@ -186,9 +150,6 @@ epi_secondary <- replace = list(secondary_cases = 0) ) -# count of secondary cases per individual -epi_secondary - # arrange in descendant order of secondary cases epi_secondary %>% arrange(desc(secondary_cases)) @@ -203,19 +164,11 @@ epi_secondary %>% ) ``` -## The individual reproduction number +The _individual reproductive number_, ν, is defined as a random variable representing the expected number of secondary cases caused by a particular infected individual. -- interpretation: is the concept, not yet a distribution -- as a random variable representing the expected number of secondary cases caused by a particular infected individual. +Values for ν are drawn from a continuous probability distribution with population mean $R_{o}$ that encodes all variation in infectious histories of individuals, including properties of the host and pathogen and environmental circumstances. -- Values for ν are drawn from a continuous probability distribution with - - population mean R0 - + that encodes all variation in infectious histories of individuals - - dispersion parameter k - + smaller values of k indicate greater heterogeneity - + larger values of k indicate less heterogeneity - -SSE are important realizations from the right-hand tail of a distribution of ν +In this framework, superspreading events (SSEs) are not exceptional events, but important realizations from the right-hand tail of a distribution of ν ([Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153)). ```{r,echo=FALSE,message=FALSE,warning=FALSE} # Load parameters @@ -265,7 +218,23 @@ ggplot() + ) ``` -## Estimate the dispersion parameter + +## Estimate the offspring distribution + +Stochastic effects in transmission are modelled using a Poisson process4, so that the number of secondary infections caused by each case, Z, is described by an ‘offspring distribution’ Pr(Z = k) where Z∼Poisson(ν). + +By considering three possible distributions of ν, we generate three candidate models for the offspring distribution: (1) in generation-based models neglecting individual variation, ν = R0 for all cases, yielding Z∼Poisson(R0); (2) in differential-equation models with homogeneous transmission and constant recovery rates, ν is exponentially distributed, yielding Z∼geometric(R0); (3) in a more general formulation, we let ν be gamma-distributed with mean R0 and dispersion parameter k, yielding Z∼negative binomial(R0,k) (ref. 23). The negative binomial model includes the conventional Poisson (k → ∞) and geometric (k = 1) models as special cases. It has variance R0(1 + R0/k), so smaller values of k indicate greater heterogeneity. + +the offspring distribution, + +- can be characterized by a statistical distribution + - negative binomial, usually +- with distribution parameters given by + - R0 as the mean and + + average number of (secondary) cases produced by a single individual in an entirely susceptible population + - k as the dispersion parameter, + +degree of heterogeneity in transmission by single individuals + fit distribution to data using {fitdistrplus} provide maximum likelihood estimates @@ -280,21 +249,6 @@ individual level variation in infectiousness ```{r} library(fitdistrplus) -conflicted::conflict_scout() -conflicted::conflict_prefer( - name = "filter", - winner = "dplyr" -) -conflicted::conflict_prefer( - name = "lag", - winner = "dplyr" -) -conflicted::conflict_prefer( - name = "select", - winner = "dplyr" -) -conflicted::conflict_scout() - ## fit distribution offspring_fit <- epi_secondary %>% pull(secondary_cases) %>% @@ -304,20 +258,18 @@ offspring_fit ## extract the "size" parameter mid <- offspring_fit$estimate[["size"]] +``` +```{r,echo=FALSE} ## calculate the 95% confidence intervals using the standard error estimate and ## the 0.025 and 0.975 quantiles of the normal distribution. lower <- mid + offspring_fit$sd[["size"]] * qnorm(0.025) upper <- mid + offspring_fit$sd[["size"]] * qnorm(0.975) - -round(mid, 4) -round(lower, 4) -round(upper, 4) ``` We can see that the dispersion parameter is estimated as -0.020 (95% CI 0.006 - 0.035). +`r round(mid, 3)` (95% CI `r `round(lower, 3)` - `r round(upper, 3)`). As this value is significantly lower than one, we can conclude that @@ -326,7 +278,7 @@ the degree of super-spreading is high. This is in line with visual inspection of the histogram made above. -```{r} +```{r,echo=FALSE} # calculate density fit fit_density <- tibble(quantile = 0:40) %>% @@ -360,6 +312,16 @@ ggplot() + ) ``` +::::::::::::::::::::::: callout + +### Transmission heterogeneity + +Heterogeneity is in the variance of the number of secondary cases generated by each infected individual + +[add table quick summary] + +::::::::::::::::::::::: + ::::::::::::::::::::::: challenge read ebola contact data and estimate R and dispersion? @@ -451,17 +413,22 @@ The Poisson distribution is an special case of the Negative Binomial. When k app :::::::::::::::::::::::: callout -### Use epiparameter +### Use {epiparameter} -```{r,message=FALSE,warning=FALSE} +Currently, `{epiparameter}` have offspring distributions for: + +```{r,message=FALSE,warning=FALSE,echo=FALSE} library(epiparameter) epidist_db( epi_dist = "offspring distribution" ) %>% list_distributions() %>% - select(disease, prob_distribution) + dplyr::select(disease) %>% + distinct() %>% pull() +``` +```{r} # Load parameters sars <- epidist_db( disease = "SARS", @@ -472,6 +439,7 @@ sars_params <- get_parameters(sars) sars_params ``` + :::::::::::::::::::::::: :::::::::::::::::::::::: callout @@ -567,11 +535,9 @@ qpois( ## Backward and forward contact tracing -Reconstruction of transmission trees (whom infected whom) can provide an understanding of who contributes more to transmission. This can be done with detailed case investigations and/or genetic data ([Cori et al., 2017](https://royalsocietypublishing.org/doi/10.1098/rstb.2016.0371)) - Contact tracing can be deployed in multiple strategies. Forward tracing targets downstream individuals who may be infected by index individual. Backward tracing targets the upstream primary case who infected the index case (or a setting or event at which the index case was infected) by retracing history of contact to the likely point of exposure up to the upper bound of the incubation period. -In the presence of heterogeneous transmission, i.e., with an overdispersed offspring distribution, if this primary case is identified, a larger fraction of the transmission chain can be detected by forward tracing each of the contacts of this primary case [Endo et al., 2020](https://wellcomeopenresearch.org/articles/5-239/v3). +In the presence of heterogeneous transmission, i.e., with an overdispersed offspring distribution, if this primary case is identified, a larger fraction of the transmission chain can be detected by forward tracing each of the contacts of this primary case ([Endo et al., 2020](https://wellcomeopenresearch.org/articles/5-239/v3)). ![Schematic representation of contact tracing strategies. Black arrows indicate the directions of transmission, blue and Orange arrows, a successful or failed contact tracing, respectivelly. When there is evidence of individual-level transmission heterogeneity, often resulting in superspreading, backward contact tracing from the index case (blue circle) increase the probability to find the primary case (green circle) or clusters with a larger fraction of cases, potentially increasing the number of quarentined cases (yellow circles). [Claire Blackmore, 2021](https://www.paho.org/sites/default/files/backward_contact_tracing_v3_0.pdf)](fig/contact-tracing-strategies.png) From ce964e5b9a86b8e83d6e098c25f3e322135ca7ae Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Thu, 4 Apr 2024 13:19:37 +0100 Subject: [PATCH 022/140] add figures on see from hong kong sars cov 2 paper --- .../fig/see-intro-secondary-cases-fig-b.png | Bin 0 -> 84087 bytes episodes/fig/see-intro-secondary-cases.png | Bin 0 -> 169707 bytes episodes/fig/see-intro-superspreading.png | Bin 0 -> 629581 bytes 3 files changed, 0 insertions(+), 0 deletions(-) create mode 100644 episodes/fig/see-intro-secondary-cases-fig-b.png create mode 100644 episodes/fig/see-intro-secondary-cases.png create mode 100644 episodes/fig/see-intro-superspreading.png diff --git a/episodes/fig/see-intro-secondary-cases-fig-b.png b/episodes/fig/see-intro-secondary-cases-fig-b.png new file mode 100644 index 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a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 379eb05e..f553b785 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -75,7 +75,7 @@ Let's use the `mers_korea_2015` linelist and contact data from `{outbreaks}` wit ```{r} ## make epicontact object -epi_contacts <- +epi_contacts <- epicontacts::make_epicontacts( linelist = mers_korea_2015$linelist, contacts = mers_korea_2015$contacts @@ -90,7 +90,7 @@ epicontacts::vis_epicontacts(epi_contacts) ```{r,echo=FALSE} # visualise contact tree network <- - epicontacts::vis_epicontacts(epi_contacts) %>% + vis_epicontacts(epi_contacts) %>% visNetwork::visPhysics(solver = "barnesHut") fname <- "network.html" @@ -424,8 +424,9 @@ epidist_db( epi_dist = "offspring distribution" ) %>% list_distributions() %>% - dplyr::select(disease) %>% - distinct() %>% pull() + dplyr::select(disease) %>% + distinct() %>% + pull() ``` ```{r} From ba898f07fe1dca888b415da3b0368be43a5eaf47 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Fri, 5 Apr 2024 09:04:11 +0100 Subject: [PATCH 024/140] rephrase contact tracing justification --- episodes/superspreading-estimate.Rmd | 4 +--- 1 file changed, 1 insertion(+), 3 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index f553b785..2b5498e2 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -563,9 +563,7 @@ proportion_cluster_size( ``` -Even though we have an $R<1$, given a highly overdispersed offspring distribution ($k=0.02$) we have a 46.9% probability to find a cluster of 25 people or larger. - -The probability of a cluster size can also inform backwards contact tracing efforts. Among other factors, high cluster sizes could imply that a contac tracing approach may no longer likely result in successful containment due to increased proportion of contacts not identified by the process or achieving low case ascertainment ([Public Health England, 2020](https://www.gov.uk/government/publications/phe-when-to-stop-contact-tracing-developing-triggers-from-phe-systems-20-february-2020)). +Even though we have an $R<1$, given a highly overdispersed offspring distribution ($k=0.02$) we have a 46.9% probability to find a cluster of 25 people or larger. Then, by following a backwards strategy, contact tracing efforts will increase their probability to find the primary case and successfully contain and quarentine an increased proportion of contacts. We can also use this number to prevent gathering of certain sized to reduce the epidemic by preventing potential superspreading events. Interventions can target to reduce the reproduction number in order to reduce the probability of having clusters of secondary cases. From e02b56265f37767c0da91a79defd3a711811342f Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Fri, 5 Apr 2024 11:10:40 +0100 Subject: [PATCH 025/140] add purrr checkpoint callout as prerequisite --- episodes/superspreading-simulate.Rmd | 17 +++++++++++++++++ 1 file changed, 17 insertions(+) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 9db036a1..9acd9bf1 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -138,11 +138,28 @@ initial_cases <- 1 ``` +:::::::::::::::::::::::::::::: checkpoint + +### Iteration using {purrr} + +[Iteration](https://r4ds.hadley.nz/iteration.html) aims to repeatedly perform the same action on different objects. + +Learn how to use the core `{purrr}` functions like the `map_*()` family of functions from the YouTube tutorial on [How to purrr](https://www.youtube.com/watch?v=nd-Y8b22YaQ) by Equitable Equations. + +Or if you previously used the `*apply` family of functions, visit the package vignette on [purrr base R](https://purrr.tidyverse.org/articles/base.html) shares key differences, direct translations, and examples. + +:::::::::::::::::::::::::::::: + +To get multiple chains, we need to apply the `simulate_chains()` function to each chain defined by a sequence of numbers from 1 to `number_chains`. + +Let's use `map()`: ```{r} simulated_chains_list <- map( + # vector of numbers (chain IDs) .x = seq_len(number_chains), + # function to iterate to each chain ID number .f = function(sim) { simulate_chains( # simulation controls From a6f378d7bb88cb3f15e14a2ba3c2a2eff32a70e0 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Fri, 5 Apr 2024 11:11:17 +0100 Subject: [PATCH 026/140] change number of simulation chain number id --- episodes/superspreading-simulate.Rmd | 41 ++++++++++++++-------------- 1 file changed, 21 insertions(+), 20 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 9acd9bf1..eeebb613 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -124,7 +124,7 @@ infectees as observation unit each infectee has a sim_id the infector sim_id of each infectee is in infector_id infectee got infected in generation and time -as part of the simulation_n chain +as part of the `chain_id` chain ## Simulate multiple chains @@ -172,7 +172,8 @@ simulated_chains_list <- # generation generation_time = function(x) generate(x = serial_inverval, times = x) ) %>% - mutate(simulation_n = sim) + # creates a column with the chain ID number + mutate(chain_id = sim) } ) @@ -185,7 +186,7 @@ sim_chains_bind # view infectee number per simulation sim_chains_bind %>% as_tibble() %>% - count(simulation_n, sort = TRUE) + count(chain_id, sort = TRUE) ``` ```{r,echo=FALSE} @@ -193,24 +194,24 @@ sim_chains_bind %>% chains_subgroup <- sim_chains_bind %>% as_tibble() %>% - group_by(simulation_n) %>% + group_by(chain_id) %>% distinct(infector_id) %>% - count(simulation_n) %>% + count(chain_id) %>% filter(n < 5, n >= 3) %>% - pull(simulation_n) + pull(chain_id) chain_to_observe <- sim_chains_bind %>% as_tibble() %>% - count(simulation_n, sort = TRUE) %>% + count(chain_id, sort = TRUE) %>% filter( magrittr::is_in( - simulation_n, chains_subgroup + chain_id, chains_subgroup ) ) %>% filter(n < 10) %>% filter(n == max(n)) %>% - slice_min(simulation_n) %>% - pull(simulation_n) + slice_min(chain_id) %>% + pull(chain_id) ``` get simulated chain `r chain_to_observe` with more infections @@ -244,19 +245,19 @@ simulated_chains_list %>% simulated_chains_day <- sim_chains_bind %>% as_tibble() %>% - mutate(simulation_n = as_factor(simulation_n)) %>% + mutate(chain_id = as_factor(chain_id)) %>% # Daily number of cases for each simulation mutate(day = ceiling(time)) %>% - count(simulation_n, day, name = "cases") %>% + count(chain_id, day, name = "cases") %>% # Cumulative number of cases for each simulation - group_by(simulation_n) %>% + group_by(chain_id) %>% mutate(cases_cumsum = cumsum(cases)) %>% ungroup() # Summarise the chain length and size sim_chains_max <- simulated_chains_day %>% - group_by(simulation_n) %>% + group_by(chain_id) %>% summarise( # length day_max = max(day), @@ -272,8 +273,8 @@ ggplot() + mapping = aes( x = day, y = cases_cumsum, - group = simulation_n, - color = simulation_n + group = chain_id, + color = chain_id ), show.legend = FALSE ) + @@ -282,8 +283,8 @@ ggplot() + mapping = aes( x = day_max, y = cases_total, - group = simulation_n, - color = simulation_n + group = chain_id, + color = chain_id ), show.legend = FALSE ) + @@ -301,8 +302,8 @@ ggplot() + mapping = aes( x = day, y = cases, - group = simulation_n, - color = simulation_n + group = chain_id, + color = chain_id ), show.legend = FALSE ) From 61fcecf03de90098d8f49484be539aa8e8d20dc2 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Fri, 5 Apr 2024 12:16:58 +0100 Subject: [PATCH 027/140] add blog post content on the episode topic --- episodes/superspreading-estimate.Rmd | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 2b5498e2..b979c8dd 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -653,9 +653,11 @@ inform backward contact tracing strategy ::::::::::::::::::::::::::::: testimonial -### Going viral +### Read these blog posts - +The [Tracing monkeypox](https://plus.maths.org/content/monkeypox) article from the [JUNIPER](https://maths.org/juniper/) consortium showcases the usefulness of network models on contact tracing. + +The [Going viral](https://kucharski.substack.com/p/going-viral) post from Adam Kucharski shares insides from marketing campaigns on the conditions that spark contagion online. ::::::::::::::::::::::::::::: From 1b8ba4f81be4d6ed88fb2ee545a000654c10d8e1 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Fri, 5 Apr 2024 12:19:54 +0100 Subject: [PATCH 028/140] expand on topics --- episodes/superspreading-estimate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index b979c8dd..bb03a696 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -657,7 +657,7 @@ inform backward contact tracing strategy The [Tracing monkeypox](https://plus.maths.org/content/monkeypox) article from the [JUNIPER](https://maths.org/juniper/) consortium showcases the usefulness of network models on contact tracing. -The [Going viral](https://kucharski.substack.com/p/going-viral) post from Adam Kucharski shares insides from marketing campaigns on the conditions that spark contagion online. +The [Going viral](https://kucharski.substack.com/p/going-viral) post from Adam Kucharski shares insides from YouTube virality, disease outbreaks, and marketing campaigns on the conditions that spark contagion online. ::::::::::::::::::::::::::::: From 07a8f491e197a3d2e8bd3812255fab47f386fab4 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Fri, 5 Apr 2024 12:32:37 +0100 Subject: [PATCH 029/140] typo addition --- episodes/superspreading-estimate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index bb03a696..dc036e6c 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -563,7 +563,7 @@ proportion_cluster_size( ``` -Even though we have an $R<1$, given a highly overdispersed offspring distribution ($k=0.02$) we have a 46.9% probability to find a cluster of 25 people or larger. Then, by following a backwards strategy, contact tracing efforts will increase their probability to find the primary case and successfully contain and quarentine an increased proportion of contacts. +Even though we have an $R<1$, given a highly overdispersed offspring distribution ($k=0.02$) we have a 46.9% probability to find a cluster of 25 people or larger. Then, by following a backwards strategy, contact tracing efforts will increase their probability to find the primary case and successfully contain and quarantine an increased proportion of contacts. We can also use this number to prevent gathering of certain sized to reduce the epidemic by preventing potential superspreading events. Interventions can target to reduce the reproduction number in order to reduce the probability of having clusters of secondary cases. From 8c467db2349123870b0752526de3fb09d5d3d4b5 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Fri, 5 Apr 2024 12:41:08 +0100 Subject: [PATCH 030/140] add empirica evidence of backward tracing --- episodes/superspreading-estimate.Rmd | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index dc036e6c..9e91f5ce 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -542,7 +542,9 @@ In the presence of heterogeneous transmission, i.e., with an overdispersed offsp ![Schematic representation of contact tracing strategies. Black arrows indicate the directions of transmission, blue and Orange arrows, a successful or failed contact tracing, respectivelly. When there is evidence of individual-level transmission heterogeneity, often resulting in superspreading, backward contact tracing from the index case (blue circle) increase the probability to find the primary case (green circle) or clusters with a larger fraction of cases, potentially increasing the number of quarentined cases (yellow circles). [Claire Blackmore, 2021](https://www.paho.org/sites/default/files/backward_contact_tracing_v3_0.pdf)](fig/contact-tracing-strategies.png) -When there is evidence of individual-level variation (i.e. overdispersion), often resulting in so-called superspreading events, a large proportion of infections may be linked to a small proportion of original clusters. As a result, finding and targeting originating clusters in combination with reducing onwards infection may substantially enhance the effectiveness of tracing methods [Endo et al., 2020](https://wellcomeopenresearch.org/articles/5-239/v3). +When there is evidence of individual-level variation (i.e. overdispersion), often resulting in so-called superspreading events, a large proportion of infections may be linked to a small proportion of original clusters. As a result, finding and targeting originating clusters in combination with reducing onwards infection may substantially enhance the effectiveness of tracing methods [Endo et al., 2020](https://wellcomeopenresearch.org/articles/5-239/v3). + +Empirical evidence focused on evaluating the efficiency of backward tracing lead to 42% more cases identified than forward tracing supporting its implementation when rigorous suppression of transmission is justified ([Raymenants et al., 2022](https://www.nature.com/articles/s41467-022-32531-6)) ## Proportion of events in a given cluster size From 8632bf8a582fd20b711e723106618e65df949433 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Fri, 5 Apr 2024 12:54:06 +0100 Subject: [PATCH 031/140] simplify epiparameter callout --- episodes/superspreading-estimate.Rmd | 13 +++++++------ 1 file changed, 7 insertions(+), 6 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 9e91f5ce..9b111995 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -415,25 +415,26 @@ The Poisson distribution is an special case of the Negative Binomial. When k app ### Use {epiparameter} -Currently, `{epiparameter}` have offspring distributions for: - ```{r,message=FALSE,warning=FALSE,echo=FALSE} library(epiparameter) -epidist_db( +epidist_string <- epidist_db( epi_dist = "offspring distribution" ) %>% list_distributions() %>% dplyr::select(disease) %>% distinct() %>% - pull() + pull() %>% + paste(collapse = ', ') ``` -```{r} +Currently, `{epiparameter}` have offspring distributions for `r epidist_string`. Let's access the offspring distribution `mean` and `dispersion` parameters for SARS: + +```{r,message=FALSE,warning=FALSE} # Load parameters sars <- epidist_db( disease = "SARS", - epi_dist = "offspring_distribution", + epi_dist = "offspring distribution", single_epidist = TRUE ) sars_params <- get_parameters(sars) From 73e46f3e2bfaf5ccba1c45799c7bdf5b66fc06f0 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Fri, 5 Apr 2024 13:01:48 +0100 Subject: [PATCH 032/140] fix lintr checks --- episodes/superspreading-estimate.Rmd | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 9b111995..2665c902 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -424,8 +424,8 @@ epidist_string <- epidist_db( list_distributions() %>% dplyr::select(disease) %>% distinct() %>% - pull() %>% - paste(collapse = ', ') + pull() %>% + paste(collapse = ", ") ``` Currently, `{epiparameter}` have offspring distributions for `r epidist_string`. Let's access the offspring distribution `mean` and `dispersion` parameters for SARS: From d05bfe134de5e361b4130d74a164d8486854768f Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Fri, 5 Apr 2024 16:26:51 +0100 Subject: [PATCH 033/140] clean individual reproduction number section --- episodes/superspreading-estimate.Rmd | 68 ++++++++++++++++++++-------- 1 file changed, 48 insertions(+), 20 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 2665c902..a2fe9faa 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -69,12 +69,14 @@ library(tidyverse) ## The individual reprodution number -Reconstruction of transmission trees (whom infected whom) can provide an understanding of who contributes more to transmission. This can be done with detailed case investigations and/or genetic data ([Cori et al., 2017](https://royalsocietypublishing.org/doi/10.1098/rstb.2016.0371)) +The individual reproduction number is defined as the number of secondary cases caused by a particular infected individual. -Let's use the `mers_korea_2015` linelist and contact data from `{outbreaks}` with `{epicontacts}` to get the distribution of secondary cases ([Campbell, 2022](https://community.appliedepi.org/t/estimating-the-degree-of-super-spreading-from-transmission-chain-data/103/2)): +Early in an outbreak we can use contact data to reconstruct transmission trees (whom infected whom) and calculate the number of secondary cases generated by each individual. Reconstruction of trees from contact data can provide an understanding of who contributes more to transmission and evaluate for heterogeneous distribution ([Cori et al., 2017](https://royalsocietypublishing.org/doi/10.1098/rstb.2016.0371)). + +Let's practice this using the `mers_korea_2015` linelist and contact data from the `{outbreaks}` package and integrate them with the `{epicontacts}` package to calculate the distribution of secondary cases ([Campbell, 2022](https://community.appliedepi.org/t/estimating-the-degree-of-super-spreading-from-transmission-chain-data/103/2)): ```{r} -## make epicontact object +## first, make an epicontacts object epi_contacts <- epicontacts::make_epicontacts( linelist = mers_korea_2015$linelist, @@ -124,7 +126,7 @@ epi_contacts %>% ::::::::::::::::::::::::::: -When each infector-infectee row is unique, the number of entries per infector corresponds to the number of secondary cases. +When each infector-infectee row is unique, the number of entries per infector corresponds to their number of secondary cases. ```{r} # count secondary cases per infector @@ -133,14 +135,16 @@ infector_secondary <- epi_contacts %>% count(from, name = "secondary_cases") ``` -The number +But this output only contains number of secondary cases for reported infectors, not for each of the individuals in the whole `epicontacts` object. + +To get this, first, we can use `epicontacts::get_id()` to get the full list of unique identifiers ("id") from the `epicontacts` class object. Second, join it with the count secondary cases per infector stored in the `infector_secondary` object. Third, replace the missing values with `0` to express no report of secondary cases from them. ```{r,message=FALSE,warning=FALSE} -epi_secondary <- - epi_contacts %>% +all_secondary <- epi_contacts %>% # extract ids in contact *and* linelist # using "which" argument epicontacts::get_id(which = "all") %>% + # transform to dataframe for the left_join() enframe(name = NULL, value = "from") %>% # join count secondary cases per infectee left_join(infector_secondary) %>% @@ -149,13 +153,21 @@ epi_secondary <- replace_na( replace = list(secondary_cases = 0) ) +``` +From `all_secondary` output we can identify the heterogeneity in the number of secondary cases. Three cases were related to more than 20 secondary cases, while the complementary cases with less than five or zero secondary cases. + +```{r} # arrange in descendant order of secondary cases -epi_secondary %>% +all_secondary %>% arrange(desc(secondary_cases)) +``` +Visualizing the number of secondary cases on a histogram will help us to relate this with the statistical distribution to fit: + +```{r} ## plot the distribution -epi_secondary %>% +all_secondary %>% ggplot(aes(secondary_cases)) + geom_histogram(binwidth = 1) + labs( @@ -164,11 +176,11 @@ epi_secondary %>% ) ``` -The _individual reproductive number_, ν, is defined as a random variable representing the expected number of secondary cases caused by a particular infected individual. +The number of secondary infections caused by each case is described by a statistical distribution called the **offspring distribution**. One candidate statistical distribution used to model this is the **negative binomial** distribution with two distribution parameters: -Values for ν are drawn from a continuous probability distribution with population mean $R_{o}$ that encodes all variation in infectious histories of individuals, including properties of the host and pathogen and environmental circumstances. +- **mean**, which represents the $R_{o}$, the average number of (secondary) cases produced by a single individual in an entirely susceptible population, and -In this framework, superspreading events (SSEs) are not exceptional events, but important realizations from the right-hand tail of a distribution of ν ([Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153)). +- **dispersion**, expressed as $k$, which represents the degree of heterogeneity in transmission by single individuals. ```{r,echo=FALSE,message=FALSE,warning=FALSE} # Load parameters @@ -218,9 +230,30 @@ ggplot() + ) ``` +From the histogram and density map, we can identify that superspreading events (SSEs) are realizations from the right-hand tail of a distribution of the individual reproductive number ([Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153)). + +::::::::::::::::::::::::::::: spoiler + +### Poisson, overdispersion, and Negative Binomial + +For occurrences of associated discrete events we can use Poisson or negative binomial discrete distributions. + +In a Poisson distribution, mean is equal to variance. But when variance is higher than the mean, this is called over-dispersion. In biological applications, over-dispersion occurs and so a negative binomial may be worth considering as an alternative to Poisson distribution. + +Negative binomial distribution is specially useful for discrete data over an unbounded positive range whose sample variance exceeds the sample mean. In such terms, the observations are overdispersed with respect to a Poisson distribution, for which the mean is equal to the variance. + +In epidemiology, [negative binomial](https://en.wikipedia.org/wiki/Negative_binomial_distribution) have being used to model disease transmission for infectious diseases where the likely number of onward infections may vary considerably from individual to individual and from setting to setting. + +::::::::::::::::::::::::::::: ## Estimate the offspring distribution +The negative binomial model has variance R0(1 + R0/k), so smaller values of k indicate greater heterogeneity. + +The negative binomial model includes the conventional Poisson (k → ∞) and geometric (k = 1) models as special cases. + + + Stochastic effects in transmission are modelled using a Poisson process4, so that the number of secondary infections caused by each case, Z, is described by an ‘offspring distribution’ Pr(Z = k) where Z∼Poisson(ν). By considering three possible distributions of ν, we generate three candidate models for the offspring distribution: (1) in generation-based models neglecting individual variation, ν = R0 for all cases, yielding Z∼Poisson(R0); (2) in differential-equation models with homogeneous transmission and constant recovery rates, ν is exponentially distributed, yielding Z∼geometric(R0); (3) in a more general formulation, we let ν be gamma-distributed with mean R0 and dispersion parameter k, yielding Z∼negative binomial(R0,k) (ref. 23). The negative binomial model includes the conventional Poisson (k → ∞) and geometric (k = 1) models as special cases. It has variance R0(1 + R0/k), so smaller values of k indicate greater heterogeneity. @@ -250,7 +283,7 @@ individual level variation in infectiousness library(fitdistrplus) ## fit distribution -offspring_fit <- epi_secondary %>% +offspring_fit <- all_secondary %>% pull(secondary_cases) %>% fitdist(distr = "nbinom") @@ -293,7 +326,7 @@ fit_density <- # plot offspring distribution with density fit ggplot() + geom_histogram( - data = epi_secondary, + data = all_secondary, mapping = aes( x = secondary_cases, @@ -332,12 +365,7 @@ read ebola contact data and estimate R and dispersion? -- for occurrences of associated discrete events we can use Poisson or negative binomial discrete distributions. -- in a Poisson distribution, mean is equal to variance. -- when variance is higher than the mean, this is called over-dispersion. -- in biological applications, over-dispersion occurs and so a negative binomial may be worth considering as an alternative to Poisson distribution. -- in epidemiology, negative binomial have being used to model disease transmission for infectious diseases where the likely number of onward infections may vary considerably from individual to individual and from setting to setting - In a sequence of independent Bernoulli trials, in each trial the probability of success is $p$ and of failure is $1-p$. We observe this sequence until a predefined number $r$ of successes occurs. Then the random number of observed failures follows the negative binomial distribution. - some authors refer to $\alpha = \frac{1}{r}$ and express variance in terms of $\alpha$: $variance = m + \alpha m^2$ where mean $ m = \frac{r(1-p)}{p}$ @@ -347,7 +375,7 @@ read ebola contact data and estimate R and dispersion? - To sync up with Lloyd-Smith and R base function for negative binomial, $k = r = {size} = {inverse-dispersion}$ -- negative binomial distribution is specially useful for discrete data over an unbounded positive range whose sample variance exceeds the sample mean. In such terms, the observations are overdispersed with respect to a Poisson distribution, for which the mean is equal to the variance. + - The additional parameter of the negative binomial distribution ($r$) can be used to adjust the variance independently of the mean. From ab472a93a7889300ef2f8ba0630f87af9e1d66c9 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Fri, 5 Apr 2024 20:00:44 +0100 Subject: [PATCH 034/140] add callout to differentiate terminologies --- episodes/superspreading-estimate.Rmd | 64 +++++++++++++--------------- 1 file changed, 29 insertions(+), 35 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index a2fe9faa..4d3ba397 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -176,11 +176,11 @@ all_secondary %>% ) ``` -The number of secondary infections caused by each case is described by a statistical distribution called the **offspring distribution**. One candidate statistical distribution used to model this is the **negative binomial** distribution with two distribution parameters: +The number of secondary infections caused by each case can be used to empirically estimate the **offspring distribution**. One candidate statistical distribution used to model the offspring distribution is the **negative binomial** distribution with two parameters: -- **mean**, which represents the $R_{o}$, the average number of (secondary) cases produced by a single individual in an entirely susceptible population, and +- **Mean**, which represents the $R_{0}$, the average number of (secondary) cases produced by a single individual in an entirely susceptible population, and -- **dispersion**, expressed as $k$, which represents the degree of heterogeneity in transmission by single individuals. +- **Dispersion**, expressed as $k$, which represents the degree of heterogeneity in transmission by single individuals. ```{r,echo=FALSE,message=FALSE,warning=FALSE} # Load parameters @@ -230,54 +230,48 @@ ggplot() + ) ``` -From the histogram and density map, we can identify that superspreading events (SSEs) are realizations from the right-hand tail of a distribution of the individual reproductive number ([Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153)). +From the histogram and density map, we can identify that the distribution is highly overdispersed. The superspreading events (SSEs) are realizations from the right-hand tail of the offspring distribution ([Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153)). -::::::::::::::::::::::::::::: spoiler +::::::::::::::::::::::::::: callout -### Poisson, overdispersion, and Negative Binomial +### Terminology recap -For occurrences of associated discrete events we can use Poisson or negative binomial discrete distributions. +- From linelist and contact data, we calculate the **number of secondary cases** caused by the observed infected individuals. +- The **individual reproductive number** is a random variable representing the _expected_ number of secondary cases caused by a infected individual. +- From the stochastic effects in transmission, the number of secondary _infections_ caused by each case is described by an **offspring distribution**. +- An _empirical_ offspring distribution can be modeled by the **negative-binomial** distribution with mean $R_{0}$ and dispersion parameter $k$. -In a Poisson distribution, mean is equal to variance. But when variance is higher than the mean, this is called over-dispersion. In biological applications, over-dispersion occurs and so a negative binomial may be worth considering as an alternative to Poisson distribution. +::::::::::::::::::::::::::: -Negative binomial distribution is specially useful for discrete data over an unbounded positive range whose sample variance exceeds the sample mean. In such terms, the observations are overdispersed with respect to a Poisson distribution, for which the mean is equal to the variance. +::::::::::::::::::::::::::::: spoiler -In epidemiology, [negative binomial](https://en.wikipedia.org/wiki/Negative_binomial_distribution) have being used to model disease transmission for infectious diseases where the likely number of onward infections may vary considerably from individual to individual and from setting to setting. +### Poisson, overdispersion, and Negative Binomial -::::::::::::::::::::::::::::: + -## Estimate the offspring distribution +For occurrences of associated discrete events we can use **Poisson** or negative binomial discrete distributions. -The negative binomial model has variance R0(1 + R0/k), so smaller values of k indicate greater heterogeneity. +In a Poisson distribution, mean is equal to variance. But when variance is higher than the mean, this is called **overdispersion**. In biological applications, overdispersion occurs and so a negative binomial may be worth considering as an alternative to Poisson distribution. -The negative binomial model includes the conventional Poisson (k → ∞) and geometric (k = 1) models as special cases. +**Negative binomial** distribution is specially useful for discrete data over an unbounded positive range whose sample variance exceeds the sample mean. In such terms, the observations are overdispersed with respect to a Poisson distribution, for which the mean is equal to the variance. +In epidemiology, [negative binomial](https://en.wikipedia.org/wiki/Negative_binomial_distribution) have being used to model disease transmission for infectious diseases where the likely number of onward infections may vary considerably from individual to individual and from setting to setting. +::::::::::::::::::::::::::::: -Stochastic effects in transmission are modelled using a Poisson process4, so that the number of secondary infections caused by each case, Z, is described by an ‘offspring distribution’ Pr(Z = k) where Z∼Poisson(ν). +## Estimate the dispersion parameter -By considering three possible distributions of ν, we generate three candidate models for the offspring distribution: (1) in generation-based models neglecting individual variation, ν = R0 for all cases, yielding Z∼Poisson(R0); (2) in differential-equation models with homogeneous transmission and constant recovery rates, ν is exponentially distributed, yielding Z∼geometric(R0); (3) in a more general formulation, we let ν be gamma-distributed with mean R0 and dispersion parameter k, yielding Z∼negative binomial(R0,k) (ref. 23). The negative binomial model includes the conventional Poisson (k → ∞) and geometric (k = 1) models as special cases. It has variance R0(1 + R0/k), so smaller values of k indicate greater heterogeneity. +To estimate the dispersion parameter, we need to fit a negative binomial distribution to data. -the offspring distribution, +The negative binomial model includes the conventional Poisson (k → ∞) and geometric (k = 1) models as special cases. -- can be characterized by a statistical distribution - - negative binomial, usually -- with distribution parameters given by - - R0 as the mean and - + average number of (secondary) cases produced by a single individual in an entirely susceptible population - - k as the dispersion parameter, - +degree of heterogeneity in transmission by single individuals +The negative binomial model has variance R0(1 + R0/k), so smaller values of k indicate greater heterogeneity. fit distribution to data using {fitdistrplus} provide maximum likelihood estimates -the estimated value of k -suggest that -SSE are an expected feature of the -individual level variation in infectiousness - - + ```{r} library(fitdistrplus) @@ -371,7 +365,7 @@ read ebola contact data and estimate R and dispersion? - some authors refer to $\alpha = \frac{1}{r}$ and express variance in terms of $\alpha$: $variance = m + \alpha m^2$ where mean $ m = \frac{r(1-p)}{p}$ - depending on the author, either the parameter or its the reciprocal of $r$, $\alpha$, is refereed to as the "dispersion parameter". -- From Lloyd-Smith, in a more general formulation, we let $v$ be gamma-distributed with mean $R_{o}$ and dispersion parameter $k$, yielding $Z$~negative binomial($R_{o}, k$). The negative binomial model includes the conventional Poisson ($k \rightarrow \inf$) as an special case. It has variance $R_{o}(1 + R_{o}/k)$, so smaller values of $k$ indicate (greater variance, thus) greater heterogeneity. +- From Lloyd-Smith, in a more general formulation, we let $v$ be gamma-distributed with mean $R_{0}$ and dispersion parameter $k$, yielding $Z$~negative binomial($R_{0}, k$). The negative binomial model includes the conventional Poisson ($k \rightarrow \inf$) as an special case. It has variance $R_{0}(1 + R_{0}/k)$, so smaller values of $k$ indicate (greater variance, thus) greater heterogeneity. - To sync up with Lloyd-Smith and R base function for negative binomial, $k = r = {size} = {inverse-dispersion}$ @@ -434,9 +428,9 @@ when mean/variance ratio gets closer to 1 In a Negative Binomial distribution, the relationship between mean (Ro), dispersion (k), variance and heterogeneity is given by: -$$ \uparrow heterogeneity = \uparrow variance = R_{o}(1+\frac{R_{o}}{\downarrow k})$$ +$$ \uparrow heterogeneity = \uparrow variance = R_{0}(1+\frac{R_{0}}{\downarrow k})$$ -The Poisson distribution is an special case of the Negative Binomial. When k approximates infinity $k \rightarrow \infty$ the variance equals the mean because $\frac{R_{o}}{\infty}=0$ +The Poisson distribution is an special case of the Negative Binomial. When k approximates infinity $k \rightarrow \infty$ the variance equals the mean because $\frac{R_{0}}{\infty}=0$ :::::::::::::::::::::::: callout @@ -615,7 +609,7 @@ Transmission heterogeneity affects epidemic establishment and the ease of contro + Conversely, heterogeneity in transmission may provide opportunities for *targeted interventions* if the individuals who contribute more to transmission (due to biological, environmental or behavioral factors) share socio-demographic or geographical characteristics that can be defined. -We can have an early understanding of a disease epidemic potential from the mean reproduction number $R_{o}$ and dispersion $k$ of an offspring distribution to answer questions like: +We can have an early understanding of a disease epidemic potential from the mean reproduction number $R_{0}$ and dispersion $k$ of an offspring distribution to answer questions like: - What is the probability of an pathogen to cause large outbreak? - What is the probability of an outbreak to get extinct? @@ -625,7 +619,7 @@ We can have an early understanding of a disease epidemic potential from the mean ### Epidemic Risk assessment accounting for superspreading -These estimates vary non-linearly with respect to the mean reproduction number $R_{o}$ and dispersion $k$ of a given disease. +These estimates vary non-linearly with respect to the mean reproduction number $R_{0}$ and dispersion $k$ of a given disease. We invite you to read the `{superspreading}` vignette on [Epidemic risk](https://epiverse-trace.github.io/superspreading/articles/epidemic_risk.html)! From f4d90c2a84be43ae02c8ad6f1c313aaf930a0da0 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Fri, 5 Apr 2024 20:44:18 +0100 Subject: [PATCH 035/140] clear content writing + add entry to estimate k --- episodes/superspreading-estimate.Rmd | 165 +++++++++++++++------------ 1 file changed, 89 insertions(+), 76 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 4d3ba397..1679a919 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -141,29 +141,27 @@ To get this, first, we can use `epicontacts::get_id()` to get the full list of u ```{r,message=FALSE,warning=FALSE} all_secondary <- epi_contacts %>% - # extract ids in contact *and* linelist - # using "which" argument + # extract ids in contact *and* linelist using "which" argument epicontacts::get_id(which = "all") %>% - # transform to dataframe for the left_join() + # transform to dataframe to use left_join() enframe(name = NULL, value = "from") %>% # join count secondary cases per infectee left_join(infector_secondary) %>% - # infectee with missing secondary cases - # are replaced with zero + # infectee with missing secondary cases are replaced with zero replace_na( replace = list(secondary_cases = 0) ) ``` -From `all_secondary` output we can identify the heterogeneity in the number of secondary cases. Three cases were related to more than 20 secondary cases, while the complementary cases with less than five or zero secondary cases. +From a histogram of the `all_secondary` object, we can identify the **heterogeneity** in the number of secondary cases. Three cases were related to more than 20 secondary cases, while the complementary cases with less than five or zero secondary cases. -```{r} +```{r,echo=FALSE} # arrange in descendant order of secondary cases all_secondary %>% arrange(desc(secondary_cases)) ``` -Visualizing the number of secondary cases on a histogram will help us to relate this with the statistical distribution to fit: + ```{r} ## plot the distribution @@ -176,7 +174,7 @@ all_secondary %>% ) ``` -The number of secondary infections caused by each case can be used to empirically estimate the **offspring distribution**. One candidate statistical distribution used to model the offspring distribution is the **negative binomial** distribution with two parameters: +The number of secondary infections caused by each case can be used to _empirically_ estimate the **offspring distribution**. One candidate statistical distribution used to model the offspring distribution is the **negative binomial** distribution with two parameters: - **Mean**, which represents the $R_{0}$, the average number of (secondary) cases produced by a single individual in an entirely susceptible population, and @@ -230,7 +228,7 @@ ggplot() + ) ``` -From the histogram and density map, we can identify that the distribution is highly overdispersed. The superspreading events (SSEs) are realizations from the right-hand tail of the offspring distribution ([Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153)). +From the histogram and density plot, we can identify that the distribution is highly skewed or **overdispersed**. The superspreading events (SSEs) are realizations from the right-hand tail of the offspring distribution ([Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153)). ::::::::::::::::::::::::::: callout @@ -261,17 +259,9 @@ In epidemiology, [negative binomial](https://en.wikipedia.org/wiki/Negative_bino ## Estimate the dispersion parameter -To estimate the dispersion parameter, we need to fit a negative binomial distribution to data. - -The negative binomial model includes the conventional Poisson (k → ∞) and geometric (k = 1) models as special cases. - -The negative binomial model has variance R0(1 + R0/k), so smaller values of k indicate greater heterogeneity. - +To empirically estimate the dispersion parameter $k$, we can to fit a negative binomial distribution to the number of secondary cases. -fit distribution to data using {fitdistrplus} -provide maximum likelihood estimates - - +We can fit distributions to data using the `{fitdistrplus}` package, which provides maximum likelihood estimates. ```{r} library(fitdistrplus) @@ -282,25 +272,85 @@ offspring_fit <- all_secondary %>% fitdist(distr = "nbinom") offspring_fit +``` + +:::::::::::::::::::::::::::::::: callout + +### Name of parameters + +From the `{fitdistrplus}` output: + +- The `size` object refers to the estimated dispersion parameter $k$, and +- The `mu` object refers to the estimated mean, which represents the $R_{0}$, +:::::::::::::::::::::::::::::::: + +```{r,echo=FALSE} ## extract the "size" parameter mid <- offspring_fit$estimate[["size"]] -``` -```{r,echo=FALSE} ## calculate the 95% confidence intervals using the standard error estimate and ## the 0.025 and 0.975 quantiles of the normal distribution. lower <- mid + offspring_fit$sd[["size"]] * qnorm(0.025) upper <- mid + offspring_fit$sd[["size"]] * qnorm(0.975) ``` -We can see that the -dispersion parameter is estimated as -`r round(mid, 3)` (95% CI `r `round(lower, 3)` - `r round(upper, 3)`). +From the number secondary cases distribution we estimated a dispersion parameter $k$ of +`r round(mid, 3)`, with a 95% Confidence Interval from `r round(lower, 3)` to `r round(upper, 3)`. + +As a value of $k = $ `r round(mid, 3)` is significantly lower than one, we can conclude that the degree of super-spreading is high. + +:::::::::::::::::::: callout + +### The distribution parameter k + +Dispersion parameter $k$ that are lower than + +The negative binomial model includes the conventional Poisson (k → ∞) and geometric (k = 1) models as special cases. + +The negative binomial model has variance R0(1 + R0/k), so smaller values of k indicate greater heterogeneity. + + + +k is inversely-proportional +to variance (i.e, to heterogeneity) +- high k -> get low variance (low heterogeneity) +- low k -> get high variance (high heterogeneity) + +when k approches infinity, +the negative binomial approaches poisson + +negative binomial +two parameters: +- mean (or R0, in offspring distribution) +- size (or k, named also dispersion) + +variance = +mean(1 + mean/k) + +higher k, +(higher inverse-dispersion), +lower variance, +(variance closer to mean) +lower heterogeneity + +lower k +(lower the inverse-dispersion), +higher the variance, +(variance further from mean) +higher heterogeneity + +a Poisson distribution can be defined as +an special case of Negative Binomial +when k approaches infinity +or +variance gets closer to mean +or +when mean/variance ratio gets closer to 1 + + -As this value is significantly lower -than one, we can conclude that -the degree of super-spreading is high. +:::::::::::::::::::: This is in line with visual inspection of the histogram made above. @@ -339,6 +389,17 @@ ggplot() + ) ``` +:::::::::::::::::::::::::::::::: callout + +### Depending on the author + +The dispersion parameter $k$ can be expressed differently across the literature. + +- In the Wikipedia page for the negative binomial, this parameter is defined in its reciprocal form (refer to the [variance equation](https://en.wikipedia.org/wiki/Negative_binomial_distribution)). +- In [the distribution zoo](https://ben18785.shinyapps.io/distribution-zoo/) shiny app, the dispersion parameter $k$ is named "Inverse-dispersion" but it is equal to parameter estimated here. We invite you to explore this! + +:::::::::::::::::::::::::::::::: + ::::::::::::::::::::::: callout ### Transmission heterogeneity @@ -374,55 +435,7 @@ read ebola contact data and estimate R and dispersion? -the "dispersion" parameter -refers to the "size" for base R -or -refer to the "k" parameter for Lloyd-Smith -of the negative binomial distribution - -k is inversely-proportional -to variance (i.e, to heterogeneity) -- high k -> get low variance (low heterogeneity) -- low k -> get high variance (high heterogeneity) - -when k approches infinity, -the negative binomial approaches poisson - -negative binomial -two parameters: -- mean (or R0, in offspring distribution) -- size (or k, named also dispersion) - -variance = -mean(1 + mean/k) -higher k, -(higher inverse-dispersion), -lower variance, -(variance closer to mean) -lower heterogeneity - -lower k -(lower the inverse-dispersion), -higher the variance, -(variance further from mean) -higher heterogeneity - -useful when variance is higher than mean -for discrete data -when observations exceed a positive range -whose sample variance exceeds the -sample mean. -thus, the observations are overdispersed -with respect to a Poisson distribution - -a Poisson distribution can be defined as -an special case of Negative Binomial -when k approaches infinity -or -variance gets closer to mean -or -when mean/variance ratio gets closer to 1 From d380199be5c43192f2884fb14e412a3b218bf436 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 09:49:19 +0100 Subject: [PATCH 036/140] edit the fitted plot + add callout on pkg helper --- episodes/superspreading-estimate.Rmd | 156 ++++++++++++++------------- 1 file changed, 79 insertions(+), 77 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 1679a919..a577d25e 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -296,9 +296,58 @@ upper <- mid + offspring_fit$sd[["size"]] * qnorm(0.975) ``` From the number secondary cases distribution we estimated a dispersion parameter $k$ of -`r round(mid, 3)`, with a 95% Confidence Interval from `r round(lower, 3)` to `r round(upper, 3)`. +`r round(mid, 3)`, with a 95% Confidence Interval from `r round(lower, 3)` to `r round(upper, 3)`. As the value of $k$ is significantly lower than one, we can conclude that the degree of superspreading is high. -As a value of $k = $ `r round(mid, 3)` is significantly lower than one, we can conclude that the degree of super-spreading is high. +We can overlap the estimated density values of the fitted negative binomial distribution and the histogram of the number of secondary cases: + +```{r,echo=FALSE} +# calculate density fit +fit_density <- + tibble(quantile = 0:40) %>% + mutate( + density = dnbinom( + x = quantile, + mu = offspring_fit$estimate[["mu"]], + size = mid + ) + ) %>% + mutate(label = "Fitted\nnegative\nbinomial\ndistribution") + +# plot offspring distribution with density fit +ggplot() + + geom_histogram( + data = all_secondary, + mapping = + aes( + x = secondary_cases, + y = after_stat(density) + ), fill = "white", color = "black", + binwidth = 1 + ) + + geom_point( + data = fit_density, + mapping = aes( + x = quantile, + y = density, + color = label + ), + alpha = 0.5 + ) + + labs( + x = "Number of secondary cases", + y = "Density", + color = "Legend" + ) + + theme_bw() +``` + +:::::::::::::::::::::::: callout + +### Select the best model + +We can use the maximum likelihood estimates from `{fitdistrplus}` to compare different models and assess fit performance using estimators like the AIC and BIC. Read further in the vignette on [Estimate individual-level transmission](https://epiverse-trace.github.io/superspreading/articles/estimate_individual_level_transmission.html) and use the `{superspreading}` helper function `ic_tbl()` for this! + +::::::::::::::::::::::::: :::::::::::::::::::: callout @@ -350,101 +399,64 @@ when mean/variance ratio gets closer to 1 -:::::::::::::::::::: - -This is in line with visual inspection -of the histogram made above. - -```{r,echo=FALSE} -# calculate density fit -fit_density <- - tibble(quantile = 0:40) %>% - mutate( - density = dnbinom( - x = quantile, - mu = offspring_fit$estimate[["mu"]], - size = mid - ) - ) - -# plot offspring distribution with density fit -ggplot() + - geom_histogram( - data = all_secondary, - mapping = - aes( - x = secondary_cases, - y = after_stat(density) - ), - binwidth = 1 - ) + - geom_point( - data = fit_density, - mapping = aes(x = quantile, y = density), - alpha = 0.3, color = "red" - ) + - labs( - xlab = "Individual reproduction number", - ylab = "Number of individuals" - ) -``` +### Interpret the dispersion parameter -:::::::::::::::::::::::::::::::: callout + -### Depending on the author -The dispersion parameter $k$ can be expressed differently across the literature. -- In the Wikipedia page for the negative binomial, this parameter is defined in its reciprocal form (refer to the [variance equation](https://en.wikipedia.org/wiki/Negative_binomial_distribution)). -- In [the distribution zoo](https://ben18785.shinyapps.io/distribution-zoo/) shiny app, the dispersion parameter $k$ is named "Inverse-dispersion" but it is equal to parameter estimated here. We invite you to explore this! +- In a sequence of independent Bernoulli trials, in each trial the probability of success is $p$ and of failure is $1-p$. We observe this sequence until a predefined number $r$ of successes occurs. Then the random number of observed failures follows the negative binomial distribution. +- some authors refer to $\alpha = \frac{1}{r}$ and express variance in terms of $\alpha$: $variance = m + \alpha m^2$ where mean $ m = \frac{r(1-p)}{p}$ +- depending on the author, either the parameter or its the reciprocal of $r$, $\alpha$, is refereed to as the "dispersion parameter". -:::::::::::::::::::::::::::::::: +- From Lloyd-Smith, in a more general formulation, we let $v$ be gamma-distributed with mean $R_{0}$ and dispersion parameter $k$, yielding $Z$~negative binomial($R_{0}, k$). The negative binomial model includes the conventional Poisson ($k \rightarrow \inf$) as an special case. It has variance $R_{0}(1 + R_{0}/k)$, so smaller values of $k$ indicate (greater variance, thus) greater heterogeneity. -::::::::::::::::::::::: callout +- To sync up with Lloyd-Smith and R base function for negative binomial, $k = r = {size} = {inverse-dispersion}$ -### Transmission heterogeneity -Heterogeneity is in the variance of the number of secondary cases generated by each infected individual +- The additional parameter of the negative binomial distribution ($r$) can be used to adjust the variance independently of the mean. -[add table quick summary] + -::::::::::::::::::::::: -::::::::::::::::::::::: challenge -read ebola contact data and estimate R and dispersion? + -::::::::::::::::::::::: +In a Negative Binomial distribution, the relationship between mean (Ro), dispersion (k), variance and heterogeneity is given by: -## Interpret the dispersion parameter +$$ \uparrow heterogeneity = \uparrow variance = R_{0}(1+\frac{R_{0}}{\downarrow k})$$ - +The Poisson distribution is an special case of the Negative Binomial. When k approximates infinity $k \rightarrow \infty$ the variance equals the mean because $\frac{R_{0}}{\infty}=0$ +:::::::::::::::::::: -- In a sequence of independent Bernoulli trials, in each trial the probability of success is $p$ and of failure is $1-p$. We observe this sequence until a predefined number $r$ of successes occurs. Then the random number of observed failures follows the negative binomial distribution. -- some authors refer to $\alpha = \frac{1}{r}$ and express variance in terms of $\alpha$: $variance = m + \alpha m^2$ where mean $ m = \frac{r(1-p)}{p}$ -- depending on the author, either the parameter or its the reciprocal of $r$, $\alpha$, is refereed to as the "dispersion parameter". +:::::::::::::::::::::::::::::::: callout -- From Lloyd-Smith, in a more general formulation, we let $v$ be gamma-distributed with mean $R_{0}$ and dispersion parameter $k$, yielding $Z$~negative binomial($R_{0}, k$). The negative binomial model includes the conventional Poisson ($k \rightarrow \inf$) as an special case. It has variance $R_{0}(1 + R_{0}/k)$, so smaller values of $k$ indicate (greater variance, thus) greater heterogeneity. +### Depending on the author -- To sync up with Lloyd-Smith and R base function for negative binomial, $k = r = {size} = {inverse-dispersion}$ +The dispersion parameter $k$ can be expressed differently across the literature. +- In the Wikipedia page for the negative binomial, this parameter is defined in its reciprocal form (refer to the [variance equation](https://en.wikipedia.org/wiki/Negative_binomial_distribution)). +- In [the distribution zoo](https://ben18785.shinyapps.io/distribution-zoo/) shiny app, the dispersion parameter $k$ is named "Inverse-dispersion" but it is equal to parameter estimated in this episode. We invite you to explore this! -- The additional parameter of the negative binomial distribution ($r$) can be used to adjust the variance independently of the mean. +:::::::::::::::::::::::::::::::: - +::::::::::::::::::::::: callout +### Transmission heterogeneity +Heterogeneity is in the variance of the number of secondary cases generated by each infected individual - +[add table quick summary] -In a Negative Binomial distribution, the relationship between mean (Ro), dispersion (k), variance and heterogeneity is given by: +::::::::::::::::::::::: -$$ \uparrow heterogeneity = \uparrow variance = R_{0}(1+\frac{R_{0}}{\downarrow k})$$ +::::::::::::::::::::::: challenge -The Poisson distribution is an special case of the Negative Binomial. When k approximates infinity $k \rightarrow \infty$ the variance equals the mean because $\frac{R_{0}}{\infty}=0$ +read ebola contact data and estimate R and dispersion? +::::::::::::::::::::::: :::::::::::::::::::::::: callout @@ -479,17 +491,7 @@ sars_params :::::::::::::::::::::::: -:::::::::::::::::::::::: callout - -### Select the best model - -Assess fit performance w/ model comparison AIC, BIC -Using Information criteria for the best fit. Read further in vignette using helper functions - - - -::::::::::::::::::::::::: ## Evidence for variation in individual reproductive number From 2f9c9392d4eeec648cb1f75b6491a3528efeefd0 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 10:11:47 +0100 Subject: [PATCH 037/140] fix heterogeneity call out text --- episodes/superspreading-estimate.Rmd | 89 +++------------------------- 1 file changed, 7 insertions(+), 82 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index a577d25e..c3145bed 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -351,83 +351,18 @@ We can use the maximum likelihood estimates from `{fitdistrplus}` to compare dif :::::::::::::::::::: callout -### The distribution parameter k - -Dispersion parameter $k$ that are lower than - -The negative binomial model includes the conventional Poisson (k → ∞) and geometric (k = 1) models as special cases. - -The negative binomial model has variance R0(1 + R0/k), so smaller values of k indicate greater heterogeneity. - - - -k is inversely-proportional -to variance (i.e, to heterogeneity) -- high k -> get low variance (low heterogeneity) -- low k -> get high variance (high heterogeneity) - -when k approches infinity, -the negative binomial approaches poisson - -negative binomial -two parameters: -- mean (or R0, in offspring distribution) -- size (or k, named also dispersion) - -variance = -mean(1 + mean/k) - -higher k, -(higher inverse-dispersion), -lower variance, -(variance closer to mean) -lower heterogeneity - -lower k -(lower the inverse-dispersion), -higher the variance, -(variance further from mean) -higher heterogeneity - -a Poisson distribution can be defined as -an special case of Negative Binomial -when k approaches infinity -or -variance gets closer to mean -or -when mean/variance ratio gets closer to 1 - - - -### Interpret the dispersion parameter - - - - - -- In a sequence of independent Bernoulli trials, in each trial the probability of success is $p$ and of failure is $1-p$. We observe this sequence until a predefined number $r$ of successes occurs. Then the random number of observed failures follows the negative binomial distribution. -- some authors refer to $\alpha = \frac{1}{r}$ and express variance in terms of $\alpha$: $variance = m + \alpha m^2$ where mean $ m = \frac{r(1-p)}{p}$ -- depending on the author, either the parameter or its the reciprocal of $r$, $\alpha$, is refereed to as the "dispersion parameter". - -- From Lloyd-Smith, in a more general formulation, we let $v$ be gamma-distributed with mean $R_{0}$ and dispersion parameter $k$, yielding $Z$~negative binomial($R_{0}, k$). The negative binomial model includes the conventional Poisson ($k \rightarrow \inf$) as an special case. It has variance $R_{0}(1 + R_{0}/k)$, so smaller values of $k$ indicate (greater variance, thus) greater heterogeneity. - -- To sync up with Lloyd-Smith and R base function for negative binomial, $k = r = {size} = {inverse-dispersion}$ - - -- The additional parameter of the negative binomial distribution ($r$) can be used to adjust the variance independently of the mean. - - - - +### Transmission heterogeneity - +Heterogeneity is defined by the relationship between the mean ($R_{0}$), dispersion ($k$), and the variance of a negative binomial distribution. -In a Negative Binomial distribution, the relationship between mean (Ro), dispersion (k), variance and heterogeneity is given by: +The negative binomial model has $variance = R_{0}(1+\frac{R_{0}}{k})$, so smaller values of $k$ indicate greater variance and, consequently, greater **heterogeneity**. -$$ \uparrow heterogeneity = \uparrow variance = R_{0}(1+\frac{R_{0}}{\downarrow k})$$ +$$\uparrow variance = R_{0}(1+\frac{R_{0}}{\downarrow k})$$ -The Poisson distribution is an special case of the Negative Binomial. When k approximates infinity $k \rightarrow \infty$ the variance equals the mean because $\frac{R_{0}}{\infty}=0$ +The negative binomial model includes two models as special cases: +- the conventional Poisson model when $k$ approaches infinity ($k \rightarrow \infty$) the variance equals the mean ($\frac{R_{0}}{\infty}=0$), and +- the Geometric model when $k$ equals 1 ($k = 1$). :::::::::::::::::::: @@ -442,16 +377,6 @@ The dispersion parameter $k$ can be expressed differently across the literature. :::::::::::::::::::::::::::::::: -::::::::::::::::::::::: callout - -### Transmission heterogeneity - -Heterogeneity is in the variance of the number of secondary cases generated by each infected individual - -[add table quick summary] - -::::::::::::::::::::::: - ::::::::::::::::::::::: challenge read ebola contact data and estimate R and dispersion? From c55e448d1f11836006571b6ec9af717b26ab5a69 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 10:53:07 +0100 Subject: [PATCH 038/140] rearrange after review --- episodes/superspreading-estimate.Rmd | 40 ++++++++++++++++------------ 1 file changed, 23 insertions(+), 17 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index c3145bed..26e47381 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -333,6 +333,14 @@ ggplot() + ), alpha = 0.5 ) + + geom_line( + data = fit_density, + mapping = aes( + x = quantile, + y = density + ), + alpha = 0.5, color = "red" + ) + labs( x = "Number of secondary cases", y = "Density", @@ -341,14 +349,6 @@ ggplot() + theme_bw() ``` -:::::::::::::::::::::::: callout - -### Select the best model - -We can use the maximum likelihood estimates from `{fitdistrplus}` to compare different models and assess fit performance using estimators like the AIC and BIC. Read further in the vignette on [Estimate individual-level transmission](https://epiverse-trace.github.io/superspreading/articles/estimate_individual_level_transmission.html) and use the `{superspreading}` helper function `ic_tbl()` for this! - -::::::::::::::::::::::::: - :::::::::::::::::::: callout ### Transmission heterogeneity @@ -361,21 +361,18 @@ $$\uparrow variance = R_{0}(1+\frac{R_{0}}{\downarrow k})$$ The negative binomial model includes two models as special cases: -- the conventional Poisson model when $k$ approaches infinity ($k \rightarrow \infty$) the variance equals the mean ($\frac{R_{0}}{\infty}=0$), and -- the Geometric model when $k$ equals 1 ($k = 1$). +- the conventional Poisson model, when $k$ approaches infinity ($k \rightarrow \infty$) and the variance equals the mean (because $\frac{R_{0}}{\infty}=0$), +- the Geometric model, when $k$ equals 1 ($k = 1$). :::::::::::::::::::: -:::::::::::::::::::::::::::::::: callout - -### Depending on the author +:::::::::::::::::::::::: callout -The dispersion parameter $k$ can be expressed differently across the literature. +### Select the best model -- In the Wikipedia page for the negative binomial, this parameter is defined in its reciprocal form (refer to the [variance equation](https://en.wikipedia.org/wiki/Negative_binomial_distribution)). -- In [the distribution zoo](https://ben18785.shinyapps.io/distribution-zoo/) shiny app, the dispersion parameter $k$ is named "Inverse-dispersion" but it is equal to parameter estimated in this episode. We invite you to explore this! +We can use the maximum likelihood estimates from `{fitdistrplus}` to compare different models and assess fit performance using estimators like the AIC and BIC. Read further in the vignette on [Estimate individual-level transmission](https://epiverse-trace.github.io/superspreading/articles/estimate_individual_level_transmission.html) and use the `{superspreading}` helper function `ic_tbl()` for this! -:::::::::::::::::::::::::::::::: +::::::::::::::::::::::::: ::::::::::::::::::::::: challenge @@ -416,7 +413,16 @@ sars_params :::::::::::::::::::::::: +:::::::::::::::::::::::::::::::: callout +### Depending on the author + +The dispersion parameter $k$ can be expressed differently across the literature. + +- In the Wikipedia page for the negative binomial, this parameter is defined in its reciprocal form (refer to the [variance equation](https://en.wikipedia.org/wiki/Negative_binomial_distribution)). +- In [the distribution zoo](https://ben18785.shinyapps.io/distribution-zoo/) shiny app, the dispersion parameter $k$ is named "Inverse-dispersion" but it is equal to parameter estimated in this episode. We invite you to explore this! + +:::::::::::::::::::::::::::::::: ## Evidence for variation in individual reproductive number From 8659d5a7188dcc6ba87eeb8db57c51552bf07d9e Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 11:20:24 +0100 Subject: [PATCH 039/140] make estimation of sse as challenge --- episodes/superspreading-estimate.Rmd | 54 +++++++++++++++++----------- 1 file changed, 34 insertions(+), 20 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 26e47381..c0cb59a5 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -483,26 +483,6 @@ proportion_transmission( ::::::::::::::::::::::::::::: -::::::::::::::::::::::::: callout - -### Define Superspreading events - -Lloyds propose a general protocol for defining a superspreading event: - -- define an SSE as any infected individual who infects more than Z(n) others, where Z(n) is the nth percentile of the Poisson(R) distribution. -- A 99th-percentile SSE is then any case causing more infections than would occur in 99% of infectious histories in a homogeneous population - -```{r} -qpois( - p = 0.99, - lambda = offspring_fit$estimate["mu"] -) -``` - -![Reported superspreading events (SSEs; diamonds) relative to estimated reproductive number R (squares) for twelve directly transmitted infections. Lines show 5–95 percentile range of Z∼Poisson(R), and crosses show the 99th-percentile proposed as threshold for SSEs. Stars represent SSEs caused by more than one source case. ‘Other’ diseases are: 1, Streptococcus group A; 2, Lassa fever; 3, Mycoplasma pneumonia; 4, pneumonic plague; 5, tuberculosis. R is not shown for ‘other’ diseases, and is off-scale for monkeypox.](fig/SEE-individual-reproductive-number-fig-d.png) - -:::::::::::::::::::::::: - ## Backward and forward contact tracing Contact tracing can be deployed in multiple strategies. Forward tracing targets downstream individuals who may be infected by index individual. Backward tracing targets the upstream primary case who infected the index case (or a setting or event at which the index case was infected) by retracing history of contact to the likely point of exposure up to the upper bound of the incubation period. @@ -579,6 +559,40 @@ use mers to estimate ... ::::::::::::::::::::::::::: +::::::::::::::::::::::::: challenge + +### Define Superspreading events + +[Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153) propose a general protocol for defining a superspreading event (SSE). If the number of secondary infections caused by each case, $Z$, follows a negative binomial distribution ($R_{o}, k$): + +- We define an SSE as any infected individual who infects more than Z(n) others, where Z(n) is the nth percentile of the Poisson(R) distribution. +- A 99th-percentile SSE is then any case causing more infections than would occur in 99% of infectious histories in a homogeneous population + +Using the corresponding distribution function in R, estimate the SSE threshold to define a SSE. + +::::::::::::::::: hint + +You can review the [R probability functions for the normal distribution](https://sakai.unc.edu/access/content/group/3d1eb92e-7848-4f55-90c3-7c72a54e7e43/public/docs/lectures/lecture13.htm#probfunc), and then read the `?dpois` reference manual. + +In a Poisson distribution, the lambda or rate parameter are equal to the estimated mean from a negative binomial distribution. You can explore this in [The distribution zoo](https://ben18785.shinyapps.io/distribution-zoo/) shiny app. + +::::::::::::::::: + +::::::::::::::::: solution + +```{r} +qpois( + p = 0.99, + lambda = offspring_fit$estimate["mu"] +) +``` + +![Reported superspreading events (SSEs; diamonds) relative to estimated reproductive number R (squares) for twelve directly transmitted infections. Lines show 5–95 percentile range of Z∼Poisson(R), and crosses show the 99th-percentile proposed as threshold for SSEs. Stars represent SSEs caused by more than one source case. ‘Other’ diseases are: 1, Streptococcus group A; 2, Lassa fever; 3, Mycoplasma pneumonia; 4, pneumonic plague; 5, tuberculosis. R is not shown for ‘other’ diseases, and is off-scale for monkeypox.](fig/SEE-individual-reproductive-number-fig-d.png) + +::::::::::::::::: + +:::::::::::::::::::::::: + :::::::::::::::::::: challenge Calculate probabilities for Ebola using data from epiparameter From 3233e7d1b6e7f87e2276c7ec96374986f3bfd1a1 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 11:46:15 +0100 Subject: [PATCH 040/140] make epiparameter explicit --- episodes/superspreading-estimate.Rmd | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index c0cb59a5..42846900 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -382,7 +382,7 @@ read ebola contact data and estimate R and dispersion? :::::::::::::::::::::::: callout -### Use {epiparameter} +### Use epiparameter R package ```{r,message=FALSE,warning=FALSE,echo=FALSE} library(epiparameter) @@ -401,12 +401,12 @@ Currently, `{epiparameter}` have offspring distributions for `r epidist_string`. ```{r,message=FALSE,warning=FALSE} # Load parameters -sars <- epidist_db( +sars <- epiparameter::epidist_db( disease = "SARS", epi_dist = "offspring distribution", single_epidist = TRUE ) -sars_params <- get_parameters(sars) +sars_params <- epiparameter::get_parameters(sars) sars_params ``` From 508f18dbd8909e4d87bd7689094ff34fd8337240 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 11:57:36 +0100 Subject: [PATCH 041/140] relocate and simplify text after review --- episodes/superspreading-estimate.Rmd | 106 ++++++++++++--------------- 1 file changed, 45 insertions(+), 61 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 42846900..c099c94d 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -359,26 +359,51 @@ The negative binomial model has $variance = R_{0}(1+\frac{R_{0}}{k})$, so smalle $$\uparrow variance = R_{0}(1+\frac{R_{0}}{\downarrow k})$$ -The negative binomial model includes two models as special cases: - -- the conventional Poisson model, when $k$ approaches infinity ($k \rightarrow \infty$) and the variance equals the mean (because $\frac{R_{0}}{\infty}=0$), -- the Geometric model, when $k$ equals 1 ($k = 1$). +When $k$ approaches infinity ($k \rightarrow \infty$) and the variance equals the mean (because $\frac{R_{0}}{\infty}=0$), the negative binomial model approaches the conventional Poisson model. :::::::::::::::::::: -:::::::::::::::::::::::: callout + + +::::::::::::::::::::::: challenge + +read ebola contact data and estimate R and dispersion? + +:::::::::::::: hint + +... + +:::::::::::::: + +:::::::::::::: solution + +... + +:::::::::::::: + +:::::::::::::: solution ### Select the best model We can use the maximum likelihood estimates from `{fitdistrplus}` to compare different models and assess fit performance using estimators like the AIC and BIC. Read further in the vignette on [Estimate individual-level transmission](https://epiverse-trace.github.io/superspreading/articles/estimate_individual_level_transmission.html) and use the `{superspreading}` helper function `ic_tbl()` for this! -::::::::::::::::::::::::: +:::::::::::::: -::::::::::::::::::::::: challenge +::::::::::::::::::::::: -read ebola contact data and estimate R and dispersion? +## Evidence for variation in individual reproductive number -::::::::::::::::::::::: +Comparing our findings to the 20/80 rule proposed for sexually transmitted and vector-borne diseases, the core principle of heterogeneous transmission is certainly supported. + +- focus on the cumulative probability distribution of the most infectious cases + + if there is a 0.2 proportion of (the most infectious) cases contributing to the 0.8 proportion of transmission, this is a highly heterogeneous distribution. (e.g. SARS) + + if there is a 0.6 proportion of (the most infectious) cases contributing to the 0.8 of transmission, this is a less heterogeneous distribution (compared to the above one, e.g. pneumonic plague) + +![Proportion of transmission expected from the most infectious 20% of cases, for 10 outbreak or surveillance data sets (triangles). Dashed lines show proportions expected under the 20/80 rule (top) and homogeneity (bottom). Superscript ‘v’ indicates a partially vaccinated population.](fig/SEE-individual-reproductive-number-fig-c.png) + +The comparison of directly transmitted infections reveals the differing degree of individual variation among diseases and outbreak settings. Like SARS, measles in highly vaccinated populations shows high variation, with heterogeneous vaccination coverage as an important environmental factor contributing to this pattern. Monkeypox and smallpox viruses show intermediate variation, consistent across multiple data sets, and pneumonic plague transmission is slightly less variable. + +![Expected proportion of all transmission due to a given proportion of infectious cases, where cases are ranked by infectiousness. For a homogeneous population (all ν = R0), this relation is linear. For five directly transmitted infections (based on specific k values), the line is concave owing to variation in ν.](fig/SEE-individual-reproductive-number-fig-b.png) :::::::::::::::::::::::: callout @@ -410,34 +435,8 @@ sars_params <- epiparameter::get_parameters(sars) sars_params ``` - :::::::::::::::::::::::: -:::::::::::::::::::::::::::::::: callout - -### Depending on the author - -The dispersion parameter $k$ can be expressed differently across the literature. - -- In the Wikipedia page for the negative binomial, this parameter is defined in its reciprocal form (refer to the [variance equation](https://en.wikipedia.org/wiki/Negative_binomial_distribution)). -- In [the distribution zoo](https://ben18785.shinyapps.io/distribution-zoo/) shiny app, the dispersion parameter $k$ is named "Inverse-dispersion" but it is equal to parameter estimated in this episode. We invite you to explore this! - -:::::::::::::::::::::::::::::::: - -## Evidence for variation in individual reproductive number - -Comparing our findings to the 20/80 rule proposed for sexually transmitted and vector-borne diseases, no general rule emerges but the core principle of heterogeneous transmission is certainly supported (Fig. 1c). - -- focus on the cumulative probability distribution of the most infectious cases - + if there is a 0.2 proportion of (the most infectious) cases contributing to the 0.8 proportion of transmission, this is a highly heterogeneous distribution. (e.g. SARS) - + if there is a 0.6 proportion of (the most infectious) cases contributing to the 0.8 of transmission, this is a less heterogeneous distribution (compared to the above one, e.g. pneumonic plague) - -![Proportion of transmission expected from the most infectious 20% of cases, for 10 outbreak or surveillance data sets (triangles). Dashed lines show proportions expected under the 20/80 rule (top) and homogeneity (bottom). Superscript ‘v’ indicates a partially vaccinated population.](fig/SEE-individual-reproductive-number-fig-c.png) - -The comparison of directly transmitted infections reveals the differing degree of individual variation among diseases and outbreak settings. Like SARS, measles in highly vaccinated populations shows high variation, with heterogeneous vaccination coverage as an important environmental factor contributing to this pattern. Monkeypox and smallpox viruses show intermediate variation, consistent across multiple data sets, and pneumonic plague transmission is slightly less variable. - -![Expected proportion of all transmission due to a given proportion of infectious cases, where cases are ranked by infectiousness. For a homogeneous population (all ν = R0), this relation is linear. For five directly transmitted infections (based on specific k values), the line is concave owing to variation in ν.](fig/SEE-individual-reproductive-number-fig-b.png) - ::::::::::::::::::::::::::::: challenge What is the proportion of cases that are responsible of the 80% of transmission? @@ -483,6 +482,17 @@ proportion_transmission( ::::::::::::::::::::::::::::: +:::::::::::::::::::::::::::::::: callout + +### Depending on the author + +The dispersion parameter $k$ can be expressed differently across the literature. + +- In the Wikipedia page for the negative binomial, this parameter is defined in its reciprocal form (refer to the [variance equation](https://en.wikipedia.org/wiki/Negative_binomial_distribution)). +- In [the distribution zoo](https://ben18785.shinyapps.io/distribution-zoo/) shiny app, the dispersion parameter $k$ is named "Inverse-dispersion" but it is equal to parameter estimated in this episode. We invite you to explore this! + +:::::::::::::::::::::::::::::::: + ## Backward and forward contact tracing Contact tracing can be deployed in multiple strategies. Forward tracing targets downstream individuals who may be infected by index individual. Backward tracing targets the upstream primary case who infected the index case (or a setting or event at which the index case was infected) by retracing history of contact to the likely point of exposure up to the upper bound of the incubation period. @@ -525,32 +535,6 @@ reuse ebola parameters? interpret ::::::::::::::::::::::: -## Superspreading in decision making - -Transmission heterogeneity affects epidemic establishment and the ease of control ([Cori et al., 2017](https://royalsocietypublishing.org/doi/10.1098/rstb.2016.0371)). - -+ Greater heterogeneity reduces the chance of an outbreak emerging from single case. Individuals with more extreme amount of secondary cases are rare. - -+ However, if the outbreak gets established, this heterogeneity can make an outbreak hard to control using *mass interventions* (which assumes transmission homogeneity), as a single uncontrolled case can generate a large number of secondary cases. - -+ Conversely, heterogeneity in transmission may provide opportunities for *targeted interventions* if the individuals who contribute more to transmission (due to biological, environmental or behavioral factors) share socio-demographic or geographical characteristics that can be defined. - -We can have an early understanding of a disease epidemic potential from the mean reproduction number $R_{0}$ and dispersion $k$ of an offspring distribution to answer questions like: - -- What is the probability of an pathogen to cause large outbreak? -- What is the probability of an outbreak to get extinct? -- What is the probability to contain the ongoing outbreak? - -::::::::::::::::::::::::::: testimonial - -### Epidemic Risk assessment accounting for superspreading - -These estimates vary non-linearly with respect to the mean reproduction number $R_{0}$ and dispersion $k$ of a given disease. - -We invite you to read the `{superspreading}` vignette on [Epidemic risk](https://epiverse-trace.github.io/superspreading/articles/epidemic_risk.html)! - -::::::::::::::::::::::::::: - ## Challenges ::::::::::::::::::::::::::: challenge From fa48ad7c59ffee964bb82cde849d37ef4f64f2a1 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 13:11:38 +0100 Subject: [PATCH 042/140] add within challenges and prioritize content --- episodes/superspreading-estimate.Rmd | 334 ++++++++++++++++----------- 1 file changed, 204 insertions(+), 130 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index c099c94d..aff079d3 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -143,7 +143,7 @@ To get this, first, we can use `epicontacts::get_id()` to get the full list of u all_secondary <- epi_contacts %>% # extract ids in contact *and* linelist using "which" argument epicontacts::get_id(which = "all") %>% - # transform to dataframe to use left_join() + # transform vector to dataframe to use left_join() enframe(name = NULL, value = "from") %>% # join count secondary cases per infectee left_join(infector_secondary) %>% @@ -155,7 +155,7 @@ all_secondary <- epi_contacts %>% From a histogram of the `all_secondary` object, we can identify the **heterogeneity** in the number of secondary cases. Three cases were related to more than 20 secondary cases, while the complementary cases with less than five or zero secondary cases. -```{r,echo=FALSE} +```{r,echo=FALSE,eval=FALSE} # arrange in descendant order of secondary cases all_secondary %>% arrange(desc(secondary_cases)) @@ -174,7 +174,7 @@ all_secondary %>% ) ``` -The number of secondary infections caused by each case can be used to _empirically_ estimate the **offspring distribution**. One candidate statistical distribution used to model the offspring distribution is the **negative binomial** distribution with two parameters: +The number of secondary cases can be used to _empirically_ estimate the **offspring distribution**, which is the number of secondary _infections_ caused by each case. One candidate statistical distribution used to model the offspring distribution is the **negative binomial** distribution with two parameters: - **Mean**, which represents the $R_{0}$, the average number of (secondary) cases produced by a single individual in an entirely susceptible population, and @@ -228,7 +228,7 @@ ggplot() + ) ``` -From the histogram and density plot, we can identify that the distribution is highly skewed or **overdispersed**. The superspreading events (SSEs) are realizations from the right-hand tail of the offspring distribution ([Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153)). +From the histogram and density plot, we can identify that the offspring distribution is highly skewed or **overdispersed**. In this framework, the superspreading events (SSEs) are realizations from the right-hand tail of the offspring distribution ([Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153)). ::::::::::::::::::::::::::: callout @@ -257,6 +257,70 @@ In epidemiology, [negative binomial](https://en.wikipedia.org/wiki/Negative_bino ::::::::::::::::::::::::::::: +:::::::::::::::::::::::::::::::::: challenge + +Calculate the distribution of secondary cases for Ebola using the `ebola_sim_clean` object from `{outbreaks}` package. + +Does the offspring distribution is skewed or overdispersed? + +:::::::::::::::::: hint + +**Note:** This dataset has `r nrow(ebola_sim_clean$linelist)` cases. Running `epicontacts::vis_epicontacts()` may overload your session! + +:::::::::::::::::: + +:::::::::::::::::: solution + +```{r} +## first, make an epicontacts object +ebola_contacts <- + epicontacts::make_epicontacts( + linelist = ebola_sim_clean$linelist, + contacts = ebola_sim_clean$contacts + ) + +# visualise contact tree +# (this network can overload your session!) +#epicontacts::vis_epicontacts(ebola_contacts) + +# count secondary cases + +ebola_infector_secondary <- ebola_contacts %>% + pluck("contacts") %>% + count(from, name = "secondary_cases") + +ebola_secondary <- ebola_contacts %>% + # extract ids in contact *and* linelist using "which" argument + epicontacts::get_id(which = "all") %>% + # transform vector to dataframe to use left_join() + enframe(name = NULL, value = "from") %>% + # join count secondary cases per infectee + left_join(ebola_infector_secondary) %>% + # infectee with missing secondary cases are replaced with zero + replace_na( + replace = list(secondary_cases = 0) + ) + +# arrange in descendant order of secondary cases +# ebola_secondary %>% +# arrange(desc(secondary_cases)) + +## plot the distribution +ebola_secondary %>% + ggplot(aes(secondary_cases)) + + geom_histogram(binwidth = 1) + + labs( + x = "Number of secondary cases", + y = "Frequency" + ) +``` + +From a visual inspection, the distribution of secondary cases for the Ebola data set in `ebola_sim_clean` shows an skewed distribution with secondary cases equal or lower than 6. We need to complement this observation with a statistical analysis to evaluate for overdispersion. + +:::::::::::::::::: + +:::::::::::::::::::::::::::::::::: + ## Estimate the dispersion parameter To empirically estimate the dispersion parameter $k$, we can to fit a negative binomial distribution to the number of secondary cases. @@ -363,21 +427,50 @@ When $k$ approaches infinity ($k \rightarrow \infty$) and the variance equals th :::::::::::::::::::: +::::::::::::::::::::::: challenge +Use the distribution of secondary cases from the `ebola_sim_clean` object from `{outbreaks}` package. -::::::::::::::::::::::: challenge +Fit a negative binomial distribution to estimate the mean and dispersion parameter of the offspring distribution. -read ebola contact data and estimate R and dispersion? +Does the estimated dispersion parameter provide evidence of transmission heterogeneity? :::::::::::::: hint -... +Review how to fit a negative binomial distribution using the `fitdistrplus::fitdist()` function. :::::::::::::: :::::::::::::: solution -... +```{r} +ebola_offspring <- ebola_secondary %>% + pull(secondary_cases) %>% + fitdist(distr = "nbinom") + +ebola_offspring +``` + +```{r} +## extract the "size" parameter +ebola_mid <- ebola_offspring$estimate[["size"]] + +## calculate the 95% confidence intervals using the standard error estimate and +## the 0.025 and 0.975 quantiles of the normal distribution. + +ebola_lower <- ebola_mid + ebola_offspring$sd[["size"]] * qnorm(0.025) + +ebola_upper <- ebola_mid + ebola_offspring$sd[["size"]] * qnorm(0.975) + +# ebola_mid +# ebola_lower +# ebola_upper +``` + +From the number secondary cases distribution we estimated a dispersion parameter $k$ of +`r round(ebola_mid, 3)`, with a 95% Confidence Interval from `r round(ebola_lower, 3)` to `r round(ebola_upper, 3)`. + +For dispersion parameter estimates higher than one we get low distribution variance, hence, low heterogeneity. :::::::::::::: @@ -391,9 +484,9 @@ We can use the maximum likelihood estimates from `{fitdistrplus}` to compare dif ::::::::::::::::::::::: -## Evidence for variation in individual reproductive number +## Evidence for variation in individual reproductive number EDIT! -Comparing our findings to the 20/80 rule proposed for sexually transmitted and vector-borne diseases, the core principle of heterogeneous transmission is certainly supported. +[Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153) use a 20/80 rule to show how the core principle of heterogeneous transmission is supported. - focus on the cumulative probability distribution of the most infectious cases + if there is a 0.2 proportion of (the most infectious) cases contributing to the 0.8 proportion of transmission, this is a highly heterogeneous distribution. (e.g. SARS) @@ -405,83 +498,6 @@ The comparison of directly transmitted infections reveals the differing degree o ![Expected proportion of all transmission due to a given proportion of infectious cases, where cases are ranked by infectiousness. For a homogeneous population (all ν = R0), this relation is linear. For five directly transmitted infections (based on specific k values), the line is concave owing to variation in ν.](fig/SEE-individual-reproductive-number-fig-b.png) -:::::::::::::::::::::::: callout - -### Use epiparameter R package - -```{r,message=FALSE,warning=FALSE,echo=FALSE} -library(epiparameter) - -epidist_string <- epidist_db( - epi_dist = "offspring distribution" -) %>% - list_distributions() %>% - dplyr::select(disease) %>% - distinct() %>% - pull() %>% - paste(collapse = ", ") -``` - -Currently, `{epiparameter}` have offspring distributions for `r epidist_string`. Let's access the offspring distribution `mean` and `dispersion` parameters for SARS: - -```{r,message=FALSE,warning=FALSE} -# Load parameters -sars <- epiparameter::epidist_db( - disease = "SARS", - epi_dist = "offspring distribution", - single_epidist = TRUE -) -sars_params <- epiparameter::get_parameters(sars) -sars_params -``` - -:::::::::::::::::::::::: - -::::::::::::::::::::::::::::: challenge - -What is the proportion of cases that are responsible of the 80% of transmission? - -Compare between SARS, MERS, Ebola - -::::::::::::::::::::: hint - -Use `proportion_transmission()` - -::::::::::::::::::::: - -::::::::::::::::::::: solution - -```{r} -# estimate -# proportion of cases that -# generate 80% of transmission -proportion_transmission( - R = sars_params[["mean"]], - k = sars_params[["dispersion"]], - percent_transmission = 0.8 -) - -## assessment --------------------------------- - -# estimate -# proportion of cases that -# generate 80% of transmission -proportion_transmission( - R = offspring_fit$estimate["mu"], - k = offspring_fit$estimate["size"], - percent_transmission = 0.8 -) - -## assessment -------------------------------------------------------------- - -#' estimate for ebola - -``` - -::::::::::::::::::::: - -::::::::::::::::::::::::::::: - :::::::::::::::::::::::::::::::: callout ### Depending on the author @@ -539,86 +555,143 @@ reuse ebola parameters? interpret ::::::::::::::::::::::::::: challenge -use mers to estimate ... +use mers to estimate ... [pending] ::::::::::::::::::::::::::: -::::::::::::::::::::::::: challenge +:::::::::::::::::::::::::: challenge -### Define Superspreading events +inform backward contact tracing strategy for ebola [pending] -[Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153) propose a general protocol for defining a superspreading event (SSE). If the number of secondary infections caused by each case, $Z$, follows a negative binomial distribution ($R_{o}, k$): +::::::::::::::::::::::::: -- We define an SSE as any infected individual who infects more than Z(n) others, where Z(n) is the nth percentile of the Poisson(R) distribution. -- A 99th-percentile SSE is then any case causing more infections than would occur in 99% of infectious histories in a homogeneous population -Using the corresponding distribution function in R, estimate the SSE threshold to define a SSE. +::::::::::::::::::::::::::::: challenge -::::::::::::::::: hint +What is the proportion of cases that are responsible of the 80% of transmission? -You can review the [R probability functions for the normal distribution](https://sakai.unc.edu/access/content/group/3d1eb92e-7848-4f55-90c3-7c72a54e7e43/public/docs/lectures/lecture13.htm#probfunc), and then read the `?dpois` reference manual. +Compare the estimates for **MERS** using the offspring distributions parameters from this tutorial episode, with **SARS** and **Ebola** offspring distributions parameter accessible via the `{epiparameter}` R package. -In a Poisson distribution, the lambda or rate parameter are equal to the estimated mean from a negative binomial distribution. You can explore this in [The distribution zoo](https://ben18785.shinyapps.io/distribution-zoo/) shiny app. +::::::::::::::::::::: hint -::::::::::::::::: +Use `superspreading::proportion_transmission()` and `{epiparameter}`. -::::::::::::::::: solution +```{r,message=FALSE,warning=FALSE,echo=FALSE} +library(epiparameter) -```{r} -qpois( - p = 0.99, - lambda = offspring_fit$estimate["mu"] +epidist_string <- epidist_db( + epi_dist = "offspring distribution" +) %>% + list_distributions() %>% + dplyr::select(disease) %>% + distinct() %>% + pull() %>% + paste(collapse = ", ") +``` + +Currently, `{epiparameter}` have offspring distributions for `r epidist_string`. Let's access the offspring distribution `mean` and `dispersion` parameters for SARS: + +```{r,message=FALSE,warning=FALSE} +# Load parameters +sars <- epiparameter::epidist_db( + disease = "SARS", + epi_dist = "offspring distribution", + single_epidist = TRUE ) +sars_params <- epiparameter::get_parameters(sars) +sars_params ``` -![Reported superspreading events (SSEs; diamonds) relative to estimated reproductive number R (squares) for twelve directly transmitted infections. Lines show 5–95 percentile range of Z∼Poisson(R), and crosses show the 99th-percentile proposed as threshold for SSEs. Stars represent SSEs caused by more than one source case. ‘Other’ diseases are: 1, Streptococcus group A; 2, Lassa fever; 3, Mycoplasma pneumonia; 4, pneumonic plague; 5, tuberculosis. R is not shown for ‘other’ diseases, and is off-scale for monkeypox.](fig/SEE-individual-reproductive-number-fig-d.png) +::::::::::::::::::::: -::::::::::::::::: +::::::::::::::::::::: solution -:::::::::::::::::::::::: +```{r} +#' estimate for ebola -------------- -:::::::::::::::::::: challenge +ebola_epiparameter <- epiparameter::epidist_db( + disease = "Ebola", + epi_dist = "offspring distribution", + single_epidist = TRUE +) +ebola_params <- epiparameter::get_parameters(ebola_epiparameter) +ebola_params -Calculate probabilities for Ebola using data from epiparameter +# estimate +# proportion of cases that +# generate 80% of transmission +proportion_transmission( + R = ebola_params[["mean"]], + k = ebola_params[["dispersion"]], + percent_transmission = 0.8 +) -:::::::::::::::::: hint +#' estimate for sars -------------- -```{r} -# estimate probability to contain -probability_contain( - R = offspring_fit$estimate["mu"], - k = offspring_fit$estimate["size"], - num_init_infect = 1, - case_threshold = 100 +# estimate +# proportion of cases that +# generate 80% of transmission +proportion_transmission( + R = sars_params[["mean"]], + k = sars_params[["dispersion"]], + percent_transmission = 0.8 ) -# Estimate probability of large outbreak -# with 5 independent imported cases -probability_epidemic( + +#' estimate for mers -------------- + +# estimate +# proportion of cases that +# generate 80% of transmission +proportion_transmission( R = offspring_fit$estimate["mu"], k = offspring_fit$estimate["size"], - num_init_infect = 5 + percent_transmission = 0.8 ) ``` -:::::::::::::::::: +Among Ebola, SARS, and MERS, MERS has the lowest percent of cases (2.1%) responsible of the 80% of the transmission, representative of highly overdispersed offspring distributions. -:::::::::::::::::: solution +Among them, Ebola has the highest percent of cases (43%) responsible of the 80% of the transmission. This is representative of offspring distributions with high dispersion parameters. -```{r} -#' get ebola params -``` +::::::::::::::::::::: -:::::::::::::::::: +::::::::::::::::::::::::::::: + +::::::::::::::::::::::::: challenge -::::::::::::::::::::::::::::::::::::: +### Define Superspreading events +[Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153) propose a general protocol for defining a superspreading event (SSE). If the number of secondary infections caused by each case, $Z$, follows a negative binomial distribution ($R_{o}, k$): -:::::::::::::::::::::::::: challenge +- We define an SSE as any infected individual who infects more than Z(n) others, where Z(n) is the nth percentile of the Poisson(R) distribution. +- A 99th-percentile SSE is then any case causing more infections than would occur in 99% of infectious histories in a homogeneous population -inform backward contact tracing strategy +Using the corresponding distribution function in R, estimate the SSE threshold to define a SSE. + +::::::::::::::::: hint + +You can review the [R probability functions for the normal distribution](https://sakai.unc.edu/access/content/group/3d1eb92e-7848-4f55-90c3-7c72a54e7e43/public/docs/lectures/lecture13.htm#probfunc), and then read the `?dpois` reference manual. + +In a Poisson distribution, the lambda or rate parameter are equal to the estimated mean from a negative binomial distribution. You can explore this in [The distribution zoo](https://ben18785.shinyapps.io/distribution-zoo/) shiny app. + +::::::::::::::::: + +::::::::::::::::: solution + +```{r} +qpois( + p = 0.99, + lambda = offspring_fit$estimate["mu"] +) +``` + +![Reported superspreading events (SSEs; diamonds) relative to estimated reproductive number R (squares) for twelve directly transmitted infections. Lines show 5–95 percentile range of Z∼Poisson(R), and crosses show the 99th-percentile proposed as threshold for SSEs. Stars represent SSEs caused by more than one source case. ‘Other’ diseases are: 1, Streptococcus group A; 2, Lassa fever; 3, Mycoplasma pneumonia; 4, pneumonic plague; 5, tuberculosis. R is not shown for ‘other’ diseases, and is off-scale for monkeypox.](fig/SEE-individual-reproductive-number-fig-d.png) + +::::::::::::::::: + +:::::::::::::::::::::::: -::::::::::::::::::::::::: ::::::::::::::::::::::::::::: testimonial @@ -630,6 +703,7 @@ The [Going viral](https://kucharski.substack.com/p/going-viral) post from Adam K ::::::::::::::::::::::::::::: + ::::::::::::::::::::::::::::::::::::: keypoints - Use `{epicontacts}` From 7666ccdc783dafd4fdfefa63111e5158e37fc73f Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 13:13:16 +0100 Subject: [PATCH 043/140] move text on decision making to simulate episode --- episodes/superspreading-simulate.Rmd | 62 ++++++++++++++++++++++++++++ 1 file changed, 62 insertions(+) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index eeebb613..1e41cb06 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -45,6 +45,32 @@ library(epichains) library(tidyverse) ``` +## Superspreading in decision making + +Transmission heterogeneity affects epidemic establishment and the ease of control ([Cori et al., 2017](https://royalsocietypublishing.org/doi/10.1098/rstb.2016.0371)). + ++ Greater heterogeneity reduces the chance of an outbreak emerging from single case. Individuals with more extreme amount of secondary cases are rare. + ++ However, if the outbreak gets established, this heterogeneity can make an outbreak hard to control using *mass interventions* (which assumes transmission homogeneity), as a single uncontrolled case can generate a large number of secondary cases. + ++ Conversely, heterogeneity in transmission may provide opportunities for *targeted interventions* if the individuals who contribute more to transmission (due to biological, environmental or behavioral factors) share socio-demographic or geographical characteristics that can be defined. + +We can have an early understanding of a disease epidemic potential from the mean reproduction number $R_{0}$ and dispersion $k$ of an offspring distribution to answer questions like: + +- What is the probability of an pathogen to cause large outbreak? +- What is the probability of an outbreak to get extinct? +- What is the probability to contain the ongoing outbreak? + +::::::::::::::::::::::::::: testimonial + +### Epidemic Risk assessment accounting for superspreading + +These estimates vary non-linearly with respect to the mean reproduction number $R_{0}$ and dispersion $k$ of a given disease. + +We invite you to read the `{superspreading}` vignette on [Epidemic risk](https://epiverse-trace.github.io/superspreading/articles/epidemic_risk.html)! + +::::::::::::::::::::::::::: + ## Simulation of uncontrolled outbreaks simulation of uncontrolled outbreaks @@ -386,6 +412,42 @@ regrowth of the epidemic. ::::::::::::::::::::::::::::: +:::::::::::::::::::: challenge + +Calculate probabilities for Ebola using data from epiparameter using `{superspreading}` + +:::::::::::::::::: hint + +```{r} +# estimate probability to contain +probability_contain( + R = offspring_fit$estimate["mu"], + k = offspring_fit$estimate["size"], + num_init_infect = 1, + case_threshold = 100 +) + +# Estimate probability of large outbreak +# with 5 independent imported cases +probability_epidemic( + R = offspring_fit$estimate["mu"], + k = offspring_fit$estimate["size"], + num_init_infect = 5 +) +``` + +:::::::::::::::::: + +:::::::::::::::::: solution + +```{r} +#' get ebola params +``` + +:::::::::::::::::: + +::::::::::::::::::::::::::::::::::::: + ::::::::::::::::::::::::: testimonial you can use early linelist data as seed cases to make short term projection of cases From 827e3c8e899404f282803726ea63169ebcc31a68 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 13:38:31 +0100 Subject: [PATCH 044/140] relocate complementary information chunk --- episodes/superspreading-estimate.Rmd | 22 ++++++++++++---------- 1 file changed, 12 insertions(+), 10 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index aff079d3..6e732985 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -498,16 +498,7 @@ The comparison of directly transmitted infections reveals the differing degree o ![Expected proportion of all transmission due to a given proportion of infectious cases, where cases are ranked by infectiousness. For a homogeneous population (all ν = R0), this relation is linear. For five directly transmitted infections (based on specific k values), the line is concave owing to variation in ν.](fig/SEE-individual-reproductive-number-fig-b.png) -:::::::::::::::::::::::::::::::: callout - -### Depending on the author - -The dispersion parameter $k$ can be expressed differently across the literature. - -- In the Wikipedia page for the negative binomial, this parameter is defined in its reciprocal form (refer to the [variance equation](https://en.wikipedia.org/wiki/Negative_binomial_distribution)). -- In [the distribution zoo](https://ben18785.shinyapps.io/distribution-zoo/) shiny app, the dispersion parameter $k$ is named "Inverse-dispersion" but it is equal to parameter estimated in this episode. We invite you to explore this! - -:::::::::::::::::::::::::::::::: +:::::::::::::::::::::::::::::::::: ## Backward and forward contact tracing @@ -677,6 +668,17 @@ In a Poisson distribution, the lambda or rate parameter are equal to the estimat ::::::::::::::::: +::::::::::::::::: hint + +### inverse-dispersion? + +The dispersion parameter $k$ can be expressed differently across the literature. + +- In the Wikipedia page for the negative binomial, this parameter is defined in its reciprocal form (refer to the [variance equation](https://en.wikipedia.org/wiki/Negative_binomial_distribution)). +- In [the distribution zoo](https://ben18785.shinyapps.io/distribution-zoo/) shiny app, the dispersion parameter $k$ is named "Inverse-dispersion" but it is equal to parameter estimated in this episode. We invite you to explore this! + +::::::::::::::::: + ::::::::::::::::: solution ```{r} From e61dc86e4643916415fcc216243e10ff144d1bf3 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 13:38:37 +0100 Subject: [PATCH 045/140] fix typo --- episodes/superspreading-estimate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 6e732985..3fbf36f1 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -709,7 +709,7 @@ The [Going viral](https://kucharski.substack.com/p/going-viral) post from Adam K ::::::::::::::::::::::::::::::::::::: keypoints - Use `{epicontacts}` -- Use `{fitdistplus}` +- Use `{fitdistrplus}` - Use `{superspreading}` to :::::::::::::::::::::::::::::::::::::::::::::::: From 8e29ba67c4a7803bc70d11e57b7389150234ef8a Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 13:40:31 +0100 Subject: [PATCH 046/140] clarify relationship between poisson and nb --- episodes/superspreading-estimate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 3fbf36f1..871e5425 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -423,7 +423,7 @@ The negative binomial model has $variance = R_{0}(1+\frac{R_{0}}{k})$, so smalle $$\uparrow variance = R_{0}(1+\frac{R_{0}}{\downarrow k})$$ -When $k$ approaches infinity ($k \rightarrow \infty$) and the variance equals the mean (because $\frac{R_{0}}{\infty}=0$), the negative binomial model approaches the conventional Poisson model. +When $k$ approaches infinity ($k \rightarrow \infty$) the variance equals the mean (because $\frac{R_{0}}{\infty}=0$). This makes the conventional Poisson model an special case of the negative binomial model. :::::::::::::::::::: From ca862e456c18b3efb1a7305e02a59fae313a394d Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 13:44:45 +0100 Subject: [PATCH 047/140] clarify challenge --- episodes/superspreading-estimate.Rmd | 10 +++++++--- 1 file changed, 7 insertions(+), 3 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 871e5425..7f270976 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -484,7 +484,9 @@ We can use the maximum likelihood estimates from `{fitdistrplus}` to compare dif ::::::::::::::::::::::: -## Evidence for variation in individual reproductive number EDIT! +:::::::::::::::::::::::::::::::::: checklist + +### Evidence for variation in individual reproductive number EDIT! [Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153) use a 20/80 rule to show how the core principle of heterogeneous transmission is supported. @@ -559,13 +561,15 @@ inform backward contact tracing strategy for ebola [pending] ::::::::::::::::::::::::::::: challenge +### Expected proportion of transmission + What is the proportion of cases that are responsible of the 80% of transmission? -Compare the estimates for **MERS** using the offspring distributions parameters from this tutorial episode, with **SARS** and **Ebola** offspring distributions parameter accessible via the `{epiparameter}` R package. +Use `{superspreading}` and compare the estimates for **MERS** using the offspring distributions parameters from this tutorial episode, with **SARS** and **Ebola** offspring distributions parameter accessible via the `{epiparameter}` R package. ::::::::::::::::::::: hint -Use `superspreading::proportion_transmission()` and `{epiparameter}`. +To use `superspreading::proportion_transmission()` we recommend to read the [Estimate what proportion of cases cause a certain proportion of transmission](https://epiverse-trace.github.io/superspreading/reference/proportion_transmission.html) reference manual. ```{r,message=FALSE,warning=FALSE,echo=FALSE} library(epiparameter) From e1f916c5004c310a99a34e9d71f31507bea578ed Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 17:17:38 +0100 Subject: [PATCH 048/140] clean all challenges --- episodes/superspreading-estimate.Rmd | 125 +++++++++++++++++---------- 1 file changed, 79 insertions(+), 46 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 7f270976..680321fd 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -437,7 +437,7 @@ Does the estimated dispersion parameter provide evidence of transmission heterog :::::::::::::: hint -Review how to fit a negative binomial distribution using the `fitdistrplus::fitdist()` function. +Review how we fitted a negative binomial distribution using the `fitdistrplus::fitdist()` function. :::::::::::::: @@ -472,6 +472,8 @@ From the number secondary cases distribution we estimated a dispersion parameter For dispersion parameter estimates higher than one we get low distribution variance, hence, low heterogeneity. +But does this mean that the secondary case distribution does not have superspreading events (SSEs)? You will later find one challenge: How do you define an SSE threshold for Ebola? + :::::::::::::: :::::::::::::: solution @@ -538,26 +540,92 @@ Even though we have an $R<1$, given a highly overdispersed offspring distributio We can also use this number to prevent gathering of certain sized to reduce the epidemic by preventing potential superspreading events. Interventions can target to reduce the reproduction number in order to reduce the probability of having clusters of secondary cases. -::::::::::::::::::::::: challenge +::::::::::::::::::::::::::::::::: challenge -reuse ebola parameters? interpret +### Backward contact tracing for Ebola -::::::::::::::::::::::: +Use the Ebola estimated parameters for `ebola_sim_clean` object from `{outbreaks}` package. + +Evaluate if the contact tracing efforts would be benefit by a backward strategy to increase their probability of contain and quarantine an increased proportion of contacts. + +Calculate the probability of having a cluster of secondary infections caused by a primary case identified by backward tracing of size 5, 10, 15 or larger. + +:::::::::::::::: hint + +Review how we estimated the probability of having clusters of a fixed size, given an offspring distribution mean and dispersion parameters, using the `superspreading::proportion_cluster_size()` function. + +:::::::::::::::: + +:::::::::::::::: solution + +```{r} +# estimate the probability of +# having a cluster size of 5, 10, or 25 +# secondary cases from a primary case, +# given known reproduction number and +# dispersion parameter. +proportion_cluster_size( + R = ebola_offspring$estimate["mu"], + k = ebola_offspring$estimate["size"], + cluster_size = c(5, 10, 25) +) +``` + +The probability of having clusters of five people is 1.8%. At this stage, given this offspring distribution parameters, a backward strategy may not increase the probability of contain and quarantine more onward cases. + +:::::::::::::::: + +::::::::::::::::::::::::::::::::: ## Challenges -::::::::::::::::::::::::::: challenge +::::::::::::::::::::::::: challenge + +### Does Ebola have any superspreading event? -use mers to estimate ... [pending] +[Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153) propose a general protocol for defining a superspreading event (SSE). If the number of secondary infections caused by each case, $Z$, follows a negative binomial distribution ($R_{o}, k$): -::::::::::::::::::::::::::: +- We define an SSE as any infected individual who infects more than Z(n) others, where Z(n) is the nth percentile of the Poisson(R) distribution. +- A 99th-percentile SSE is then any case causing more infections than would occur in 99% of infectious histories in a homogeneous population + +Using the corresponding distribution function, estimate the SSE threshold to define a SSE for the Ebola offspring distribution estimates for the `ebola_sim_clean` object from `{outbreaks}` package. + +::::::::::::::::: hint + +In a Poisson distribution, the lambda or rate parameter are equal to the estimated mean from a negative binomial distribution. You can explore this in [The distribution zoo](https://ben18785.shinyapps.io/distribution-zoo/) shiny app. + +::::::::::::::::: + +::::::::::::::::: solution + +To get the quantile value for the 99th-percentile we need to use the [density function](https://sakai.unc.edu/access/content/group/3d1eb92e-7848-4f55-90c3-7c72a54e7e43/public/docs/lectures/lecture13.htm#probfunc) for the Poisson distribution `dpois()`. + +```{r} +# get mean +ebola_mu_mid <- ebola_offspring$estimate["mu"] +# get upper 95% CI +ebola_mu_upper <- ebola_mu_mid + offspring_fit$sd[["mu"]] * qnorm(0.975) + +# get 99th-percentile from poisson distribution with mean = mu +qpois( + p = 0.99, + lambda = ebola_mu_mid +) -:::::::::::::::::::::::::: challenge +# get 99th-percentile from poisson distribution with mean = mu upper 95% CI +qpois( + p = 0.99, + lambda = ebola_mu_upper +) +``` -inform backward contact tracing strategy for ebola [pending] +These values are closer to the ones reported by [Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153). See figure below: -::::::::::::::::::::::::: +![Reported superspreading events (SSEs; diamonds) relative to estimated reproductive number R (squares) for twelve directly transmitted infections. Lines show 5–95 percentile range of Z∼Poisson(R), and crosses show the 99th-percentile proposed as threshold for SSEs. Stars represent SSEs caused by more than one source case. ‘Other’ diseases are: 1, Streptococcus group A; 2, Lassa fever; 3, Mycoplasma pneumonia; 4, pneumonic plague; 5, tuberculosis. R is not shown for ‘other’ diseases, and is off-scale for monkeypox.](fig/SEE-individual-reproductive-number-fig-d.png) +::::::::::::::::: + +:::::::::::::::::::::::: ::::::::::::::::::::::::::::: challenge @@ -653,26 +721,7 @@ Among them, Ebola has the highest percent of cases (43%) responsible of the 80% ::::::::::::::::::::::::::::: -::::::::::::::::::::::::: challenge - -### Define Superspreading events - -[Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153) propose a general protocol for defining a superspreading event (SSE). If the number of secondary infections caused by each case, $Z$, follows a negative binomial distribution ($R_{o}, k$): - -- We define an SSE as any infected individual who infects more than Z(n) others, where Z(n) is the nth percentile of the Poisson(R) distribution. -- A 99th-percentile SSE is then any case causing more infections than would occur in 99% of infectious histories in a homogeneous population - -Using the corresponding distribution function in R, estimate the SSE threshold to define a SSE. - -::::::::::::::::: hint - -You can review the [R probability functions for the normal distribution](https://sakai.unc.edu/access/content/group/3d1eb92e-7848-4f55-90c3-7c72a54e7e43/public/docs/lectures/lecture13.htm#probfunc), and then read the `?dpois` reference manual. - -In a Poisson distribution, the lambda or rate parameter are equal to the estimated mean from a negative binomial distribution. You can explore this in [The distribution zoo](https://ben18785.shinyapps.io/distribution-zoo/) shiny app. - -::::::::::::::::: - -::::::::::::::::: hint +::::::::::::::::: callout ### inverse-dispersion? @@ -683,22 +732,6 @@ The dispersion parameter $k$ can be expressed differently across the literature. ::::::::::::::::: -::::::::::::::::: solution - -```{r} -qpois( - p = 0.99, - lambda = offspring_fit$estimate["mu"] -) -``` - -![Reported superspreading events (SSEs; diamonds) relative to estimated reproductive number R (squares) for twelve directly transmitted infections. Lines show 5–95 percentile range of Z∼Poisson(R), and crosses show the 99th-percentile proposed as threshold for SSEs. Stars represent SSEs caused by more than one source case. ‘Other’ diseases are: 1, Streptococcus group A; 2, Lassa fever; 3, Mycoplasma pneumonia; 4, pneumonic plague; 5, tuberculosis. R is not shown for ‘other’ diseases, and is off-scale for monkeypox.](fig/SEE-individual-reproductive-number-fig-d.png) - -::::::::::::::::: - -:::::::::::::::::::::::: - - ::::::::::::::::::::::::::::: testimonial ### Read these blog posts From a9aefa3448c879e658cebae21f9c4eed7f94c3c2 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 17:40:06 +0100 Subject: [PATCH 049/140] clean variation across diseases chunk --- episodes/superspreading-estimate.Rmd | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 680321fd..c0ed4c98 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -488,19 +488,19 @@ We can use the maximum likelihood estimates from `{fitdistrplus}` to compare dif :::::::::::::::::::::::::::::::::: checklist -### Evidence for variation in individual reproductive number EDIT! +### The dispersion parameter across diseases [Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153) use a 20/80 rule to show how the core principle of heterogeneous transmission is supported. -- focus on the cumulative probability distribution of the most infectious cases - + if there is a 0.2 proportion of (the most infectious) cases contributing to the 0.8 proportion of transmission, this is a highly heterogeneous distribution. (e.g. SARS) - + if there is a 0.6 proportion of (the most infectious) cases contributing to the 0.8 of transmission, this is a less heterogeneous distribution (compared to the above one, e.g. pneumonic plague) +- When the 20% most infectious cases contribute to the ~80% of transmission, this is a highly heterogeneous offspring distribution, e.g., SARS and Measles with a partially vaccinated population. + +- When the 20% most infectious cases contribute to the ~50% of transmission, this is a less heterogeneous offspring distribution, e.g. Pneumonic plague. ![Proportion of transmission expected from the most infectious 20% of cases, for 10 outbreak or surveillance data sets (triangles). Dashed lines show proportions expected under the 20/80 rule (top) and homogeneity (bottom). Superscript ‘v’ indicates a partially vaccinated population.](fig/SEE-individual-reproductive-number-fig-c.png) -The comparison of directly transmitted infections reveals the differing degree of individual variation among diseases and outbreak settings. Like SARS, measles in highly vaccinated populations shows high variation, with heterogeneous vaccination coverage as an important environmental factor contributing to this pattern. Monkeypox and smallpox viruses show intermediate variation, consistent across multiple data sets, and pneumonic plague transmission is slightly less variable. +The comparison of directly transmitted infections reveals the differing degree of individual variation among diseases and outbreak settings. Like SARS, Measles in highly vaccinated populations shows high variation with heterogeneous vaccination coverage as an important environmental factor contributing to this pattern. Monkeypox and Smallpox viruses show intermediate variation, consistent across multiple data sets, and Pneumonic plague transmission is slightly less variable. -![Expected proportion of all transmission due to a given proportion of infectious cases, where cases are ranked by infectiousness. For a homogeneous population (all ν = R0), this relation is linear. For five directly transmitted infections (based on specific k values), the line is concave owing to variation in ν.](fig/SEE-individual-reproductive-number-fig-b.png) +![Expected proportion of all transmission due to a given proportion of infectious cases, where cases are ranked by infectiousness. For a homogeneous population (all individual reproductive number equal to $R_{0}$), this relation is linear. For five directly transmitted infections (based on specific k values), the line is concave owing to variation in the individual reproductive number.](fig/SEE-individual-reproductive-number-fig-b.png) :::::::::::::::::::::::::::::::::: From 5d7103d12d050a38f5a8e5fb56be7725332a4ce4 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 18:01:05 +0100 Subject: [PATCH 050/140] clean output after review --- episodes/superspreading-estimate.Rmd | 34 +++++++++++++++------------- 1 file changed, 18 insertions(+), 16 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index c0ed4c98..7874be69 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -271,7 +271,7 @@ Does the offspring distribution is skewed or overdispersed? :::::::::::::::::: solution -```{r} +```{r,message=FALSE,warning=FALSE} ## first, make an epicontacts object ebola_contacts <- epicontacts::make_epicontacts( @@ -472,7 +472,7 @@ From the number secondary cases distribution we estimated a dispersion parameter For dispersion parameter estimates higher than one we get low distribution variance, hence, low heterogeneity. -But does this mean that the secondary case distribution does not have superspreading events (SSEs)? You will later find one challenge: How do you define an SSE threshold for Ebola? +But does this mean that the secondary case distribution does not have superspreading events (SSEs)? You will later find one additional challenge: How do you define an SSE threshold for Ebola? :::::::::::::: @@ -492,9 +492,9 @@ We can use the maximum likelihood estimates from `{fitdistrplus}` to compare dif [Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153) use a 20/80 rule to show how the core principle of heterogeneous transmission is supported. -- When the 20% most infectious cases contribute to the ~80% of transmission, this is a highly heterogeneous offspring distribution, e.g., SARS and Measles with a partially vaccinated population. +- When the 20% most infectious cases contribute to the ~80% of transmission, this is a highly heterogeneous offspring distribution ($k<0.02$), e.g., SARS and Measles with a partially vaccinated population. -- When the 20% most infectious cases contribute to the ~50% of transmission, this is a less heterogeneous offspring distribution, e.g. Pneumonic plague. +- When the 20% most infectious cases contribute to the ~50% of transmission, this is a less heterogeneous offspring distribution ($k>0.1$), e.g. Pneumonic plague. ![Proportion of transmission expected from the most infectious 20% of cases, for 10 outbreak or surveillance data sets (triangles). Dashed lines show proportions expected under the 20/80 rule (top) and homogeneity (bottom). Superscript ‘v’ indicates a partially vaccinated population.](fig/SEE-individual-reproductive-number-fig-c.png) @@ -512,14 +512,14 @@ In the presence of heterogeneous transmission, i.e., with an overdispersed offsp ![Schematic representation of contact tracing strategies. Black arrows indicate the directions of transmission, blue and Orange arrows, a successful or failed contact tracing, respectivelly. When there is evidence of individual-level transmission heterogeneity, often resulting in superspreading, backward contact tracing from the index case (blue circle) increase the probability to find the primary case (green circle) or clusters with a larger fraction of cases, potentially increasing the number of quarentined cases (yellow circles). [Claire Blackmore, 2021](https://www.paho.org/sites/default/files/backward_contact_tracing_v3_0.pdf)](fig/contact-tracing-strategies.png) -When there is evidence of individual-level variation (i.e. overdispersion), often resulting in so-called superspreading events, a large proportion of infections may be linked to a small proportion of original clusters. As a result, finding and targeting originating clusters in combination with reducing onwards infection may substantially enhance the effectiveness of tracing methods [Endo et al., 2020](https://wellcomeopenresearch.org/articles/5-239/v3). +When there is evidence of individual-level variation (i.e. overdispersion), often resulting in so-called superspreading events, a large proportion of infections may be linked to a small proportion of original clusters. As a result, finding and targeting originating clusters in combination with reducing onwards infection may substantially enhance the effectiveness of tracing methods ([Endo et al., 2020](https://wellcomeopenresearch.org/articles/5-239/v3)). Empirical evidence focused on evaluating the efficiency of backward tracing lead to 42% more cases identified than forward tracing supporting its implementation when rigorous suppression of transmission is justified ([Raymenants et al., 2022](https://www.nature.com/articles/s41467-022-32531-6)) ## Proportion of events in a given cluster size -By looking at the tail of the probability offspring distribution, we can identify the size of the cluster of secondary infections. The probability that a cluster of secondary infections caused by a primary case identified by backward tracing has a size of $X$ or larger ([Endo et al., 2020](https://wellcomeopenresearch.org/articles/5-239/v3)). +Using `{superspreading}`, we can calculate the probability of having a cluster of secondary infections caused by a primary case identified by backward tracing of size $X$ or larger ([Endo et al., 2020](https://wellcomeopenresearch.org/articles/5-239/v3)). ```{r} # estimate the probability of @@ -583,16 +583,16 @@ The probability of having clusters of five people is 1.8%. At this stage, given ### Does Ebola have any superspreading event? -[Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153) propose a general protocol for defining a superspreading event (SSE). If the number of secondary infections caused by each case, $Z$, follows a negative binomial distribution ($R_{o}, k$): +[Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153) propose a general protocol for defining a superspreading event (SSE). If the number of secondary infections caused by each case, $Z$, follows a negative binomial distribution ($R, k$): -- We define an SSE as any infected individual who infects more than Z(n) others, where Z(n) is the nth percentile of the Poisson(R) distribution. +- We define an SSE as any infected individual who infects more than $Z(n)$ others, where $Z(n)$ is the nth percentile of the $Poisson(R)$ distribution. - A 99th-percentile SSE is then any case causing more infections than would occur in 99% of infectious histories in a homogeneous population Using the corresponding distribution function, estimate the SSE threshold to define a SSE for the Ebola offspring distribution estimates for the `ebola_sim_clean` object from `{outbreaks}` package. ::::::::::::::::: hint -In a Poisson distribution, the lambda or rate parameter are equal to the estimated mean from a negative binomial distribution. You can explore this in [The distribution zoo](https://ben18785.shinyapps.io/distribution-zoo/) shiny app. +In a Poisson distribution, the **lambda** or **rate** parameter are equal to the estimated **mean** from a negative binomial distribution. You can explore this in [The distribution zoo](https://ben18785.shinyapps.io/distribution-zoo/) shiny app. ::::::::::::::::: @@ -606,22 +606,24 @@ ebola_mu_mid <- ebola_offspring$estimate["mu"] # get upper 95% CI ebola_mu_upper <- ebola_mu_mid + offspring_fit$sd[["mu"]] * qnorm(0.975) -# get 99th-percentile from poisson distribution with mean = mu +# get 99th-percentile from poisson distribution +# with mean equal to mu qpois( p = 0.99, lambda = ebola_mu_mid ) -# get 99th-percentile from poisson distribution with mean = mu upper 95% CI +# get 99th-percentile from poisson distribution +# with mean = mu upper 95% CI qpois( p = 0.99, lambda = ebola_mu_upper ) ``` -These values are closer to the ones reported by [Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153). See figure below: +These values are close to the ones reported by [Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153). See figure below: -![Reported superspreading events (SSEs; diamonds) relative to estimated reproductive number R (squares) for twelve directly transmitted infections. Lines show 5–95 percentile range of Z∼Poisson(R), and crosses show the 99th-percentile proposed as threshold for SSEs. Stars represent SSEs caused by more than one source case. ‘Other’ diseases are: 1, Streptococcus group A; 2, Lassa fever; 3, Mycoplasma pneumonia; 4, pneumonic plague; 5, tuberculosis. R is not shown for ‘other’ diseases, and is off-scale for monkeypox.](fig/SEE-individual-reproductive-number-fig-d.png) +![Reported superspreading events (SSEs; diamonds) relative to estimated reproductive number R (squares) for twelve directly transmitted infections. Lines show 5–95 percentile range of the number of secondary cases following a Poisson distribution with lambda equal to $R$ ($Z∼Poisson(R)$), and crosses show the 99th-percentile proposed as threshold for SSEs. Stars represent SSEs caused by more than one source case. ‘Other’ diseases are: 1, Streptococcus group A; 2, Lassa fever; 3, Mycoplasma pneumonia; 4, pneumonic plague; 5, tuberculosis. R is not shown for ‘other’ diseases, and is off-scale for monkeypox.](fig/SEE-individual-reproductive-number-fig-d.png) ::::::::::::::::: @@ -669,7 +671,7 @@ sars_params ::::::::::::::::::::: solution -```{r} +```{r,message=FALSE,warning=FALSE} #' estimate for ebola -------------- ebola_epiparameter <- epiparameter::epidist_db( @@ -713,9 +715,9 @@ proportion_transmission( ) ``` -Among Ebola, SARS, and MERS, MERS has the lowest percent of cases (2.1%) responsible of the 80% of the transmission, representative of highly overdispersed offspring distributions. +MERS has the lowest percent of cases (2.1%) responsible of the 80% of the transmission, representative of highly overdispersed offspring distributions. -Among them, Ebola has the highest percent of cases (43%) responsible of the 80% of the transmission. This is representative of offspring distributions with high dispersion parameters. +Ebola has the highest percent of cases (43%) responsible of the 80% of the transmission. This is representative of offspring distributions with high dispersion parameters. ::::::::::::::::::::: From 8834aa2a782f43bd9bde9385c69aba8a8390532e Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 18:01:15 +0100 Subject: [PATCH 051/140] add keypoints --- episodes/superspreading-estimate.Rmd | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 7874be69..14b889ba 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -747,9 +747,9 @@ The [Going viral](https://kucharski.substack.com/p/going-viral) post from Adam K ::::::::::::::::::::::::::::::::::::: keypoints -- Use `{epicontacts}` -- Use `{fitdistrplus}` -- Use `{superspreading}` to +- Use `{epicontacts}` to calculate the number of secondary cases cause by a particular individual from linelist and contact data. +- Use `{fitdistrplus}` to empirically estimate the offspring distribution from the number of secondary cases distribution. +- Use `{superspreading}` to estimate the probability of having clusters of a given size from primary cases and inform contact tracing efforts. :::::::::::::::::::::::::::::::::::::::::::::::: From eb0150e72e3f3cd5850abb68ce4ce8a504889840 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 19:53:48 +0100 Subject: [PATCH 052/140] test plot from epiparameter and superspreading --- episodes/superspreading-estimate.Rmd | 115 ++++++++++++++++++++++----- 1 file changed, 97 insertions(+), 18 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 14b889ba..764fd044 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -492,15 +492,103 @@ We can use the maximum likelihood estimates from `{fitdistrplus}` to compare dif [Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153) use a 20/80 rule to show how the core principle of heterogeneous transmission is supported. -- When the 20% most infectious cases contribute to the ~80% of transmission, this is a highly heterogeneous offspring distribution ($k<0.02$), e.g., SARS and Measles with a partially vaccinated population. +- When the 20% most infectious cases contribute to the ~80% of transmission, this is a highly heterogeneous offspring distribution ($k<0.03$), e.g., SARS. -- When the 20% most infectious cases contribute to the ~50% of transmission, this is a less heterogeneous offspring distribution ($k>0.1$), e.g. Pneumonic plague. +- When the 20% most infectious cases contribute to the ~50% of transmission, this is a less heterogeneous offspring distribution ($k \sim 1$), e.g. Pneumonic plague. -![Proportion of transmission expected from the most infectious 20% of cases, for 10 outbreak or surveillance data sets (triangles). Dashed lines show proportions expected under the 20/80 rule (top) and homogeneity (bottom). Superscript ‘v’ indicates a partially vaccinated population.](fig/SEE-individual-reproductive-number-fig-c.png) + -The comparison of directly transmitted infections reveals the differing degree of individual variation among diseases and outbreak settings. Like SARS, Measles in highly vaccinated populations shows high variation with heterogeneous vaccination coverage as an important environmental factor contributing to this pattern. Monkeypox and Smallpox viruses show intermediate variation, consistent across multiple data sets, and Pneumonic plague transmission is slightly less variable. +```{r,message=FALSE,warning=FALSE} +library(epiparameter) +library(tidyverse) + +epidist_string <- epidist_db( + epi_dist = "offspring distribution" +) %>% + list_distributions() %>% + dplyr::select(disease) %>% + distinct() + +across_offspring <- epidist_string %>% + mutate( + epidist_out = + map( + .x = disease, + .f = epiparameter::epidist_db, + epi_dist = "offspring distribution", + single_epidist = TRUE) + ) %>% + mutate( + epidist_params = + map( + .x = epidist_out, + .f = epiparameter::get_parameters + ) + ) %>% + unnest_wider(col = epidist_params) %>% + expand_grid(percent_transmission = seq(0.01,1,0.01)) %>% + # mutate(percent_transmission = 0.8) %>% + mutate( + transmission_output = + pmap( + .l = select(., R = mean, k = dispersion, percent_transmission), + .f = superspreading::proportion_transmission, + format_prop = FALSE + ) + ) %>% + unnest_wider(col = transmission_output) %>% + rowwise() %>% + mutate(percent_cases = sum(c_across(cols = starts_with("prop_")),na.rm = T)) %>% + select(-starts_with("prop_")) + +across_offspring_tip <- across_offspring %>% + group_by(disease) %>% + filter(percent_transmission < 0.98, percent_transmission > 0.85) %>% + slice_max(percent_transmission) %>% + # filter(percent_transmission == max(percent_transmission)) %>% + ungroup() %>% + # filter(!str_detect(disease,"SARS|Mpox")) %>% + mutate(disease = case_when( + str_detect(disease,"Hantavirus") ~ "Hantavirus", + str_detect(disease,"Ebola") ~ "Ebola", + TRUE ~ disease + )) + +across_offspring %>% + # as_tibble() + ggplot() + + geom_line( + aes( + x = percent_cases, + y = percent_transmission, + color = dispersion, + group = disease + ) + ) + + geom_text( + data = across_offspring_tip, + aes( + x = percent_cases, + y = percent_transmission, + label = disease + ), + hjust = 0.0, + vjust = 1.0, + angle = 25, + size = 3 + ) + + scale_y_continuous(breaks = scales::breaks_pretty(n = 5)) + + colorspace::scale_color_continuous_diverging(trans = "log10") + + labs( + x = "Proportion of infectious cases", + y = "Expected proportion of transmission", + color = "Dispersion\nparameter (k)" + ) + + geom_hline(aes(yintercept = 0.8),lty = 3) + + geom_vline(aes(xintercept = 0.2),lty = 2) + + coord_fixed(ratio = 1) +``` -![Expected proportion of all transmission due to a given proportion of infectious cases, where cases are ranked by infectiousness. For a homogeneous population (all individual reproductive number equal to $R_{0}$), this relation is linear. For five directly transmitted infections (based on specific k values), the line is concave owing to variation in the individual reproductive number.](fig/SEE-individual-reproductive-number-fig-b.png) :::::::::::::::::::::::::::::::::: @@ -546,10 +634,10 @@ We can also use this number to prevent gathering of certain sized to reduce the Use the Ebola estimated parameters for `ebola_sim_clean` object from `{outbreaks}` package. -Evaluate if the contact tracing efforts would be benefit by a backward strategy to increase their probability of contain and quarantine an increased proportion of contacts. - Calculate the probability of having a cluster of secondary infections caused by a primary case identified by backward tracing of size 5, 10, 15 or larger. +Would implementing a backward strategy increase the probability of containing and quarantining more onward cases? + :::::::::::::::: hint Review how we estimated the probability of having clusters of a fixed size, given an offspring distribution mean and dispersion parameters, using the `superspreading::proportion_cluster_size()` function. @@ -603,8 +691,6 @@ To get the quantile value for the 99th-percentile we need to use the [density fu ```{r} # get mean ebola_mu_mid <- ebola_offspring$estimate["mu"] -# get upper 95% CI -ebola_mu_upper <- ebola_mu_mid + offspring_fit$sd[["mu"]] * qnorm(0.975) # get 99th-percentile from poisson distribution # with mean equal to mu @@ -612,18 +698,11 @@ qpois( p = 0.99, lambda = ebola_mu_mid ) - -# get 99th-percentile from poisson distribution -# with mean = mu upper 95% CI -qpois( - p = 0.99, - lambda = ebola_mu_upper -) ``` -These values are close to the ones reported by [Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153). See figure below: +Compare this values with the ones reported by [Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153). See figure below: -![Reported superspreading events (SSEs; diamonds) relative to estimated reproductive number R (squares) for twelve directly transmitted infections. Lines show 5–95 percentile range of the number of secondary cases following a Poisson distribution with lambda equal to $R$ ($Z∼Poisson(R)$), and crosses show the 99th-percentile proposed as threshold for SSEs. Stars represent SSEs caused by more than one source case. ‘Other’ diseases are: 1, Streptococcus group A; 2, Lassa fever; 3, Mycoplasma pneumonia; 4, pneumonic plague; 5, tuberculosis. R is not shown for ‘other’ diseases, and is off-scale for monkeypox.](fig/SEE-individual-reproductive-number-fig-d.png) +![Reported superspreading events (SSEs; diamonds) relative to estimated reproductive number R (squares) for twelve directly transmitted infections. Lines show 5–95 percentile range of the number of secondary cases following a Poisson distribution with lambda equal to the reproduction number ($Z∼Poisson(R)$), and crosses show the 99th-percentile proposed as threshold for SSEs. Stars represent SSEs caused by more than one source case. ‘Other’ diseases are: 1, Streptococcus group A; 2, Lassa fever; 3, Mycoplasma pneumonia; 4, pneumonic plague; 5, tuberculosis. R is not shown for ‘other’ diseases, and is off-scale for monkeypox.](fig/SEE-individual-reproductive-number-fig-d.png) ::::::::::::::::: From dfd86119abdff03bf049d34b7cf09ed2935be869 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 20:00:24 +0100 Subject: [PATCH 053/140] fix text and figure after review --- episodes/superspreading-estimate.Rmd | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 764fd044..b9a92b94 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -492,13 +492,13 @@ We can use the maximum likelihood estimates from `{fitdistrplus}` to compare dif [Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153) use a 20/80 rule to show how the core principle of heterogeneous transmission is supported. -- When the 20% most infectious cases contribute to the ~80% of transmission, this is a highly heterogeneous offspring distribution ($k<0.03$), e.g., SARS. +- When the 20% most infectious cases contribute to the ~90% of transmission, this is a highly heterogeneous offspring distribution ($k<0.3$), e.g., SARS. -- When the 20% most infectious cases contribute to the ~50% of transmission, this is a less heterogeneous offspring distribution ($k \sim 1$), e.g. Pneumonic plague. +- When the 20% most infectious cases contribute to the ~50% of transmission, this is a less heterogeneous offspring distribution ($k > 3$), e.g. Ebola. -```{r,message=FALSE,warning=FALSE} +```{r,message=FALSE,warning=FALSE,echo=FALSE} library(epiparameter) library(tidyverse) @@ -580,11 +580,11 @@ across_offspring %>% scale_y_continuous(breaks = scales::breaks_pretty(n = 5)) + colorspace::scale_color_continuous_diverging(trans = "log10") + labs( - x = "Proportion of infectious cases", + x = "Proportion of infectious cases (ranked)", y = "Expected proportion of transmission", color = "Dispersion\nparameter (k)" ) + - geom_hline(aes(yintercept = 0.8),lty = 3) + + # geom_hline(aes(yintercept = 0.8),lty = 3) + geom_vline(aes(xintercept = 0.2),lty = 2) + coord_fixed(ratio = 1) ``` From 892fa23351c757aadb3fce2cd04d13f904d7d1ec Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 20:15:00 +0100 Subject: [PATCH 054/140] clarify challenges questions + text and subtitles --- episodes/superspreading-estimate.Rmd | 12 +++++------- 1 file changed, 5 insertions(+), 7 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index b9a92b94..b7578f42 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -261,7 +261,7 @@ In epidemiology, [negative binomial](https://en.wikipedia.org/wiki/Negative_bino Calculate the distribution of secondary cases for Ebola using the `ebola_sim_clean` object from `{outbreaks}` package. -Does the offspring distribution is skewed or overdispersed? +Does the offspring distribution of Ebola is skewed or overdispersed? :::::::::::::::::: hint @@ -433,7 +433,7 @@ Use the distribution of secondary cases from the `ebola_sim_clean` object from ` Fit a negative binomial distribution to estimate the mean and dispersion parameter of the offspring distribution. -Does the estimated dispersion parameter provide evidence of transmission heterogeneity? +Does the estimated dispersion parameter of Ebola provide evidence of transmission heterogeneity? :::::::::::::: hint @@ -492,12 +492,10 @@ We can use the maximum likelihood estimates from `{fitdistrplus}` to compare dif [Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153) use a 20/80 rule to show how the core principle of heterogeneous transmission is supported. -- When the 20% most infectious cases contribute to the ~90% of transmission, this is a highly heterogeneous offspring distribution ($k<0.3$), e.g., SARS. +- When the 20% most infectious cases contribute to the 80% of transmission (or more), this is a highly heterogeneous offspring distribution ($k<0.3$), e.g., SARS. - When the 20% most infectious cases contribute to the ~50% of transmission, this is a less heterogeneous offspring distribution ($k > 3$), e.g. Ebola. - - ```{r,message=FALSE,warning=FALSE,echo=FALSE} library(epiparameter) library(tidyverse) @@ -605,7 +603,7 @@ When there is evidence of individual-level variation (i.e. overdispersion), ofte Empirical evidence focused on evaluating the efficiency of backward tracing lead to 42% more cases identified than forward tracing supporting its implementation when rigorous suppression of transmission is justified ([Raymenants et al., 2022](https://www.nature.com/articles/s41467-022-32531-6)) -## Proportion of events in a given cluster size +## Probability of cases in a given cluster Using `{superspreading}`, we can calculate the probability of having a cluster of secondary infections caused by a primary case identified by backward tracing of size $X$ or larger ([Endo et al., 2020](https://wellcomeopenresearch.org/articles/5-239/v3)). @@ -636,7 +634,7 @@ Use the Ebola estimated parameters for `ebola_sim_clean` object from `{outbreaks Calculate the probability of having a cluster of secondary infections caused by a primary case identified by backward tracing of size 5, 10, 15 or larger. -Would implementing a backward strategy increase the probability of containing and quarantining more onward cases? +Would implementing a backward strategy at this stage of the Ebola outbreak increase the probability of containing and quarantining more onward cases? :::::::::::::::: hint From f7258e09ced20953474839dff9ca2011d05ee2c3 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 20:23:25 +0100 Subject: [PATCH 055/140] fix lintr checks --- episodes/superspreading-estimate.Rmd | 66 +++++++++++++--------------- 1 file changed, 31 insertions(+), 35 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index b7578f42..c6b8b5ab 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -279,10 +279,6 @@ ebola_contacts <- contacts = ebola_sim_clean$contacts ) -# visualise contact tree -# (this network can overload your session!) -#epicontacts::vis_epicontacts(ebola_contacts) - # count secondary cases ebola_infector_secondary <- ebola_contacts %>% @@ -301,10 +297,6 @@ ebola_secondary <- ebola_contacts %>% replace = list(secondary_cases = 0) ) -# arrange in descendant order of secondary cases -# ebola_secondary %>% -# arrange(desc(secondary_cases)) - ## plot the distribution ebola_secondary %>% ggplot(aes(secondary_cases)) + @@ -374,7 +366,7 @@ fit_density <- mu = offspring_fit$estimate[["mu"]], size = mid ) - ) %>% + ) %>% mutate(label = "Fitted\nnegative\nbinomial\ndistribution") # plot offspring distribution with density fit @@ -507,53 +499,57 @@ epidist_string <- epidist_db( dplyr::select(disease) %>% distinct() -across_offspring <- epidist_string %>% +across_offspring <- epidist_string %>% mutate( - epidist_out = + epidist_out = map( .x = disease, .f = epiparameter::epidist_db, epi_dist = "offspring distribution", - single_epidist = TRUE) - ) %>% + single_epidist = TRUE + ) + ) %>% mutate( - epidist_params = + epidist_params = map( .x = epidist_out, .f = epiparameter::get_parameters ) - ) %>% - unnest_wider(col = epidist_params) %>% - expand_grid(percent_transmission = seq(0.01,1,0.01)) %>% - # mutate(percent_transmission = 0.8) %>% + ) %>% + unnest_wider(col = epidist_params) %>% + expand_grid(percent_transmission = seq(0.01, 1, 0.01)) %>% + # mutate(percent_transmission = 0.8) %>% mutate( - transmission_output = + transmission_output = pmap( .l = select(., R = mean, k = dispersion, percent_transmission), .f = superspreading::proportion_transmission, format_prop = FALSE ) - ) %>% + ) %>% unnest_wider(col = transmission_output) %>% - rowwise() %>% - mutate(percent_cases = sum(c_across(cols = starts_with("prop_")),na.rm = T)) %>% + rowwise() %>% + mutate( + percent_cases = + sum( + c_across(cols = starts_with("prop_")), + na.rm = TRUE + ) + ) %>% select(-starts_with("prop_")) -across_offspring_tip <- across_offspring %>% - group_by(disease) %>% - filter(percent_transmission < 0.98, percent_transmission > 0.85) %>% - slice_max(percent_transmission) %>% - # filter(percent_transmission == max(percent_transmission)) %>% - ungroup() %>% - # filter(!str_detect(disease,"SARS|Mpox")) %>% +across_offspring_tip <- across_offspring %>% + group_by(disease) %>% + filter(percent_transmission < 0.98, percent_transmission > 0.85) %>% + slice_max(percent_transmission) %>% + ungroup() %>% mutate(disease = case_when( - str_detect(disease,"Hantavirus") ~ "Hantavirus", - str_detect(disease,"Ebola") ~ "Ebola", + str_detect(disease, stringr::fixed("Hantavirus")) ~ "Hantavirus", + str_detect(disease, stringr::fixed("Ebola")) ~ "Ebola", TRUE ~ disease )) -across_offspring %>% - # as_tibble() +across_offspring %>% ggplot() + geom_line( aes( @@ -583,7 +579,7 @@ across_offspring %>% color = "Dispersion\nparameter (k)" ) + # geom_hline(aes(yintercept = 0.8),lty = 3) + - geom_vline(aes(xintercept = 0.2),lty = 2) + + geom_vline(aes(xintercept = 0.2), lty = 2) + coord_fixed(ratio = 1) ``` @@ -690,7 +686,7 @@ To get the quantile value for the 99th-percentile we need to use the [density fu # get mean ebola_mu_mid <- ebola_offspring$estimate["mu"] -# get 99th-percentile from poisson distribution +# get 99th-percentile from poisson distribution # with mean equal to mu qpois( p = 0.99, From c5803d34bd48fca8a014d64ce7d36265bcf3f4d5 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 20:29:15 +0100 Subject: [PATCH 056/140] clear question writing Co-authored-by: Adam Kucharski --- episodes/superspreading-estimate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index c6b8b5ab..07473915 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -12,7 +12,7 @@ webshot::install_phantomjs(force = TRUE) :::::::::::::::::::::::::::::::::::::: questions -- How to evaluate for transmission heterogeneity from contact tracing data? +- How can we estimate individual-level variation in transmission (i.e. superspreading potential) from contact tracing data? - How to account for transmission heterogeneity in decision-making? :::::::::::::::::::::::::::::::::::::::::::::::: From 7716b51c1a03dfd440ffcad4b06f2990dfe91a2b Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 21:03:45 +0100 Subject: [PATCH 057/140] fix code clarity --- episodes/superspreading-simulate.Rmd | 56 +++++++++++++--------------- 1 file changed, 25 insertions(+), 31 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 1e41cb06..92b57bec 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -28,8 +28,6 @@ Learners should familiarise themselves with following concept dependencies befor ::::::::::::::::::::::::::::::::: -## questions - ## Introduction @@ -42,6 +40,7 @@ We are going to use `{purrr}` ```{r,message=FALSE,warning=FALSE} library(epichains) +library(epiparameter) library(tidyverse) ``` @@ -110,22 +109,18 @@ lambda = rate = mean ## Get generation time -```{r} -library(epiparameter) - +```{r,message=FALSE,warning=FALSE} serial_inverval <- epidist_db( disease = "mers", epi_dist = "serial", single_epidist = TRUE ) - -serial_inverval ``` Similar to the `{cfr}` interface for `{epiparameter}` ```r -function(x) generate(x = serial_inverval,times = x) +function(x) generate(x = serial_inverval, times = x) ``` ## Simulate a single chain @@ -141,8 +136,7 @@ simulate_chains( size = mers_offspring["dispersion"], # generation generation_time = function(x) generate(x = serial_inverval, times = x) -) %>% - as_tibble() +) ``` the output dataframe collects @@ -164,9 +158,9 @@ initial_cases <- 1 ``` -:::::::::::::::::::::::::::::: checkpoint +:::::::::::::::::::::::::::::: checklist -### Iteration using {purrr} +### Iteration using purrr [Iteration](https://r4ds.hadley.nz/iteration.html) aims to repeatedly perform the same action on different objects. @@ -181,8 +175,8 @@ To get multiple chains, we need to apply the `simulate_chains()` function to eac Let's use `map()`: ```{r} -simulated_chains_list <- - map( +simulated_chains_map <- + map_df( # vector of numbers (chain IDs) .x = seq_len(number_chains), # function to iterate to each chain ID number @@ -202,15 +196,11 @@ simulated_chains_list <- mutate(chain_id = sim) } ) - -sim_chains_bind <- bind_rows(simulated_chains_list) - -sim_chains_bind ``` ```{r} # view infectee number per simulation -sim_chains_bind %>% +simulated_chains_map %>% as_tibble() %>% count(chain_id, sort = TRUE) ``` @@ -218,7 +208,7 @@ sim_chains_bind %>% ```{r,echo=FALSE} #### get simulated chain with more infections -------------------------------- -chains_subgroup <- sim_chains_bind %>% +chains_subgroup <- simulated_chains_map %>% as_tibble() %>% group_by(chain_id) %>% distinct(infector_id) %>% @@ -226,7 +216,7 @@ chains_subgroup <- sim_chains_bind %>% filter(n < 5, n >= 3) %>% pull(chain_id) -chain_to_observe <- sim_chains_bind %>% +chain_to_observe <- simulated_chains_map %>% as_tibble() %>% count(chain_id, sort = TRUE) %>% filter( @@ -240,15 +230,15 @@ chain_to_observe <- sim_chains_bind %>% pull(chain_id) ``` -get simulated chain `r chain_to_observe` with more infections +Let's observe closely the simulated `chain_id` number `r chain_to_observe` with three generations. get epichain summary ```{r} #### get epichain summary ---------------------------------------------------- -simulated_chains_list %>% - pluck(chain_to_observe) +simulated_chains_map %>% + filter(chain_id == chain_to_observe) ``` the `NA` includes the infector of the index case, for that reason (known) cases @@ -258,9 +248,9 @@ infectee-infector data frame ```{r} #### infector-infectee data frame -------------------------------------------- -simulated_chains_list %>% - pluck(chain_to_observe) %>% - as.data.frame() +simulated_chains_map %>% + filter(chain_id == chain_to_observe) %>% + as_tibble() ``` @@ -269,7 +259,7 @@ simulated_chains_list %>% ```{r} # daily aggregate of cases simulated_chains_day <- - sim_chains_bind %>% + simulated_chains_map %>% as_tibble() %>% mutate(chain_id = as_factor(chain_id)) %>% # Daily number of cases for each simulation @@ -279,7 +269,9 @@ simulated_chains_day <- group_by(chain_id) %>% mutate(cases_cumsum = cumsum(cases)) %>% ungroup() +``` +```{r} # Summarise the chain length and size sim_chains_max <- simulated_chains_day %>% @@ -291,7 +283,9 @@ sim_chains_max <- cases_total = max(cases_cumsum) ) %>% ungroup() +``` +```{r} # Visualize transmission chains by cumulative cases ggplot() + geom_line( @@ -320,7 +314,7 @@ ggplot() + NULL ``` -```{r,eval=FALSE} +```{r,eval=FALSE,echo=FALSE} # Visualize transmission chains by daily cases ggplot() + geom_line( @@ -351,7 +345,7 @@ We invite you to read the vignette on [Projecting infectious disease incidence: Evaluate for ebola with know data from previous outbreaks -```{r} +```{r,message=FALSE,warning=FALSE} epidist_db( disease = "ebola", epi_dist = "offspring", @@ -376,7 +370,7 @@ Christian Althaus data from Fayre et al on ebola -```{r} +```{r,message=FALSE,warning=FALSE} # Number of individuals in the trees n <- 152 # Number of secondary cases for all individuals From f89474c3b34bb3f0615d94d8b73c672945598df0 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 22:28:27 +0100 Subject: [PATCH 058/140] clean code output --- episodes/superspreading-simulate.Rmd | 31 +++++++++++++++++++++++++++- 1 file changed, 30 insertions(+), 1 deletion(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 92b57bec..7b294069 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -115,6 +115,13 @@ serial_inverval <- epidist_db( epi_dist = "serial", single_epidist = TRUE ) + +plot(serial_inverval,day_range = 0:25) + +serial_inverval$summary_stats %>% + as_tibble() %>% + select(mean,sd) %>% + distinct(.keep_all = TRUE) ``` Similar to the `{cfr}` interface for `{epiparameter}` @@ -125,7 +132,7 @@ function(x) generate(x = serial_inverval, times = x) ## Simulate a single chain -```{r} +```{r,message=FALSE,warning=FALSE} simulate_chains( # simulation controls index_cases = 5, @@ -314,6 +321,24 @@ ggplot() + NULL ``` +```{r} +# chains that reached the 100-case threshold +sim_chains_max %>% + arrange(desc(day_max)) %>% + filter(cases_total>100) +``` + +```{r} +# proportion that reached the 100-case threshold +sim_chains_max %>% + arrange(desc(day_max)) %>% + filter(cases_total>100) %>% + count(name = "chains_theshold") %>% + mutate(chains_number = number_chains) %>% + mutate(chains_percentage = chains_theshold / chains_number*100) +``` + + ```{r,eval=FALSE,echo=FALSE} # Visualize transmission chains by daily cases ggplot() + @@ -412,6 +437,10 @@ Calculate probabilities for Ebola using data from epiparameter using `{superspre :::::::::::::::::: hint +```{r,message=FALSE,warning=FALSE} +library(superspreading) +``` + ```{r} # estimate probability to contain probability_contain( From a3aa244a86294c4550fbc96fc847aa0d10c8edbf Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 22:45:19 +0100 Subject: [PATCH 059/140] pass lintr checks --- episodes/superspreading-simulate.Rmd | 28 ++++++++++++++-------------- 1 file changed, 14 insertions(+), 14 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 7b294069..9f72bf26 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -116,11 +116,11 @@ serial_inverval <- epidist_db( single_epidist = TRUE ) -plot(serial_inverval,day_range = 0:25) +plot(serial_inverval, day_range = 0:25) -serial_inverval$summary_stats %>% - as_tibble() %>% - select(mean,sd) %>% +serial_inverval$summary_stats %>% + as_tibble() %>% + select(mean, sd) %>% distinct(.keep_all = TRUE) ``` @@ -256,7 +256,7 @@ infectee-infector data frame #### infector-infectee data frame -------------------------------------------- simulated_chains_map %>% - filter(chain_id == chain_to_observe) %>% + filter(chain_id == chain_to_observe) %>% as_tibble() ``` @@ -323,19 +323,19 @@ ggplot() + ```{r} # chains that reached the 100-case threshold -sim_chains_max %>% - arrange(desc(day_max)) %>% - filter(cases_total>100) +sim_chains_max %>% + arrange(desc(day_max)) %>% + filter(cases_total > 100) ``` ```{r} # proportion that reached the 100-case threshold -sim_chains_max %>% - arrange(desc(day_max)) %>% - filter(cases_total>100) %>% - count(name = "chains_theshold") %>% - mutate(chains_number = number_chains) %>% - mutate(chains_percentage = chains_theshold / chains_number*100) +sim_chains_max %>% + arrange(desc(day_max)) %>% + filter(cases_total > 100) %>% + count(name = "chains_theshold") %>% + mutate(chains_number = number_chains) %>% + mutate(chains_percentage = chains_theshold / chains_number * 100) ``` From 8f3f1cf8e76adb7e97532da37d9306a6aca93eba Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 22:56:59 +0100 Subject: [PATCH 060/140] update to not superseded functions --- episodes/superspreading-simulate.Rmd | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 9f72bf26..588bfeb8 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -183,7 +183,7 @@ Let's use `map()`: ```{r} simulated_chains_map <- - map_df( + map( # vector of numbers (chain IDs) .x = seq_len(number_chains), # function to iterate to each chain ID number @@ -202,7 +202,8 @@ simulated_chains_map <- # creates a column with the chain ID number mutate(chain_id = sim) } - ) + ) %>% + list_rbind() ``` ```{r} From 826eb63fe325db3090431ba349d8a839e156eb29 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Sun, 7 Apr 2024 22:57:32 +0100 Subject: [PATCH 061/140] pass lintr edits --- episodes/superspreading-simulate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 588bfeb8..428d7da5 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -202,7 +202,7 @@ simulated_chains_map <- # creates a column with the chain ID number mutate(chain_id = sim) } - ) %>% + ) %>% list_rbind() ``` From 32b451943df2ee0cb0bc7776c8bd3d06f64c67c7 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 9 Apr 2024 15:31:14 +0100 Subject: [PATCH 062/140] add spoiler on simulated over observed cases --- episodes/superspreading-simulate.Rmd | 69 ++++++++++++++++++++++++++-- 1 file changed, 65 insertions(+), 4 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 428d7da5..230674e5 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -316,10 +316,7 @@ ggplot() + ), show.legend = FALSE ) + - geom_hline(aes(yintercept = 100), lty = 2) + - # xlim(0,150) + - # ylim(0,300) + - NULL + geom_hline(aes(yintercept = 100), lty = 2) ``` ```{r} @@ -355,6 +352,70 @@ ggplot() + ) ``` +::::::::::::::::::::::::::::::::: spoiler + +### Observed vs simulated cases + +Let's overlap the cumulative number of observed cases using the linelist object from the `mers_korea_2015` dataset of the `{outbreaks}` R package. To prepare the dataset we use `{incidence2}` to convert the linelist to an `` object, complete the missing dates of the time series with `complete_dates()` + +```{r} +library(outbreaks) +library(incidence2) + +mers_cumcases <- mers_korea_2015$linelist %>% + # incidence2 workflow + incidence2::incidence(date_index = "dt_onset") %>% + incidence2::complete_dates() %>% + # wrangling using {dplyr} + mutate(count_cumsum = cumsum(count)) %>% + rownames_to_column(var = "day") %>% + mutate(day = as.numeric(day)) +``` + +```{r} +# plot the incidence2 object +plot(mers_cumcases) +``` + + +```{r,echo=FALSE} +# Observed cases vs Simulated transmission chains +ggplot() + + geom_line( + data = simulated_chains_day, + mapping = aes( + x = day, + y = cases_cumsum, + group = chain_id + ), + color = "grey", + show.legend = FALSE + ) + + geom_point( + data = sim_chains_max, + mapping = aes( + x = day_max, + y = cases_total, + group = chain_id, + color = chain_id + ), + color = "grey", + show.legend = FALSE + ) + + geom_hline(aes(yintercept = 100), lty = 2) + + geom_line( + data = mers_cumcases, + mapping = aes( + x = day, + y = count_cumsum + ), + show.legend = FALSE + ) +``` + +::::::::::::::::::::::::::::::::: + + :::::::::::::::::::::: testimonial ### Early spread projections From b2a6564af7fcbf3f41393de9a9d45879d7a71135 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 9 Apr 2024 15:41:09 +0100 Subject: [PATCH 063/140] add labels to ggplots --- episodes/superspreading-simulate.Rmd | 53 ++++++++++++++++++---------- 1 file changed, 34 insertions(+), 19 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 230674e5..3d00733e 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -316,7 +316,11 @@ ggplot() + ), show.legend = FALSE ) + - geom_hline(aes(yintercept = 100), lty = 2) + geom_hline(aes(yintercept = 100), lty = 2) + + labs( + x = "Day", + y = "Cumulative cases" + ) ``` ```{r} @@ -380,36 +384,47 @@ plot(mers_cumcases) ```{r,echo=FALSE} # Observed cases vs Simulated transmission chains +mers_cumcases_type <- + mers_cumcases %>% + mutate(type = "Observed") +simulated_chains_day_type <- + simulated_chains_day %>% + mutate(type = "Simulated") + ggplot() + geom_line( - data = simulated_chains_day, + data = simulated_chains_day_type, mapping = aes( x = day, y = cases_cumsum, - group = chain_id - ), - color = "grey", - show.legend = FALSE - ) + - geom_point( - data = sim_chains_max, - mapping = aes( - x = day_max, - y = cases_total, group = chain_id, - color = chain_id - ), - color = "grey", - show.legend = FALSE + color = type + ) ) + + # geom_point( + # data = sim_chains_max, + # mapping = aes( + # x = day_max, + # y = cases_total, + # group = chain_id + # ), + # color = "grey", + # show.legend = FALSE + # ) + geom_hline(aes(yintercept = 100), lty = 2) + geom_line( - data = mers_cumcases, + data = mers_cumcases_type, mapping = aes( x = day, - y = count_cumsum + y = count_cumsum, + color = type ), - show.legend = FALSE + size = 1 + ) + + labs( + x = "Day", + y = "Cumulative cases", + color = "Type" ) ``` From 9129769f87d6b919a2025152f2f54b360575db01 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 9 Apr 2024 15:44:58 +0100 Subject: [PATCH 064/140] focus on map in the checkpoint callout --- episodes/superspreading-simulate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 3d00733e..5e4272d5 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -171,7 +171,7 @@ initial_cases <- 1 [Iteration](https://r4ds.hadley.nz/iteration.html) aims to repeatedly perform the same action on different objects. -Learn how to use the core `{purrr}` functions like the `map_*()` family of functions from the YouTube tutorial on [How to purrr](https://www.youtube.com/watch?v=nd-Y8b22YaQ) by Equitable Equations. +Learn how to use the core `{purrr}` functions like `map()` from the YouTube tutorial on [How to purrr](https://www.youtube.com/watch?v=nd-Y8b22YaQ) by Equitable Equations. Or if you previously used the `*apply` family of functions, visit the package vignette on [purrr base R](https://purrr.tidyverse.org/articles/base.html) shares key differences, direct translations, and examples. From 978b34ca21d9e761aa97295794ae9f7d7b8f7477 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 9 Apr 2024 15:49:46 +0100 Subject: [PATCH 065/140] clean spoiler code --- episodes/superspreading-simulate.Rmd | 11 +++++++---- 1 file changed, 7 insertions(+), 4 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 5e4272d5..50177a72 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -206,7 +206,7 @@ simulated_chains_map <- list_rbind() ``` -```{r} +```{r,echo=FALSE,eval=FALSE} # view infectee number per simulation simulated_chains_map %>% as_tibble() %>% @@ -358,11 +358,11 @@ ggplot() + ::::::::::::::::::::::::::::::::: spoiler -### Observed vs simulated cases +### Observed cases vs simulated chains Let's overlap the cumulative number of observed cases using the linelist object from the `mers_korea_2015` dataset of the `{outbreaks}` R package. To prepare the dataset we use `{incidence2}` to convert the linelist to an `` object, complete the missing dates of the time series with `complete_dates()` -```{r} +```{r,warning=FALSE,message=FALSE} library(outbreaks) library(incidence2) @@ -376,11 +376,14 @@ mers_cumcases <- mers_korea_2015$linelist %>% mutate(day = as.numeric(day)) ``` +Use `plot()` to make an incidence plot: + ```{r} # plot the incidence2 object plot(mers_cumcases) ``` +Plot the observed cumulative number of cases over the previously simulated chains. ```{r,echo=FALSE} # Observed cases vs Simulated transmission chains @@ -419,7 +422,7 @@ ggplot() + y = count_cumsum, color = type ), - size = 1 + size = 1.5 ) + labs( x = "Day", From b1fd319ef3d764bc7a34b2533d24a6dfdb0acf7e Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 9 Apr 2024 16:34:29 +0100 Subject: [PATCH 066/140] clear ggplot actions --- episodes/superspreading-simulate.Rmd | 2 ++ 1 file changed, 2 insertions(+) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 50177a72..97d84349 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -183,6 +183,7 @@ Let's use `map()`: ```{r} simulated_chains_map <- + # iterate one function across multiple numbers (chain IDs) map( # vector of numbers (chain IDs) .x = seq_len(number_chains), @@ -203,6 +204,7 @@ simulated_chains_map <- mutate(chain_id = sim) } ) %>% + # combine list outputs (for each chain ID) into a single data frame list_rbind() ``` From 869d1760664d922acf22282f2814d76abc97d056 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 9 Apr 2024 16:35:01 +0100 Subject: [PATCH 067/140] increase visibility of chains size and length --- episodes/superspreading-simulate.Rmd | 60 ++++++++++++++++------------ 1 file changed, 35 insertions(+), 25 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 97d84349..e1b8e53b 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -325,6 +325,23 @@ ggplot() + ) ``` +```{r,echo=FALSE} +sim_chains_max %>% + ggplot() + + geom_point( + aes( + x = day_max, + y = cases_total + ), + alpha = 0.25 + ) + + geom_hline(aes(yintercept = 100), lty = 2) + + labs( + x = "Length of chain", + y = "Size of chain" + ) +``` + ```{r} # chains that reached the 100-case threshold sim_chains_max %>% @@ -332,9 +349,9 @@ sim_chains_max %>% filter(cases_total > 100) ``` -```{r} +```{r,echo=FALSE,message=FALSE,warning=FALSE} # proportion that reached the 100-case threshold -sim_chains_max %>% +threshhold_summary <- sim_chains_max %>% arrange(desc(day_max)) %>% filter(cases_total > 100) %>% count(name = "chains_theshold") %>% @@ -342,21 +359,7 @@ sim_chains_max %>% mutate(chains_percentage = chains_theshold / chains_number * 100) ``` - -```{r,eval=FALSE,echo=FALSE} -# Visualize transmission chains by daily cases -ggplot() + - geom_line( - data = simulated_chains_day, - mapping = aes( - x = day, - y = cases, - group = chain_id, - color = chain_id - ), - show.legend = FALSE - ) -``` +Although most outbreaks rapidly become extinct, only `r threshhold_summary$chains_theshold` epidemic trajectories among `r threshhold_summary$chains_number` simulations (`r threshhold_summary$chains_percentage`%) can reach to more than 100 infected cases. This finding is particularly remarkable because $R_0$ is less than 1, and shows the potential for explosive outbreaks of MERS disease. ::::::::::::::::::::::::::::::::: spoiler @@ -424,10 +427,10 @@ ggplot() + y = count_cumsum, color = type ), - size = 1.5 + linewidth = 1.5 ) + labs( - x = "Day", + x = "Day since first report", y = "Cumulative cases", color = "Type" ) @@ -452,20 +455,27 @@ We invite you to read the vignette on [Projecting infectious disease incidence: Evaluate for ebola with know data from previous outbreaks +:::::::::::::: hint + +:::::::::::::: + +:::::::::::::: solution + ```{r,message=FALSE,warning=FALSE} -epidist_db( +ebola_offspring <- epidist_db( disease = "ebola", epi_dist = "offspring", single_epidist = TRUE ) -epidist_db( +ebola_serial <- epidist_db( disease = "ebola", epi_dist = "serial interval", single_epidist = TRUE ) ``` +:::::::::::::: ::::::::::::::::::::::::: @@ -526,8 +536,8 @@ library(superspreading) ```{r} # estimate probability to contain probability_contain( - R = offspring_fit$estimate["mu"], - k = offspring_fit$estimate["size"], + R = mers_offspring["mean"], + k = mers_offspring["dispersion"], num_init_infect = 1, case_threshold = 100 ) @@ -535,8 +545,8 @@ probability_contain( # Estimate probability of large outbreak # with 5 independent imported cases probability_epidemic( - R = offspring_fit$estimate["mu"], - k = offspring_fit$estimate["size"], + R = mers_offspring["mean"], + k = mers_offspring["dispersion"], num_init_infect = 5 ) ``` From f4282a80ff2d22e206930469c797d2c0df5ebb49 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 9 Apr 2024 17:20:21 +0100 Subject: [PATCH 068/140] introduce epichains class object --- episodes/superspreading-simulate.Rmd | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index e1b8e53b..2a7ec2df 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -132,7 +132,9 @@ function(x) generate(x = serial_inverval, times = x) ## Simulate a single chain -```{r,message=FALSE,warning=FALSE} +`simulate_chains()` generates a `` object + +```{r,message=FALSE,warning=FALSE,eval=FALSE} simulate_chains( # simulation controls index_cases = 5, From b223a70b5d6645bc02e751b5373bf8075d24fb23 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 9 Apr 2024 17:20:59 +0100 Subject: [PATCH 069/140] show distribution of outbreaks and null intros --- episodes/superspreading-simulate.Rmd | 19 +++++++++++++++---- 1 file changed, 15 insertions(+), 4 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 2a7ec2df..1a1853b3 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -327,8 +327,11 @@ ggplot() + ) ``` -```{r,echo=FALSE} -sim_chains_max %>% +```{r,echo=FALSE,warning=FALSE,message=FALSE} +library(ggExtra) + +p <- sim_chains_max %>% + filter(day_max>0) %>% ggplot() + geom_point( aes( @@ -337,13 +340,16 @@ sim_chains_max %>% ), alpha = 0.25 ) + - geom_hline(aes(yintercept = 100), lty = 2) + + scale_y_continuous(breaks = scales::breaks_pretty(n = 5)) + + scale_x_continuous(breaks = scales::breaks_pretty(n = 5)) + labs( x = "Length of chain", y = "Size of chain" ) +ggExtra::ggMarginal(p) ``` + ```{r} # chains that reached the 100-case threshold sim_chains_max %>% @@ -359,9 +365,14 @@ threshhold_summary <- sim_chains_max %>% count(name = "chains_theshold") %>% mutate(chains_number = number_chains) %>% mutate(chains_percentage = chains_theshold / chains_number * 100) + +chains_null <- sim_chains_max %>% + arrange(desc(cases_total)) %>% + filter(day_max < 1) %>% + nrow() ``` -Although most outbreaks rapidly become extinct, only `r threshhold_summary$chains_theshold` epidemic trajectories among `r threshhold_summary$chains_number` simulations (`r threshhold_summary$chains_percentage`%) can reach to more than 100 infected cases. This finding is particularly remarkable because $R_0$ is less than 1, and shows the potential for explosive outbreaks of MERS disease. +Although most introductions do not generate secondary cases (`r chains_null`) or most outbreaks rapidly become extinct, only `r threshhold_summary$chains_theshold` epidemic trajectories among `r threshhold_summary$chains_number` simulations (`r threshhold_summary$chains_percentage`%) can reach to more than 100 infected cases. This finding is particularly remarkable because $R_0$ is less than 1, and shows the potential for explosive outbreaks of MERS disease. ::::::::::::::::::::::::::::::::: spoiler From a829a33e346ac9bf2a94f58d37811eca14ba2da9 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 9 Apr 2024 17:30:03 +0100 Subject: [PATCH 070/140] make observed over simulated cases visible --- episodes/superspreading-simulate.Rmd | 126 +++++++++++++++------------ 1 file changed, 68 insertions(+), 58 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 1a1853b3..4d88b7e6 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -327,54 +327,7 @@ ggplot() + ) ``` -```{r,echo=FALSE,warning=FALSE,message=FALSE} -library(ggExtra) - -p <- sim_chains_max %>% - filter(day_max>0) %>% - ggplot() + - geom_point( - aes( - x = day_max, - y = cases_total - ), - alpha = 0.25 - ) + - scale_y_continuous(breaks = scales::breaks_pretty(n = 5)) + - scale_x_continuous(breaks = scales::breaks_pretty(n = 5)) + - labs( - x = "Length of chain", - y = "Size of chain" - ) -ggExtra::ggMarginal(p) -``` - - -```{r} -# chains that reached the 100-case threshold -sim_chains_max %>% - arrange(desc(day_max)) %>% - filter(cases_total > 100) -``` - -```{r,echo=FALSE,message=FALSE,warning=FALSE} -# proportion that reached the 100-case threshold -threshhold_summary <- sim_chains_max %>% - arrange(desc(day_max)) %>% - filter(cases_total > 100) %>% - count(name = "chains_theshold") %>% - mutate(chains_number = number_chains) %>% - mutate(chains_percentage = chains_theshold / chains_number * 100) - -chains_null <- sim_chains_max %>% - arrange(desc(cases_total)) %>% - filter(day_max < 1) %>% - nrow() -``` - -Although most introductions do not generate secondary cases (`r chains_null`) or most outbreaks rapidly become extinct, only `r threshhold_summary$chains_theshold` epidemic trajectories among `r threshhold_summary$chains_number` simulations (`r threshhold_summary$chains_percentage`%) can reach to more than 100 infected cases. This finding is particularly remarkable because $R_0$ is less than 1, and shows the potential for explosive outbreaks of MERS disease. - -::::::::::::::::::::::::::::::::: spoiler +::::::::::::::::::::::::::::::::::: spoiler ### Observed cases vs simulated chains @@ -401,6 +354,8 @@ Use `plot()` to make an incidence plot: plot(mers_cumcases) ``` +::::::::::::::::::::::::::::::::::: + Plot the observed cumulative number of cases over the previously simulated chains. ```{r,echo=FALSE} @@ -422,16 +377,6 @@ ggplot() + color = type ) ) + - # geom_point( - # data = sim_chains_max, - # mapping = aes( - # x = day_max, - # y = cases_total, - # group = chain_id - # ), - # color = "grey", - # show.legend = FALSE - # ) + geom_hline(aes(yintercept = 100), lty = 2) + geom_line( data = mers_cumcases_type, @@ -449,6 +394,71 @@ ggplot() + ) ``` +```{r,echo=FALSE,message=FALSE,warning=FALSE} +# proportion that reached the 100-case threshold +threshhold_summary <- sim_chains_max %>% + arrange(desc(day_max)) %>% + filter(cases_total > 100) %>% + count(name = "chains_theshold") %>% + mutate(chains_number = number_chains) %>% + mutate(chains_percentage = chains_theshold / chains_number * 100) + +chains_null <- sim_chains_max %>% + arrange(desc(cases_total)) %>% + filter(day_max < 1) %>% + nrow() +``` + +Although most introductions do not generate secondary cases (`r chains_null`) or most outbreaks rapidly become extinct, only `r threshhold_summary$chains_theshold` epidemic trajectories among `r threshhold_summary$chains_number` simulations (`r threshhold_summary$chains_percentage`%) can reach to more than 100 infected cases. This finding is particularly remarkable because $R_0$ is less than 1, and shows the potential for explosive outbreaks of MERS disease. + + + +::::::::::::::::::::::::::::::::: spoiler + +### Outbreaks size and length distribution + +We can use `{dplyr}` to get the chains that reached the 100-case threshold: + +```{r} +# chains that reached the 100-case threshold +sim_chains_max %>% + arrange(desc(day_max)) %>% + filter(cases_total > 100) +``` + +We can use `{skimr}` or `{ggExtra}` to get the distribution of the size and length of simulated outbreaks: + +```{r,message=FALSE,warning=FALSE} +library(skimr) + +sim_chains_max %>% + filter(day_max>0) %>% + skim() +``` + +```{r,warning=FALSE,message=FALSE} +library(ggExtra) + +chains_extinct <- sim_chains_max %>% + filter(day_max>0) %>% + ggplot() + + geom_point( + aes( + x = day_max, + y = cases_total + ), + alpha = 0.25 + ) + + scale_y_continuous(breaks = scales::breaks_pretty(n = 5)) + + scale_x_continuous(breaks = scales::breaks_pretty(n = 5)) + + labs( + x = "Length of chain", + y = "Size of chain" + ) + +ggExtra::ggMarginal(chains_extinct) +``` + ::::::::::::::::::::::::::::::::: From 0bbdfc30d213c81144fddeb62632f8fa39637915 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 9 Apr 2024 17:40:43 +0100 Subject: [PATCH 071/140] add intro text to spoiler section --- episodes/superspreading-simulate.Rmd | 2 ++ 1 file changed, 2 insertions(+) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 4d88b7e6..17ae7a7e 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -417,6 +417,8 @@ Although most introductions do not generate secondary cases (`r chains_null`) or ### Outbreaks size and length distribution +We can consider that, among simulated chains, the ones that generate secondary cases (`length > 0`) are simulated outbreaks. + We can use `{dplyr}` to get the chains that reached the 100-case threshold: ```{r} From cbfe443ed0e57610366579751b0283adad09d28e Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 9 Apr 2024 18:07:29 +0100 Subject: [PATCH 072/140] remove distribution chunk + text median outbreaks --- episodes/superspreading-simulate.Rmd | 63 ++++------------------------ 1 file changed, 9 insertions(+), 54 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 17ae7a7e..95439489 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -403,66 +403,21 @@ threshhold_summary <- sim_chains_max %>% mutate(chains_number = number_chains) %>% mutate(chains_percentage = chains_theshold / chains_number * 100) +chains_extinct <- sim_chains_max %>% + arrange(desc(day_max)) %>% + filter(day_max > 0) %>% + summarise( + extinct_length_median = median(day_max), + extinct_size_median = median(cases_total) + ) + chains_null <- sim_chains_max %>% arrange(desc(cases_total)) %>% filter(day_max < 1) %>% nrow() ``` -Although most introductions do not generate secondary cases (`r chains_null`) or most outbreaks rapidly become extinct, only `r threshhold_summary$chains_theshold` epidemic trajectories among `r threshhold_summary$chains_number` simulations (`r threshhold_summary$chains_percentage`%) can reach to more than 100 infected cases. This finding is particularly remarkable because $R_0$ is less than 1, and shows the potential for explosive outbreaks of MERS disease. - - - -::::::::::::::::::::::::::::::::: spoiler - -### Outbreaks size and length distribution - -We can consider that, among simulated chains, the ones that generate secondary cases (`length > 0`) are simulated outbreaks. - -We can use `{dplyr}` to get the chains that reached the 100-case threshold: - -```{r} -# chains that reached the 100-case threshold -sim_chains_max %>% - arrange(desc(day_max)) %>% - filter(cases_total > 100) -``` - -We can use `{skimr}` or `{ggExtra}` to get the distribution of the size and length of simulated outbreaks: - -```{r,message=FALSE,warning=FALSE} -library(skimr) - -sim_chains_max %>% - filter(day_max>0) %>% - skim() -``` - -```{r,warning=FALSE,message=FALSE} -library(ggExtra) - -chains_extinct <- sim_chains_max %>% - filter(day_max>0) %>% - ggplot() + - geom_point( - aes( - x = day_max, - y = cases_total - ), - alpha = 0.25 - ) + - scale_y_continuous(breaks = scales::breaks_pretty(n = 5)) + - scale_x_continuous(breaks = scales::breaks_pretty(n = 5)) + - labs( - x = "Length of chain", - y = "Size of chain" - ) - -ggExtra::ggMarginal(chains_extinct) -``` - -::::::::::::::::::::::::::::::::: - +Although most introductions do not generate secondary cases (N = `r chains_null`) or most outbreaks rapidly become extinct (median length of `r chains_extinct$extinct_length_median` and median size of `r chains_extinct$extinct_size_median`), only `r threshhold_summary$chains_theshold` epidemic trajectories among `r threshhold_summary$chains_number` simulations (`r threshhold_summary$chains_percentage`%) can reach to more than 100 infected cases. This finding is particularly remarkable because $R_0$ is less than 1, and shows the potential for explosive outbreaks of MERS disease. :::::::::::::::::::::: testimonial From c86026f3687bcd9299b221b642f2047f9edd74f4 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 9 Apr 2024 19:52:46 +0100 Subject: [PATCH 073/140] pass lintr checks + complement explanation text --- episodes/superspreading-simulate.Rmd | 25 ++++++++++++------------- 1 file changed, 12 insertions(+), 13 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 95439489..68b7b585 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -335,15 +335,14 @@ Let's overlap the cumulative number of observed cases using the linelist object ```{r,warning=FALSE,message=FALSE} library(outbreaks) -library(incidence2) -mers_cumcases <- mers_korea_2015$linelist %>% +mers_cumcases <- mers_korea_2015$linelist %>% # incidence2 workflow - incidence2::incidence(date_index = "dt_onset") %>% - incidence2::complete_dates() %>% + incidence2::incidence(date_index = "dt_onset") %>% + incidence2::complete_dates() %>% # wrangling using {dplyr} - mutate(count_cumsum = cumsum(count)) %>% - rownames_to_column(var = "day") %>% + mutate(count_cumsum = cumsum(count)) %>% + rownames_to_column(var = "day") %>% mutate(day = as.numeric(day)) ``` @@ -361,10 +360,10 @@ Plot the observed cumulative number of cases over the previously simulated chain ```{r,echo=FALSE} # Observed cases vs Simulated transmission chains mers_cumcases_type <- - mers_cumcases %>% - mutate(type = "Observed") + mers_cumcases %>% + mutate(type = "Observed") simulated_chains_day_type <- - simulated_chains_day %>% + simulated_chains_day %>% mutate(type = "Simulated") ggplot() + @@ -381,7 +380,7 @@ ggplot() + geom_line( data = mers_cumcases_type, mapping = aes( - x = day, + x = day, y = count_cumsum, color = type ), @@ -405,7 +404,7 @@ threshhold_summary <- sim_chains_max %>% chains_extinct <- sim_chains_max %>% arrange(desc(day_max)) %>% - filter(day_max > 0) %>% + filter(day_max > 0) %>% summarise( extinct_length_median = median(day_max), extinct_size_median = median(cases_total) @@ -413,11 +412,11 @@ chains_extinct <- sim_chains_max %>% chains_null <- sim_chains_max %>% arrange(desc(cases_total)) %>% - filter(day_max < 1) %>% + filter(day_max < 1) %>% nrow() ``` -Although most introductions do not generate secondary cases (N = `r chains_null`) or most outbreaks rapidly become extinct (median length of `r chains_extinct$extinct_length_median` and median size of `r chains_extinct$extinct_size_median`), only `r threshhold_summary$chains_theshold` epidemic trajectories among `r threshhold_summary$chains_number` simulations (`r threshhold_summary$chains_percentage`%) can reach to more than 100 infected cases. This finding is particularly remarkable because $R_0$ is less than 1, and shows the potential for explosive outbreaks of MERS disease. +Although most introductions do not generate secondary cases (N = `r chains_null`) or most outbreaks rapidly become extinct (median length of `r chains_extinct$extinct_length_median` and median size of `r chains_extinct$extinct_size_median`), only `r threshhold_summary$chains_theshold` epidemic trajectories among `r threshhold_summary$chains_number` simulations (`r threshhold_summary$chains_percentage`%) can reach to more than 100 infected cases. This finding is particularly remarkable because the basic reproduction number $R_0$ is less than 1 (offspring distribution mean of `r mers_offspring[["mean"]]`), and shows the potential for explosive outbreaks of MERS disease given a offspring distribution dispersion parameter of `r mers_offspring[["dispersion"]]`. :::::::::::::::::::::: testimonial From 8dc2dbd079f1ed31dc719f76cbed62684acb067e Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 9 Apr 2024 19:54:07 +0100 Subject: [PATCH 074/140] rephrase conclusion --- episodes/superspreading-simulate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 68b7b585..d8a8e40b 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -416,7 +416,7 @@ chains_null <- sim_chains_max %>% nrow() ``` -Although most introductions do not generate secondary cases (N = `r chains_null`) or most outbreaks rapidly become extinct (median length of `r chains_extinct$extinct_length_median` and median size of `r chains_extinct$extinct_size_median`), only `r threshhold_summary$chains_theshold` epidemic trajectories among `r threshhold_summary$chains_number` simulations (`r threshhold_summary$chains_percentage`%) can reach to more than 100 infected cases. This finding is particularly remarkable because the basic reproduction number $R_0$ is less than 1 (offspring distribution mean of `r mers_offspring[["mean"]]`), and shows the potential for explosive outbreaks of MERS disease given a offspring distribution dispersion parameter of `r mers_offspring[["dispersion"]]`. +Although most introductions do not generate secondary cases (N = `r chains_null`) or most outbreaks rapidly become extinct (median length of `r chains_extinct$extinct_length_median` and median size of `r chains_extinct$extinct_size_median`), only `r threshhold_summary$chains_theshold` epidemic trajectories among `r threshhold_summary$chains_number` simulations (`r threshhold_summary$chains_percentage`%) can reach to more than 100 infected cases. This finding is particularly remarkable because the basic reproduction number $R_0$ is less than 1 (offspring distribution mean of `r mers_offspring[["mean"]]`), but, given an offspring distribution dispersion parameter of `r mers_offspring[["dispersion"]]`, it shows the potential for explosive outbreaks of MERS disease. :::::::::::::::::::::: testimonial From 3178dae64b46edd555ee1b118eb8e079afa5c570 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 9 Apr 2024 20:09:11 +0100 Subject: [PATCH 075/140] relocated interpretation from simulations --- episodes/superspreading-simulate.Rmd | 51 ++++++++++++++-------------- 1 file changed, 26 insertions(+), 25 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index d8a8e40b..856205c1 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -327,6 +327,32 @@ ggplot() + ) ``` + +```{r,echo=FALSE,message=FALSE,warning=FALSE} +# proportion that reached the 100-case threshold +threshhold_summary <- sim_chains_max %>% + arrange(desc(day_max)) %>% + filter(cases_total > 100) %>% + count(name = "chains_theshold") %>% + mutate(chains_number = number_chains) %>% + mutate(chains_percentage = chains_theshold / chains_number * 100) + +chains_extinct <- sim_chains_max %>% + arrange(desc(day_max)) %>% + filter(day_max > 0) %>% + summarise( + extinct_length_median = median(day_max), + extinct_size_median = median(cases_total) + ) + +chains_null <- sim_chains_max %>% + arrange(desc(cases_total)) %>% + filter(day_max < 1) %>% + nrow() +``` + +Although most introductions do not generate secondary cases (N = `r chains_null`) or most outbreaks rapidly become extinct (median length of `r chains_extinct$extinct_length_median` and median size of `r chains_extinct$extinct_size_median`), only `r threshhold_summary$chains_theshold` epidemic trajectories among `r threshhold_summary$chains_number` simulations (`r threshhold_summary$chains_percentage`%) can reach to more than 100 infected cases. This finding is particularly remarkable because the basic reproduction number $R_0$ is less than 1 (offspring distribution mean of `r mers_offspring[["mean"]]`), but, given an offspring distribution dispersion parameter of `r mers_offspring[["dispersion"]]`, it shows the potential for explosive outbreaks of MERS disease. + ::::::::::::::::::::::::::::::::::: spoiler ### Observed cases vs simulated chains @@ -393,31 +419,6 @@ ggplot() + ) ``` -```{r,echo=FALSE,message=FALSE,warning=FALSE} -# proportion that reached the 100-case threshold -threshhold_summary <- sim_chains_max %>% - arrange(desc(day_max)) %>% - filter(cases_total > 100) %>% - count(name = "chains_theshold") %>% - mutate(chains_number = number_chains) %>% - mutate(chains_percentage = chains_theshold / chains_number * 100) - -chains_extinct <- sim_chains_max %>% - arrange(desc(day_max)) %>% - filter(day_max > 0) %>% - summarise( - extinct_length_median = median(day_max), - extinct_size_median = median(cases_total) - ) - -chains_null <- sim_chains_max %>% - arrange(desc(cases_total)) %>% - filter(day_max < 1) %>% - nrow() -``` - -Although most introductions do not generate secondary cases (N = `r chains_null`) or most outbreaks rapidly become extinct (median length of `r chains_extinct$extinct_length_median` and median size of `r chains_extinct$extinct_size_median`), only `r threshhold_summary$chains_theshold` epidemic trajectories among `r threshhold_summary$chains_number` simulations (`r threshhold_summary$chains_percentage`%) can reach to more than 100 infected cases. This finding is particularly remarkable because the basic reproduction number $R_0$ is less than 1 (offspring distribution mean of `r mers_offspring[["mean"]]`), but, given an offspring distribution dispersion parameter of `r mers_offspring[["dispersion"]]`, it shows the potential for explosive outbreaks of MERS disease. - :::::::::::::::::::::: testimonial ### Early spread projections From b7b825e38c930cf55aa22a739b0efabb24552160 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 9 Apr 2024 20:09:39 +0100 Subject: [PATCH 076/140] add interpretation of observed over simulated --- episodes/superspreading-simulate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 856205c1..917cece6 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -381,7 +381,7 @@ plot(mers_cumcases) ::::::::::::::::::::::::::::::::::: -Plot the observed cumulative number of cases over the previously simulated chains. +When plotting the observed number of cumulative cases from the Middle East respiratory syndrome (MERS) outbreak in South Korea in 2015, alongside the previously simulated chains, we identify that the observed cases followed a trajectory that resembled one of the simulated explosive outbreaks. ```{r,echo=FALSE} # Observed cases vs Simulated transmission chains From 52ee7c7dd451cca02538bcdcf28eaecb973dd489 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 9 Apr 2024 20:10:19 +0100 Subject: [PATCH 077/140] add figure introduce cases generations size length --- episodes/superspreading-simulate.Rmd | 2 ++ 1 file changed, 2 insertions(+) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 917cece6..7fdf0f2b 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -83,6 +83,8 @@ simulation of uncontrolled outbreaks with estimated parameter we then can reconstruct tranmission chains to forecast and simulate interventions +![**An example of a transmission chain starting with a single case C1.** Cases are represented by blue circles and arrows indicate who infected whom. The chain grows through generations Gen 1, Gen 2, and Gen 3, producing cases C2, C3, C4, C5, and C6. The chain ends at generation Gen 3 with cases C4, C5, and C6. The size of C1’s chain is 6, including C1 (that is, the sum of all blue circles) and the length is 3, which includes Gen 1 (maximum number of generations reached by C1’s chain).](https://raw.githubusercontent.com/epiverse-trace/epichains/main/vignettes/img/transmission_chain_example.png) + ### branching process - probability generating function (pgf) of the offspring distribution From 608887c4601dbbc67b4292b74ec8fd62a34b4292 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 9 Apr 2024 20:54:40 +0100 Subject: [PATCH 078/140] use duration of chain instead of length --- episodes/superspreading-simulate.Rmd | 18 ++++++++++-------- 1 file changed, 10 insertions(+), 8 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 7fdf0f2b..9a92a9e0 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -272,26 +272,28 @@ simulated_chains_map %>% ```{r} # daily aggregate of cases -simulated_chains_day <- - simulated_chains_map %>% +simulated_chains_day <- simulated_chains_map %>% + # use data.frame output from epichains object as_tibble() %>% + # transform chain ID column to factor mutate(chain_id = as_factor(chain_id)) %>% - # Daily number of cases for each simulation + # get the round number (day) of infection times mutate(day = ceiling(time)) %>% + # count the daily number of cases each simulation (chain ID) count(chain_id, day, name = "cases") %>% - # Cumulative number of cases for each simulation + # calculate the cumulative number of cases for each simulation (chain ID) group_by(chain_id) %>% mutate(cases_cumsum = cumsum(cases)) %>% ungroup() ``` ```{r} -# Summarise the chain length and size +# Summarise the chain duration and size sim_chains_max <- simulated_chains_day %>% group_by(chain_id) %>% summarise( - # length + # duration day_max = max(day), # size cases_total = max(cases_cumsum) @@ -343,7 +345,7 @@ chains_extinct <- sim_chains_max %>% arrange(desc(day_max)) %>% filter(day_max > 0) %>% summarise( - extinct_length_median = median(day_max), + extinct_duration_median = median(day_max), extinct_size_median = median(cases_total) ) @@ -353,7 +355,7 @@ chains_null <- sim_chains_max %>% nrow() ``` -Although most introductions do not generate secondary cases (N = `r chains_null`) or most outbreaks rapidly become extinct (median length of `r chains_extinct$extinct_length_median` and median size of `r chains_extinct$extinct_size_median`), only `r threshhold_summary$chains_theshold` epidemic trajectories among `r threshhold_summary$chains_number` simulations (`r threshhold_summary$chains_percentage`%) can reach to more than 100 infected cases. This finding is particularly remarkable because the basic reproduction number $R_0$ is less than 1 (offspring distribution mean of `r mers_offspring[["mean"]]`), but, given an offspring distribution dispersion parameter of `r mers_offspring[["dispersion"]]`, it shows the potential for explosive outbreaks of MERS disease. +Although most introductions do not generate secondary cases (N = `r chains_null`) or most outbreaks rapidly become extinct (median duration of `r chains_extinct$extinct_duration_median` and median size of `r chains_extinct$extinct_size_median`), only `r threshhold_summary$chains_theshold` epidemic trajectories among `r threshhold_summary$chains_number` simulations (`r threshhold_summary$chains_percentage`%) can reach to more than 100 infected cases. This finding is particularly remarkable because the basic reproduction number $R_0$ is less than 1 (offspring distribution mean of `r mers_offspring[["mean"]]`), but, given an offspring distribution dispersion parameter of `r mers_offspring[["dispersion"]]`, it shows the potential for explosive outbreaks of MERS disease. ::::::::::::::::::::::::::::::::::: spoiler From a9f2084983c5c0f99b503e09abb183af061ad024 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 9 Apr 2024 20:58:53 +0100 Subject: [PATCH 079/140] show why to transform chain ID to factor --- episodes/superspreading-simulate.Rmd | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 9a92a9e0..a4517d9c 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -273,9 +273,9 @@ simulated_chains_map %>% ```{r} # daily aggregate of cases simulated_chains_day <- simulated_chains_map %>% - # use data.frame output from epichains object + # use data.frame output from object as_tibble() %>% - # transform chain ID column to factor + # transform chain ID column to factor (categorical variable) mutate(chain_id = as_factor(chain_id)) %>% # get the round number (day) of infection times mutate(day = ceiling(time)) %>% From 9115c17ced7122810c9a55a975c91edd3deae486 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 9 Apr 2024 21:12:08 +0100 Subject: [PATCH 080/140] rewrite referral to an explosive outbreal --- episodes/superspreading-simulate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index a4517d9c..a3dd4332 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -385,7 +385,7 @@ plot(mers_cumcases) ::::::::::::::::::::::::::::::::::: -When plotting the observed number of cumulative cases from the Middle East respiratory syndrome (MERS) outbreak in South Korea in 2015, alongside the previously simulated chains, we identify that the observed cases followed a trajectory that resembled one of the simulated explosive outbreaks. +When plotting the observed number of cumulative cases from the Middle East respiratory syndrome (MERS) outbreak in South Korea in 2015, alongside the previously simulated chains, we identify that the observed cases followed a trajectory that resembled a simulated explosive outbreak. ```{r,echo=FALSE} # Observed cases vs Simulated transmission chains From 00e6e44b06dee70e6a08b96afa8f1804104e8cd2 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 9 Apr 2024 21:13:12 +0100 Subject: [PATCH 081/140] use mean and sd from serial interval in text --- episodes/superspreading-simulate.Rmd | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index a3dd4332..eee6fa09 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -119,13 +119,17 @@ serial_inverval <- epidist_db( ) plot(serial_inverval, day_range = 0:25) +``` -serial_inverval$summary_stats %>% +```{r,echo=FALSE} +serial_summary <- serial_inverval$summary_stats %>% as_tibble() %>% select(mean, sd) %>% distinct(.keep_all = TRUE) ``` +mean `r serial_summary$mean` and standard deviation `r serial_summary$sd`. + Similar to the `{cfr}` interface for `{epiparameter}` ```r From 2089ecba5432dfb92fb549d9ecec1baef0711251 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 9 Apr 2024 21:33:51 +0100 Subject: [PATCH 082/140] clean offspring definition --- episodes/superspreading-simulate.Rmd | 8 +------- 1 file changed, 1 insertion(+), 7 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index eee6fa09..63ee704f 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -94,13 +94,7 @@ with estimated parameter we then can reconstruct tranmission chains to forecast from MERS estimates in estimate episode ```{r} -mers_offspring <- - c( - mean = 0.60, - dispersion = 0.02 - ) - -mers_offspring +mers_offspring <- c(mean = 0.60, dispersion = 0.02) ``` instead of the offspring distribution From 763287fb8c24696e5587916a58f6973a56151187 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 9 Apr 2024 21:44:11 +0100 Subject: [PATCH 083/140] homogenize term to reproduction over reproductive --- episodes/superspreading-estimate.Rmd | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 07473915..20367f67 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -223,7 +223,7 @@ ggplot() + colour = "red" ) + labs( - x = "Individual reproductive number", + x = "Individual reproduction number", y = "Density" ) ``` @@ -235,7 +235,7 @@ From the histogram and density plot, we can identify that the offspring distribu ### Terminology recap - From linelist and contact data, we calculate the **number of secondary cases** caused by the observed infected individuals. -- The **individual reproductive number** is a random variable representing the _expected_ number of secondary cases caused by a infected individual. +- The **individual reproduction number** is a random variable representing the _expected_ number of secondary cases caused by a infected individual. - From the stochastic effects in transmission, the number of secondary _infections_ caused by each case is described by an **offspring distribution**. - An _empirical_ offspring distribution can be modeled by the **negative-binomial** distribution with mean $R_{0}$ and dispersion parameter $k$. @@ -696,7 +696,7 @@ qpois( Compare this values with the ones reported by [Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153). See figure below: -![Reported superspreading events (SSEs; diamonds) relative to estimated reproductive number R (squares) for twelve directly transmitted infections. Lines show 5–95 percentile range of the number of secondary cases following a Poisson distribution with lambda equal to the reproduction number ($Z∼Poisson(R)$), and crosses show the 99th-percentile proposed as threshold for SSEs. Stars represent SSEs caused by more than one source case. ‘Other’ diseases are: 1, Streptococcus group A; 2, Lassa fever; 3, Mycoplasma pneumonia; 4, pneumonic plague; 5, tuberculosis. R is not shown for ‘other’ diseases, and is off-scale for monkeypox.](fig/SEE-individual-reproductive-number-fig-d.png) +![Reported superspreading events (SSEs; diamonds) relative to estimated reproduction number R (squares) for twelve directly transmitted infections. Lines show 5–95 percentile range of the number of secondary cases following a Poisson distribution with lambda equal to the reproduction number ($Z∼Poisson(R)$), and crosses show the 99th-percentile proposed as threshold for SSEs. Stars represent SSEs caused by more than one source case. ‘Other’ diseases are: 1, Streptococcus group A; 2, Lassa fever; 3, Mycoplasma pneumonia; 4, pneumonic plague; 5, tuberculosis. R is not shown for ‘other’ diseases, and is off-scale for monkeypox.](fig/SEE-individual-reproductive-number-fig-d.png) ::::::::::::::::: From f1fd6630db053df151166306a7b993d7a1bad63f Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 9 Apr 2024 22:50:14 +0100 Subject: [PATCH 084/140] homogenize reproduction number across episode --- episodes/superspreading-simulate.Rmd | 25 +++++++++++++++---------- 1 file changed, 15 insertions(+), 10 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 63ee704f..4abc2a31 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -54,7 +54,7 @@ Transmission heterogeneity affects epidemic establishment and the ease of contro + Conversely, heterogeneity in transmission may provide opportunities for *targeted interventions* if the individuals who contribute more to transmission (due to biological, environmental or behavioral factors) share socio-demographic or geographical characteristics that can be defined. -We can have an early understanding of a disease epidemic potential from the mean reproduction number $R_{0}$ and dispersion $k$ of an offspring distribution to answer questions like: +We can have an early understanding of a disease epidemic potential from the mean reproduction number $R$ and dispersion $k$ of an offspring distribution to answer questions like: - What is the probability of an pathogen to cause large outbreak? - What is the probability of an outbreak to get extinct? @@ -64,7 +64,7 @@ We can have an early understanding of a disease epidemic potential from the mean ### Epidemic Risk assessment accounting for superspreading -These estimates vary non-linearly with respect to the mean reproduction number $R_{0}$ and dispersion $k$ of a given disease. +These estimates vary non-linearly with respect to the mean reproduction number $R$ and dispersion $k$ of a given disease. We invite you to read the `{superspreading}` vignette on [Epidemic risk](https://epiverse-trace.github.io/superspreading/articles/epidemic_risk.html)! @@ -91,18 +91,12 @@ with estimated parameter we then can reconstruct tranmission chains to forecast ## Get the offspring distribution -from MERS estimates in estimate episode +The MERS offspring distribution will follow a negative binomial distribution with mean (reproduction number $R$) and dispersion $k$ values estimated from the linelist and contact data of the previous episode. ```{r} mers_offspring <- c(mean = 0.60, dispersion = 0.02) ``` -instead of the offspring distribution -we can also define a poisson process -using the lambda distribution parameter -lambda = rate = mean - - ## Get generation time ```{r,message=FALSE,warning=FALSE} @@ -155,6 +149,17 @@ the infector sim_id of each infectee is in infector_id infectee got infected in generation and time as part of the `chain_id` chain +:::::::::::::::::::::::::: callout + +`{epichains}` accepts either + +Instead of the offspring distribution +we can also define a poisson process +using the lambda distribution parameter +lambda = rate = mean + +:::::::::::::::::::::::::: + ## Simulate multiple chains ```{r} @@ -353,7 +358,7 @@ chains_null <- sim_chains_max %>% nrow() ``` -Although most introductions do not generate secondary cases (N = `r chains_null`) or most outbreaks rapidly become extinct (median duration of `r chains_extinct$extinct_duration_median` and median size of `r chains_extinct$extinct_size_median`), only `r threshhold_summary$chains_theshold` epidemic trajectories among `r threshhold_summary$chains_number` simulations (`r threshhold_summary$chains_percentage`%) can reach to more than 100 infected cases. This finding is particularly remarkable because the basic reproduction number $R_0$ is less than 1 (offspring distribution mean of `r mers_offspring[["mean"]]`), but, given an offspring distribution dispersion parameter of `r mers_offspring[["dispersion"]]`, it shows the potential for explosive outbreaks of MERS disease. +Although most introductions do not generate secondary cases (N = `r chains_null`) or most outbreaks rapidly become extinct (median duration of `r chains_extinct$extinct_duration_median` and median size of `r chains_extinct$extinct_size_median`), only `r threshhold_summary$chains_theshold` epidemic trajectories among `r threshhold_summary$chains_number` simulations (`r threshhold_summary$chains_percentage`%) can reach to more than 100 infected cases. This finding is particularly remarkable because the reproduction number $R$ is less than 1 (offspring distribution mean of `r mers_offspring[["mean"]]`), but, given an offspring distribution dispersion parameter of `r mers_offspring[["dispersion"]]`, it shows the potential for explosive outbreaks of MERS disease. ::::::::::::::::::::::::::::::::::: spoiler From 9770315cf28b5290ca016664168aca6c644850c4 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 9 Apr 2024 23:35:23 +0100 Subject: [PATCH 085/140] add text about argument --- episodes/superspreading-simulate.Rmd | 72 ++++++++++++++++++++++------ 1 file changed, 57 insertions(+), 15 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 4abc2a31..2c5427a5 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -91,14 +91,55 @@ with estimated parameter we then can reconstruct tranmission chains to forecast ## Get the offspring distribution -The MERS offspring distribution will follow a negative binomial distribution with mean (reproduction number $R$) and dispersion $k$ values estimated from the linelist and contact data of the previous episode. +The MERS offspring distribution will follow a negative binomial distribution with mean (reproduction number $R$) and dispersion $k$ values estimated from the linelist and contact data of `mers_korea_2015` in the `{outbreaks}` R package in the previous episode. ```{r} mers_offspring <- c(mean = 0.60, dispersion = 0.02) ``` +The way we input an offspring distribution to `{epichains}` is by defining the R function that generates random values. For example, for a negative binomial distribution we use `rnbinom` with its corresponding `mu` and `size` arguments: + +```r + offspring_dist = rnbinom, + mu = mers_offspring["mean"], + size = mers_offspring["dispersion"], +``` + +The reference manual in `?rnbinom` tell us the specific arguments we require. + +:::::::::::::::::::::::::: spoiler + +### Poisson and other distributions + +`{epichains}` can accept any R function that generates random numbers, so the specified arguments will change depending of the R function used. The way to know this is by accessing the function reference manual. + +For example, let's say that for the offspring distribution we want to use a Poisson distribution. First, read the argument required in the `?rpois` reference manual. Second, specify the `lambda` argument parameter, which is also known as rate or mean in the literature. In `{epichains}`, this can look like this: + +```r + offspring_dist = rpois, + lambda = mers_offspring["mean"], +``` + +In this example we can specify `lambda = mers_offspring["mean"]` because in a negative binomial model, when the dispersion parameter $k$ approaches infinity ($k \rightarrow \infty$) the variance equals the mean. This makes the conventional Poisson model an special case of the negative binomial model. + +:::::::::::::::::::::::::: + ## Get generation time +The generation time distribution is often approximated by the [serial interval](../learners/reference.md#serialinterval) distribution. This approximation is frequent because it is easier to observe and measure the onset of symptoms than the onset of infectiousness. + +:::::::::::::::::::::::::::::::: spoiler + +### generation time vs serial interval + +![A schematic of the relationship of different time periods of transmission between an infector and an infectee in a transmission pair. Exposure window is defined as the time interval having viral exposure, and transmission window is defined as the time interval for onward transmission with respect to the infection time ([Chung Lau et al., 2021](https://academic.oup.com/jid/article/224/10/1664/6356465)).](fig/serial-interval-observed.jpeg) + +However, using the *serial interval* as an approximation of the *generation time* is primarily valid for diseases in which infectiousness starts after symptom onset ([Chung Lau et al., 2021](https://academic.oup.com/jid/article/224/10/1664/6356465)). In cases where infectiousness starts before symptom onset, the serial intervals can have negative values, which is the case for diseases with pre-symptomatic transmission ([Nishiura et al., 2020](https://www.ijidonline.com/article/S1201-9712(20)30119-3/fulltext#gr2)). + +:::::::::::::::::::::::::::::::: + +Let's use the `{epiparameter}` package to access and use the available serial interval for MERS disease: + ```{r,message=FALSE,warning=FALSE} serial_inverval <- epidist_db( disease = "mers", @@ -116,17 +157,19 @@ serial_summary <- serial_inverval$summary_stats %>% distinct(.keep_all = TRUE) ``` -mean `r serial_summary$mean` and standard deviation `r serial_summary$sd`. +The serial interval for MERS has a mean of `r serial_summary$mean` days and standard deviation `r serial_summary$sd` days. -Similar to the `{cfr}` interface for `{epiparameter}` +In `{epichains}` we need to specify the generation time as a function that generates random numbers. Using `{epiparameter}` has the advantage of using the distribution function `epiparameter::generate()` for this input. This will look like this: ```r function(x) generate(x = serial_inverval, times = x) ``` +This interface is similar to the one used by `{cfr}` to link with `{epiparameter}`. For further context, read the [work with delay distributions](https://epiverse-trace.github.io/cfr/articles/delay_distributions.html) vignette. + ## Simulate a single chain -`simulate_chains()` generates a `` object +Now we are prepared to use the `simulate_chains()` function from `{epichains}` to create one transmission chain: ```{r,message=FALSE,warning=FALSE,eval=FALSE} simulate_chains( @@ -142,6 +185,16 @@ simulate_chains( ) ``` +`simulate_chains()` requires, at least, three sets of arguments: + +- simulation controls, +- offspring distribution, and +- generation time. + +Lines above we described how to specify the offspring distribution and generation time. The simulation controls + +generates a `` object + the output dataframe collects infectees as observation unit each infectee has a sim_id @@ -149,17 +202,6 @@ the infector sim_id of each infectee is in infector_id infectee got infected in generation and time as part of the `chain_id` chain -:::::::::::::::::::::::::: callout - -`{epichains}` accepts either - -Instead of the offspring distribution -we can also define a poisson process -using the lambda distribution parameter -lambda = rate = mean - -:::::::::::::::::::::::::: - ## Simulate multiple chains ```{r} From 3819e370885bf55ba092c5146f116728fff8f9e6 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Wed, 10 Apr 2024 00:29:44 +0100 Subject: [PATCH 086/140] complete writing content --- episodes/superspreading-simulate.Rmd | 68 +++++++++++++++++++++------- 1 file changed, 51 insertions(+), 17 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 2c5427a5..7425946d 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -169,7 +169,7 @@ This interface is similar to the one used by `{cfr}` to link with `{epiparameter ## Simulate a single chain -Now we are prepared to use the `simulate_chains()` function from `{epichains}` to create one transmission chain: +Now we are prepared to use the `simulate_chains()` function from `{epichains}` to create **one** transmission chain: ```{r,message=FALSE,warning=FALSE,eval=FALSE} simulate_chains( @@ -191,19 +191,31 @@ simulate_chains( - offspring distribution, and - generation time. -Lines above we described how to specify the offspring distribution and generation time. The simulation controls +Lines above we described how to specify the offspring distribution and generation time. The **simulation controls** include, at least, two arguments: -generates a `` object +- `index_case`, which define the number of index cases to simulate transmission chains for, and +- `statistic`, which define a chain statistic to track (either `"size"` or `"length"`) as the stopping criteria for each chain being simulated. -the output dataframe collects -infectees as observation unit -each infectee has a sim_id -the infector sim_id of each infectee is in infector_id -infectee got infected in generation and time -as part of the `chain_id` chain +::::::::::::::::::::::::::: callout + +### Stopping criteria + +This is an exclusive feature of `{epichains}`. Branching process simulations end when they have gone extinct, that is, no more offspring are being produced, or because of some stopping criterion. + +::::::::::::::::::::::::::: + +The output of the `simulate_chains()` function creates a `` class object. ## Simulate multiple chains +We can use `simulate_chains()` to create multiple chains and increase the probability to simulate uncontrolled outbreaks projections. + +We need to specify three additional elements: + +- `set.seed()`, which is a random number generator function with a specified seed value, the `` number, to ensure consistent results across different runs of the code. +- `number_chains`, which defines the number of simulation to run. +- `initial_cases`, which defines the number of initial cases to input to the `index_cases` argument explained lines above. + ```{r} # Set seed for random number generator set.seed(33) @@ -211,9 +223,10 @@ set.seed(33) number_chains <- 1000 # Number of initial cases initial_cases <- 1 - ``` +`number_chains` and `initial_cases` are conveniently stored in objects to facilitate its reuse downstream in the workflow. + :::::::::::::::::::::::::::::: checklist ### Iteration using purrr @@ -228,7 +241,7 @@ Or if you previously used the `*apply` family of functions, visit the package vi To get multiple chains, we need to apply the `simulate_chains()` function to each chain defined by a sequence of numbers from 1 to `number_chains`. -Let's use `map()`: +Let's use `map()` to iterate `simulate_chains()` in a vector from 1 to `r number_chains`: ```{r} simulated_chains_map <- @@ -264,6 +277,10 @@ simulated_chains_map %>% count(chain_id, sort = TRUE) ``` +::::::::::::::::::::::::::::::::: callout + +### Read the epichains output + ```{r,echo=FALSE} #### get simulated chain with more infections -------------------------------- @@ -289,9 +306,7 @@ chain_to_observe <- simulated_chains_map %>% pull(chain_id) ``` -Let's observe closely the simulated `chain_id` number `r chain_to_observe` with three generations. - -get epichain summary +To explore the output format of the `` class object of name `simulated_chains_map`, let's observe closely the simulated `chain_id` number `r chain_to_observe`. Let's use `dplyr::filter()` for this: ```{r} #### get epichain summary ---------------------------------------------------- @@ -300,9 +315,14 @@ simulated_chains_map %>% filter(chain_id == chain_to_observe) ``` -the `NA` includes the infector of the index case, for that reason (known) cases +Key elements exclusive from this output are in the **footer**: -infectee-infector data frame +```output +Number of infectors (known): 3 +Number of generations: 3 +``` + +The simulated `chain_id` number `r chain_to_observe` has three known infector and three generations. These numbers are more visible when reading the `` objects as a data frame: ```{r} #### infector-infectee data frame -------------------------------------------- @@ -312,9 +332,16 @@ simulated_chains_map %>% as_tibble() ``` +The output data frame collects **infectees** as the observation unit. Each infectee has a `sim_id`. Under the `infector_id` column we have the `sim_id` of each _infectee_ that behaved as an _infector_. Within the simulation number, under the `chain_id` column, each infectee got infected in a specific `generation` and (continuous) `time`. + +The `Number of infectors (known)` includes the `NA` observation under the `infector_id` column. This refers to the infector specified as index case (in the `index_cases` argument), which started the transmission chain to the infectee of `sim_id = 1`, at `generation = 1`, and `time = 0`. + +::::::::::::::::::::::::::::: ## Visualize multiple chains +To visualize the simulated chains, we need some pre-processing. First, let's use `{dplyr}` to get round time numbers, to resemble surveillance days. Second, count the daily number of cases in each simulation (by `chain_id`). Third, calculate the cumulative number of cases within simulation. + ```{r} # daily aggregate of cases simulated_chains_day <- simulated_chains_map %>% @@ -332,6 +359,8 @@ simulated_chains_day <- simulated_chains_map %>% ungroup() ``` +Previous to the plot, let's create a summary table with the total time duration and size of each chain. We can use the `{dplyr}` "combo" of `group_by()`, `summarise()` and `ungroup()`: + ```{r} # Summarise the chain duration and size sim_chains_max <- @@ -346,9 +375,12 @@ sim_chains_max <- ungroup() ``` +Now, we are prepared for using the `{ggplot2}` package: + ```{r} # Visualize transmission chains by cumulative cases ggplot() + + # create grouped chain trajectories geom_line( data = simulated_chains_day, mapping = aes( @@ -359,6 +391,7 @@ ggplot() + ), show.legend = FALSE ) + + # create points to visualize the chain end point geom_point( data = sim_chains_max, mapping = aes( @@ -369,6 +402,7 @@ ggplot() + ), show.legend = FALSE ) + + # define a 100-case threshold geom_hline(aes(yintercept = 100), lty = 2) + labs( x = "Day", @@ -400,7 +434,7 @@ chains_null <- sim_chains_max %>% nrow() ``` -Although most introductions do not generate secondary cases (N = `r chains_null`) or most outbreaks rapidly become extinct (median duration of `r chains_extinct$extinct_duration_median` and median size of `r chains_extinct$extinct_size_median`), only `r threshhold_summary$chains_theshold` epidemic trajectories among `r threshhold_summary$chains_number` simulations (`r threshhold_summary$chains_percentage`%) can reach to more than 100 infected cases. This finding is particularly remarkable because the reproduction number $R$ is less than 1 (offspring distribution mean of `r mers_offspring[["mean"]]`), but, given an offspring distribution dispersion parameter of `r mers_offspring[["dispersion"]]`, it shows the potential for explosive outbreaks of MERS disease. +Although most introductions of `r initial_cases` case per chain do not generate secondary cases (N = `r chains_null`) or most outbreaks rapidly become extinct (median duration of `r chains_extinct$extinct_duration_median` and median size of `r chains_extinct$extinct_size_median`), only `r threshhold_summary$chains_theshold` epidemic trajectories among `r threshhold_summary$chains_number` simulations (`r threshhold_summary$chains_percentage`%) can reach to more than 100 infected cases. This finding is particularly remarkable because the reproduction number $R$ is less than 1 (offspring distribution mean of `r mers_offspring[["mean"]]`), but, given an offspring distribution dispersion parameter of `r mers_offspring[["dispersion"]]`, it shows the potential for explosive outbreaks of MERS disease. ::::::::::::::::::::::::::::::::::: spoiler From fce7d094671f40941b21a42ebcf120f24b6be73f Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Wed, 10 Apr 2024 01:33:32 +0100 Subject: [PATCH 087/140] edit the challenges --- episodes/superspreading-simulate.Rmd | 104 +++++++++++++++++++-------- 1 file changed, 73 insertions(+), 31 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 7425946d..3fa4c517 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -97,6 +97,8 @@ The MERS offspring distribution will follow a negative binomial distribution wit mers_offspring <- c(mean = 0.60, dispersion = 0.02) ``` +:::::::::::::::::::::::::::: callout + The way we input an offspring distribution to `{epichains}` is by defining the R function that generates random values. For example, for a negative binomial distribution we use `rnbinom` with its corresponding `mu` and `size` arguments: ```r @@ -107,6 +109,8 @@ The way we input an offspring distribution to `{epichains}` is by defining the R The reference manual in `?rnbinom` tell us the specific arguments we require. +:::::::::::::::::::::::::::: + :::::::::::::::::::::::::: spoiler ### Poisson and other distributions @@ -120,7 +124,7 @@ For example, let's say that for the offspring distribution we want to use a Pois lambda = mers_offspring["mean"], ``` -In this example we can specify `lambda = mers_offspring["mean"]` because in a negative binomial model, when the dispersion parameter $k$ approaches infinity ($k \rightarrow \infty$) the variance equals the mean. This makes the conventional Poisson model an special case of the negative binomial model. +In this example we can specify `lambda = mers_offspring["mean"]` because in a negative binomial model, when the dispersion parameter $k$ approaches infinity ($k \rightarrow \infty$) the variance equals the mean. This makes the conventional Poisson model an special case of the negative binomial model. The mean of the negative binomial model (`mu`) can also be the mean of the poisson model (`lambda`). :::::::::::::::::::::::::: @@ -159,6 +163,8 @@ serial_summary <- serial_inverval$summary_stats %>% The serial interval for MERS has a mean of `r serial_summary$mean` days and standard deviation `r serial_summary$sd` days. +:::::::::::::::::::::::::::: callout + In `{epichains}` we need to specify the generation time as a function that generates random numbers. Using `{epiparameter}` has the advantage of using the distribution function `epiparameter::generate()` for this input. This will look like this: ```r @@ -167,6 +173,8 @@ function(x) generate(x = serial_inverval, times = x) This interface is similar to the one used by `{cfr}` to link with `{epiparameter}`. For further context, read the [work with delay distributions](https://epiverse-trace.github.io/cfr/articles/delay_distributions.html) vignette. +:::::::::::::::::::::::::::: + ## Simulate a single chain Now we are prepared to use the `simulate_chains()` function from `{epichains}` to create **one** transmission chain: @@ -208,7 +216,7 @@ The output of the `simulate_chains()` function creates a `` class obj ## Simulate multiple chains -We can use `simulate_chains()` to create multiple chains and increase the probability to simulate uncontrolled outbreaks projections. +We can use `simulate_chains()` to create multiple chains and increase the probability to simulate uncontrolled outbreaks projections given an overdispersed offspring distribution. We need to specify three additional elements: @@ -241,7 +249,29 @@ Or if you previously used the `*apply` family of functions, visit the package vi To get multiple chains, we need to apply the `simulate_chains()` function to each chain defined by a sequence of numbers from 1 to `number_chains`. -Let's use `map()` to iterate `simulate_chains()` in a vector from 1 to `r number_chains`: +First, let's make a draft sketch of how we use `purrr::map()` with `epichains::simulate_chains()`. The `map()` function requires two arguments: + +- `.x`, with a vector of numbers, and +- `.f`, a function to iterate to each value of the vector. + +The `sim` element is placed to register the iteration number (**chain ID**) as a new column in the `` output. The `purrr::list_rbind()` function aims to combine all the list outputs from `map()`: + +```r +map( + # vector of numbers (chain IDs) + .x = seq_len(number_chains), + # function to iterate to each chain ID number + .f = function(sim) { + simulate_chains(...) %>% + # creates a column with the chain ID number + mutate(chain_id = sim) + } +) %>% + # combine list outputs (for each chain ID) into a single data frame + list_rbind() +``` + +Now, we are prepared to use `map()` to iterate `simulate_chains()` in a vector from 1 to `r number_chains`: ```{r} simulated_chains_map <- @@ -332,9 +362,15 @@ simulated_chains_map %>% as_tibble() ``` -The output data frame collects **infectees** as the observation unit. Each infectee has a `sim_id`. Under the `infector_id` column we have the `sim_id` of each _infectee_ that behaved as an _infector_. Within the simulation number, under the `chain_id` column, each infectee got infected in a specific `generation` and (continuous) `time`. +The **story** that chain `r chain_to_observe` is telling is: "One index case infected `sim_id = 1`. Then, in the second generation of transmissions, `sim_id = 1` infected five cases. Later, in the third generation of transmissions, `sim_id = 2` infected three new cases." -The `Number of infectors (known)` includes the `NA` observation under the `infector_id` column. This refers to the infector specified as index case (in the `index_cases` argument), which started the transmission chain to the infectee of `sim_id = 1`, at `generation = 1`, and `time = 0`. +The output data frame collects **infectees** as the observation unit: +- Each infectee has a `sim_id`. +- Each _infectee_ that behaved as an _infector_ is registered in the `infector_id` column using `sim_id` of that infectee. +- Each infectee got infected in a specific `generation` and (continuous) `time`. +- The simulation number is registered under the `chain_id` column. + +**Note:** The `Number of infectors (known)` includes the `NA` observation under the `infector_id` column. This refers to the infector specified as index case (in the `index_cases` argument), which started the transmission chain to the infectee of `sim_id = 1`, at `generation = 1`, and `time = 0`. ::::::::::::::::::::::::::::: @@ -386,9 +422,9 @@ ggplot() + mapping = aes( x = day, y = cases_cumsum, - group = chain_id, - color = chain_id + group = chain_id ), + color = "gray", show.legend = FALSE ) + # create points to visualize the chain end point @@ -434,7 +470,7 @@ chains_null <- sim_chains_max %>% nrow() ``` -Although most introductions of `r initial_cases` case per chain do not generate secondary cases (N = `r chains_null`) or most outbreaks rapidly become extinct (median duration of `r chains_extinct$extinct_duration_median` and median size of `r chains_extinct$extinct_size_median`), only `r threshhold_summary$chains_theshold` epidemic trajectories among `r threshhold_summary$chains_number` simulations (`r threshhold_summary$chains_percentage`%) can reach to more than 100 infected cases. This finding is particularly remarkable because the reproduction number $R$ is less than 1 (offspring distribution mean of `r mers_offspring[["mean"]]`), but, given an offspring distribution dispersion parameter of `r mers_offspring[["dispersion"]]`, it shows the potential for explosive outbreaks of MERS disease. +Although most introductions of `r initial_cases` index case do not generate secondary cases (N = `r chains_null`) or most outbreaks rapidly become extinct (median duration of `r chains_extinct$extinct_duration_median` and median size of `r chains_extinct$extinct_size_median`), only `r threshhold_summary$chains_theshold` epidemic trajectories among `r threshhold_summary$chains_number` simulations (`r threshhold_summary$chains_percentage`%) can reach to more than 100 infected cases. This finding is particularly remarkable because the reproduction number $R$ is less than 1 (offspring distribution mean of `r mers_offspring[["mean"]]`), but, given an offspring distribution dispersion parameter of `r mers_offspring[["dispersion"]]`, it shows the potential for explosive outbreaks of MERS disease. ::::::::::::::::::::::::::::::::::: spoiler @@ -502,6 +538,10 @@ ggplot() + ) ``` +Notice that the proportion of simulated outbreaks that reached the 100-case threshold increases with the increase of the dispersion parameter $k$. + +![**Growth of simulated outbreaks with R0 = 1.5 and one initial case, conditional on non-extinction.** Boxes show median and interquartile range (IQR) of the first disease generation with 100 cases; whiskers show most extreme values within 1.5 × IQR of the boxes, and crosses show outliers. Percentages show the proportion of 10,000 simulated outbreaks that reached the 100-case threshold ([Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153)).](fig/see-nature04153_Fig2-c.jpg) + :::::::::::::::::::::: testimonial ### Early spread projections @@ -516,10 +556,12 @@ We invite you to read the vignette on [Projecting infectious disease incidence: :::::::::::::::::::::::::: challenge -Evaluate for ebola with know data from previous outbreaks +Evaluate the potential of Ebola to generate explosive outbreaks. Use the appropriate package to access delay data from previous outbreaks. :::::::::::::: hint +With `{epiparameter}` you can access and use delay distributions from previous outbreaks. + :::::::::::::: :::::::::::::: solution @@ -538,17 +580,15 @@ ebola_serial <- epidist_db( ) ``` + + :::::::::::::: ::::::::::::::::::::::::: :::::::::::::::::::::::::: challenge -from paper -Christian Althaus - - -data from Fayre et al on ebola +[Christian Althaus](https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(15)70135-0/fulltext) reused data published by [Faye et al., 2015 (Figure 2)](https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(14)71075-8/fulltext#gr2) on the transmission tree on Ebola virus disease in Conakry, Guinea, 2014. ```{r,message=FALSE,warning=FALSE} # Number of individuals in the trees @@ -565,6 +605,7 @@ c0 %>% geom_histogram() ``` +Estimate the offspring distribution from the distribution of secondary cases. Then estimate the large outbreak potential from this data. ::::::::::: hint @@ -574,13 +615,11 @@ c0 %>% ::::::::::: solution -remarkable even with R0 less than 1 -with potentially explosive outbreaks + -the observed variation in individual infectiousness in Ebola -means that although the probability of extinction is high, -new index cases also have the potential for explosive -regrowth of the epidemic. +Remarkable, even with R0 less than 1 +with potentially explosive outbreaks. the observed variation in individual infectiousness in Ebola +means that although the probability of extinction is high, new index cases also have the potential for explosive regrowth of the epidemic. ::::::::::: @@ -588,10 +627,20 @@ regrowth of the epidemic. :::::::::::::::::::: challenge -Calculate probabilities for Ebola using data from epiparameter using `{superspreading}` +Calculate probabilities for Ebola of a large outbreak and to contain an epidemic. Use the appropriate package to access delay data from previous outbreaks. :::::::::::::::::: hint +With `{epiparameter}` you can access and use delay distributions from previous outbreaks. + +With `{superspreading}` you can get numerical solutions to processes that `{epichains}` solve using branching processes. We invite you to read the `{superspreading}` vignette on [Epidemic risk](https://epiverse-trace.github.io/superspreading/articles/epidemic_risk.html)! + +:::::::::::::::::: + +::::::::::::::::::::: hint + +Here is an example with the MERS offspring distribution estimates: + ```{r,message=FALSE,warning=FALSE} library(superspreading) ``` @@ -622,23 +671,16 @@ probability_epidemic( #' get ebola params ``` + + :::::::::::::::::: ::::::::::::::::::::::::::::::::::::: -::::::::::::::::::::::::: testimonial - -you can use early linelist data as seed cases to make short term projection of cases - -take a look to vignette - - - -::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::: keypoints -- Use `{epichains}` +- Use `{epichains}` to simulate the large outbreak potential of diseases with overdispersed offspring distributions. :::::::::::::::::::::::::::::::::::::::::::::::: From d3ca8dd5c934d0cbc97eca83106194749a9ef89b Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Wed, 10 Apr 2024 01:36:19 +0100 Subject: [PATCH 088/140] clean challenge section writing --- episodes/superspreading-simulate.Rmd | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 3fa4c517..88294a01 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -588,7 +588,13 @@ ebola_serial <- epidist_db( :::::::::::::::::::::::::: challenge -[Christian Althaus](https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(15)70135-0/fulltext) reused data published by [Faye et al., 2015 (Figure 2)](https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(14)71075-8/fulltext#gr2) on the transmission tree on Ebola virus disease in Conakry, Guinea, 2014. +[Christian Althaus, 2015](https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(15)70135-0/fulltext) reused data published by [Faye et al., 2015 (Figure 2)](https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(14)71075-8/fulltext#gr2) on the transmission tree on Ebola virus disease in Conakry, Guinea, 2014. + +Using the data under the **hint** tab, estimate the offspring distribution from the distribution of secondary cases. Then estimate the large outbreak potential from this data. + +::::::::::: hint + +Code with the transmission tree data written by [Christian Althaus, 2015](https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(15)70135-0/fulltext): ```{r,message=FALSE,warning=FALSE} # Number of individuals in the trees @@ -605,12 +611,6 @@ c0 %>% geom_histogram() ``` -Estimate the offspring distribution from the distribution of secondary cases. Then estimate the large outbreak potential from this data. - -::::::::::: hint - -... - ::::::::::: ::::::::::: solution From 71fc68ba75b19d05a81eeabac36b68d179c3ef59 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Wed, 10 Apr 2024 01:43:07 +0100 Subject: [PATCH 089/140] provide dosified reading of the epichains output --- episodes/superspreading-simulate.Rmd | 32 ++++++++++++++++++++++++---- 1 file changed, 28 insertions(+), 4 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 88294a01..0cfd6c31 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -249,6 +249,10 @@ Or if you previously used the `*apply` family of functions, visit the package vi To get multiple chains, we need to apply the `simulate_chains()` function to each chain defined by a sequence of numbers from 1 to `number_chains`. +::::::::::::::::::::::::::::::: callout + +### purrr and epichains + First, let's make a draft sketch of how we use `purrr::map()` with `epichains::simulate_chains()`. The `map()` function requires two arguments: - `.x`, with a vector of numbers, and @@ -271,6 +275,8 @@ map( list_rbind() ``` +::::::::::::::::::::::::::::::: + Now, we are prepared to use `map()` to iterate `simulate_chains()` in a vector from 1 to `r number_chains`: ```{r} @@ -307,7 +313,7 @@ simulated_chains_map %>% count(chain_id, sort = TRUE) ``` -::::::::::::::::::::::::::::::::: callout +::::::::::::::::::::::::::::::::: discussion ### Read the epichains output @@ -336,7 +342,15 @@ chain_to_observe <- simulated_chains_map %>% pull(chain_id) ``` -To explore the output format of the `` class object of name `simulated_chains_map`, let's observe closely the simulated `chain_id` number `r chain_to_observe`. Let's use `dplyr::filter()` for this: +To explore the output format of the `` class object of name `simulated_chains_map`, let's observe closely the simulated `chain_id` number `r chain_to_observe`. + +::::::::::::::::::::::::::::::::: + +::::::::::::::::::::::::: solution + +### epidemics object + +Let's use `dplyr::filter()` for this: ```{r} #### get epichain summary ---------------------------------------------------- @@ -352,7 +366,13 @@ Number of infectors (known): 3 Number of generations: 3 ``` -The simulated `chain_id` number `r chain_to_observe` has three known infector and three generations. These numbers are more visible when reading the `` objects as a data frame: +The simulated `chain_id` number `r chain_to_observe` has three known infector and three generations. These numbers are more visible when reading the `` objects as a data frame. + +::::::::::::::::::::::::: + +::::::::::::::::::::::::: solution + +### epichains data frame ```{r} #### infector-infectee data frame -------------------------------------------- @@ -364,6 +384,10 @@ simulated_chains_map %>% The **story** that chain `r chain_to_observe` is telling is: "One index case infected `sim_id = 1`. Then, in the second generation of transmissions, `sim_id = 1` infected five cases. Later, in the third generation of transmissions, `sim_id = 2` infected three new cases." +::::::::::::::::::::::::: solution + +### an infectee data frame + The output data frame collects **infectees** as the observation unit: - Each infectee has a `sim_id`. - Each _infectee_ that behaved as an _infector_ is registered in the `infector_id` column using `sim_id` of that infectee. @@ -372,7 +396,7 @@ The output data frame collects **infectees** as the observation unit: **Note:** The `Number of infectors (known)` includes the `NA` observation under the `infector_id` column. This refers to the infector specified as index case (in the `index_cases` argument), which started the transmission chain to the infectee of `sim_id = 1`, at `generation = 1`, and `time = 0`. -::::::::::::::::::::::::::::: +::::::::::::::::::::::::: ## Visualize multiple chains From e8e3bfb3c615847bce9e8b99b7b10261d01d7d16 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Wed, 10 Apr 2024 01:50:23 +0100 Subject: [PATCH 090/140] fix closing of tag callout --- episodes/superspreading-simulate.Rmd | 2 ++ 1 file changed, 2 insertions(+) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 0cfd6c31..1dbf9505 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -384,6 +384,8 @@ simulated_chains_map %>% The **story** that chain `r chain_to_observe` is telling is: "One index case infected `sim_id = 1`. Then, in the second generation of transmissions, `sim_id = 1` infected five cases. Later, in the third generation of transmissions, `sim_id = 2` infected three new cases." +::::::::::::::::::::::::: + ::::::::::::::::::::::::: solution ### an infectee data frame From 6b4ae733eae363303061daf7202635ca1c3b4280 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Wed, 10 Apr 2024 02:30:12 +0100 Subject: [PATCH 091/140] fill introduction --- episodes/superspreading-simulate.Rmd | 97 ++++++++++++++++------------ 1 file changed, 54 insertions(+), 43 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 1dbf9505..6180fe32 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -32,20 +32,6 @@ Learners should familiarise themselves with following concept dependencies befor - - - - -We are going to use `{purrr}` - -```{r,message=FALSE,warning=FALSE} -library(epichains) -library(epiparameter) -library(tidyverse) -``` - -## Superspreading in decision making - Transmission heterogeneity affects epidemic establishment and the ease of control ([Cori et al., 2017](https://royalsocietypublishing.org/doi/10.1098/rstb.2016.0371)). + Greater heterogeneity reduces the chance of an outbreak emerging from single case. Individuals with more extreme amount of secondary cases are rare. @@ -54,40 +40,41 @@ Transmission heterogeneity affects epidemic establishment and the ease of contro + Conversely, heterogeneity in transmission may provide opportunities for *targeted interventions* if the individuals who contribute more to transmission (due to biological, environmental or behavioral factors) share socio-demographic or geographical characteristics that can be defined. -We can have an early understanding of a disease epidemic potential from the mean reproduction number $R$ and dispersion $k$ of an offspring distribution to answer questions like: + -- What is the probability of an pathogen to cause large outbreak? -- What is the probability of an outbreak to get extinct? -- What is the probability to contain the ongoing outbreak? +However, how can we have an early understanding of a disease epidemic potential from the mean reproduction number $R$ and dispersion $k$ of an offspring distribution? -::::::::::::::::::::::::::: testimonial + -### Epidemic Risk assessment accounting for superspreading +In this episode we are going to use the `{epichains}` package to simulate transmission chains to estimate the potential for explosive outbreaks. We are going to use it with functions from `{epiparameter}`, `{dplyr}` and `{purrr}`, so also loading the `{tidyverse}` package: + +```{r,message=FALSE,warning=FALSE} +library(epichains) +library(epiparameter) +library(tidyverse) +``` -These estimates vary non-linearly with respect to the mean reproduction number $R$ and dispersion $k$ of a given disease. +## Simulation of uncontrolled outbreaks -We invite you to read the `{superspreading}` vignette on [Epidemic risk](https://epiverse-trace.github.io/superspreading/articles/epidemic_risk.html)! +Infectious disease epidemics spread through populations when a chain of infected individuals transmit the infection to others. [Branching processes](https://epiverse-trace.github.io/epichains/articles/theoretical_background.html) can be used to model this process. A branching process is a stochastic process where each infectious individual in a generation gives rise to a random number of individuals in the next generation, starting with the index case in generation 1. The distribution of the number of offspring is called the offspring distribution. -::::::::::::::::::::::::::: +`{epichains}` provides methods to analyse and simulate the *size* and *length* of branching processes with an arbitrary offspring distribution. `{epichains}` implements a rapid and low detail model to reconstruct transmission chains to assess epidemic risk, project cases into the future, and simulate interventions. -## Simulation of uncontrolled outbreaks +::::::::::::::::::: discussion -simulation of uncontrolled outbreaks +### chain size and length -- branching process - + To assess the effect of individual variation on disease outbreaks, we analyse a branching process model with negative binomial offspring distribution +- The **size** of the transmission chain is the total number of individuals infected by a single case, and -- estimate tree parameters using branching process - + estimate size - + estimate length +- the **length** of the transmission chain is the number of generations from the first case to the last case they produced before the chain ended. -with estimated parameter we then can reconstruct tranmission chains to forecast and simulate interventions +The *size* calculation includes the first case and the *length* calculation includes the first generation when the first case starts the chain (See figure below). ![**An example of a transmission chain starting with a single case C1.** Cases are represented by blue circles and arrows indicate who infected whom. The chain grows through generations Gen 1, Gen 2, and Gen 3, producing cases C2, C3, C4, C5, and C6. The chain ends at generation Gen 3 with cases C4, C5, and C6. The size of C1’s chain is 6, including C1 (that is, the sum of all blue circles) and the length is 3, which includes Gen 1 (maximum number of generations reached by C1’s chain).](https://raw.githubusercontent.com/epiverse-trace/epichains/main/vignettes/img/transmission_chain_example.png) -### branching process +:::::::::::::::::::: -- probability generating function (pgf) of the offspring distribution +To use `{epichains}` we need two key delays: the offspring distribution and the generation time! ## Get the offspring distribution @@ -99,6 +86,8 @@ mers_offspring <- c(mean = 0.60, dispersion = 0.02) :::::::::::::::::::::::::::: callout +### offspring distribution for epichains + The way we input an offspring distribution to `{epichains}` is by defining the R function that generates random values. For example, for a negative binomial distribution we use `rnbinom` with its corresponding `mu` and `size` arguments: ```r @@ -165,6 +154,8 @@ The serial interval for MERS has a mean of `r serial_summary$mean` days and stan :::::::::::::::::::::::::::: callout +### generation time for epichains + In `{epichains}` we need to specify the generation time as a function that generates random numbers. Using `{epiparameter}` has the advantage of using the distribution function `epiparameter::generate()` for this input. This will look like this: ```r @@ -253,13 +244,11 @@ To get multiple chains, we need to apply the `simulate_chains()` function to eac ### purrr and epichains -First, let's make a draft sketch of how we use `purrr::map()` with `epichains::simulate_chains()`. The `map()` function requires two arguments: +First, let's make a minimal sketch of how we use `purrr::map()` with `epichains::simulate_chains()`. The `map()` function requires two arguments: - `.x`, with a vector of numbers, and - `.f`, a function to iterate to each value of the vector. -The `sim` element is placed to register the iteration number (**chain ID**) as a new column in the `` output. The `purrr::list_rbind()` function aims to combine all the list outputs from `map()`: - ```r map( # vector of numbers (chain IDs) @@ -275,6 +264,8 @@ map( list_rbind() ``` +The `sim` element is placed to register the iteration number (**chain ID**) as a new column in the `` output. The `purrr::list_rbind()` function aims to combine all the list outputs from `map()`. + ::::::::::::::::::::::::::::::: Now, we are prepared to use `map()` to iterate `simulate_chains()` in a vector from 1 to `r number_chains`: @@ -348,7 +339,7 @@ To explore the output format of the `` class object of name `simulate ::::::::::::::::::::::::: solution -### epidemics object +### the epichains object Let's use `dplyr::filter()` for this: @@ -372,7 +363,7 @@ The simulated `chain_id` number `r chain_to_observe` has three known infector an ::::::::::::::::::::::::: solution -### epichains data frame +### the epichains data frame ```{r} #### infector-infectee data frame -------------------------------------------- @@ -382,7 +373,7 @@ simulated_chains_map %>% as_tibble() ``` -The **story** that chain `r chain_to_observe` is telling is: "One index case infected `sim_id = 1`. Then, in the second generation of transmissions, `sim_id = 1` infected five cases. Later, in the third generation of transmissions, `sim_id = 2` infected three new cases." +Chain `r chain_to_observe` is telling us an **story**: "In the first transmission generation at `time = 0`, one index case infected the first case with `sim_id = 1`. Then, in the second transmission generation (between `time` 10 to 16), `sim_id = 1` infected five cases. Later, in the third transmission generation (between `time` 26 to 30), `sim_id = 2` infected three new cases." ::::::::::::::::::::::::: @@ -391,6 +382,7 @@ The **story** that chain `r chain_to_observe` is telling is: "One index case inf ### an infectee data frame The output data frame collects **infectees** as the observation unit: + - Each infectee has a `sim_id`. - Each _infectee_ that behaved as an _infector_ is registered in the `infector_id` column using `sim_id` of that infectee. - Each infectee got infected in a specific `generation` and (continuous) `time`. @@ -450,7 +442,8 @@ ggplot() + y = cases_cumsum, group = chain_id ), - color = "gray", + color = "black", + alpha = 0.25, show.legend = FALSE ) + # create points to visualize the chain end point @@ -564,9 +557,9 @@ ggplot() + ) ``` -Notice that the proportion of simulated outbreaks that reached the 100-case threshold increases with the increase of the dispersion parameter $k$. +Notice that when we increase the dispersion parameter from $k = 0.01$ to $k = \infty$, given a fixed reproduction number $R = 1.5$, the proportion of simulated outbreaks that reached the 100-case threshold increases. -![**Growth of simulated outbreaks with R0 = 1.5 and one initial case, conditional on non-extinction.** Boxes show median and interquartile range (IQR) of the first disease generation with 100 cases; whiskers show most extreme values within 1.5 × IQR of the boxes, and crosses show outliers. Percentages show the proportion of 10,000 simulated outbreaks that reached the 100-case threshold ([Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153)).](fig/see-nature04153_Fig2-c.jpg) +![**Growth of simulated outbreaks with R = 1.5 and one initial case, conditional on non-extinction.** Boxes show median and interquartile range (IQR) of the first disease generation with 100 cases; whiskers show most extreme values within 1.5 × IQR of the boxes, and crosses show outliers. Percentages show the proportion of 10,000 simulated outbreaks that reached the 100-case threshold ([Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153)).](fig/see-nature04153_Fig2-c.jpg) :::::::::::::::::::::: testimonial @@ -582,6 +575,8 @@ We invite you to read the vignette on [Projecting infectious disease incidence: :::::::::::::::::::::::::: challenge +### Ebola's large outbreak potential + Evaluate the potential of Ebola to generate explosive outbreaks. Use the appropriate package to access delay data from previous outbreaks. :::::::::::::: hint @@ -614,6 +609,8 @@ ebola_serial <- epidist_db( :::::::::::::::::::::::::: challenge +### From a distribution of secondary cases + [Christian Althaus, 2015](https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(15)70135-0/fulltext) reused data published by [Faye et al., 2015 (Figure 2)](https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(14)71075-8/fulltext#gr2) on the transmission tree on Ebola virus disease in Conakry, Guinea, 2014. Using the data under the **hint** tab, estimate the offspring distribution from the distribution of secondary cases. Then estimate the large outbreak potential from this data. @@ -653,13 +650,27 @@ means that although the probability of extinction is high, new index cases also :::::::::::::::::::: challenge +### Probability to contain an epidemic + Calculate probabilities for Ebola of a large outbreak and to contain an epidemic. Use the appropriate package to access delay data from previous outbreaks. :::::::::::::::::: hint With `{epiparameter}` you can access and use delay distributions from previous outbreaks. -With `{superspreading}` you can get numerical solutions to processes that `{epichains}` solve using branching processes. We invite you to read the `{superspreading}` vignette on [Epidemic risk](https://epiverse-trace.github.io/superspreading/articles/epidemic_risk.html)! +::::::::::::::::::::: + +::::::::::::::::::: hint + +### Epidemic Risk assessment accounting for superspreading + +With `{superspreading}` you can get numerical solutions to processes that `{epichains}` solve using branching processes. We invite you to read the `{superspreading}` vignette on [Epidemic risk](https://epiverse-trace.github.io/superspreading/articles/epidemic_risk.html) and respond to: + +- What is the probability of an pathogen to cause large outbreak? +- What is the probability of an outbreak to get extinct? +- What is the probability to contain the ongoing outbreak? + +Check how these estimates vary non-linearly with respect to the mean reproduction number $R$ and dispersion $k$ of a given disease. :::::::::::::::::: From c78e3d125a5e7a30cba9a0fb20b38bb268c7c665 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Wed, 10 Apr 2024 02:30:47 +0100 Subject: [PATCH 092/140] add figures for k and percent of large outbreaks --- episodes/fig/see-nature04153_Fig2-c.jpg | Bin 0 -> 7325 bytes episodes/fig/see-nature04153_Fig2.jpg | Bin 0 -> 21641 bytes 2 files changed, 0 insertions(+), 0 deletions(-) create mode 100644 episodes/fig/see-nature04153_Fig2-c.jpg create mode 100644 episodes/fig/see-nature04153_Fig2.jpg diff --git a/episodes/fig/see-nature04153_Fig2-c.jpg b/episodes/fig/see-nature04153_Fig2-c.jpg new file mode 100644 index 0000000000000000000000000000000000000000..1edbfe75b896f3c8a776f0cb58fad88c2b20c18b GIT binary patch literal 7325 zcmbW5by!qg)aVZm-Q6LLQi8zH`O*#`N|%6?fC$pzAV`;@3?(2XpbiZ~BOOC`clXda zb9wLmzVF`W{&QoUz5Y1oti7N0TjxA$ueC8#m?eN*OHES^z{0`;Ufo{+W)@HZKo1`L zJMIPhe&FEa;9z6p5aQwC;u8}R6B7{<5s{Eml9P~9kP;D*(~?tAQPa@S5R=i-(^At@ zQqxfXy9gHOehxMc0S*oUH3<<3_5ZVA{sI*Ez$c&qgv9|opuhrAU}4$;HUPlFx%c*8 zhyO#c9^Ctgi-%7@NOW&dMGic`0)ZZ2gZ}mU-a6?1J%CMtL&+|pgiH0@8jr)BTJ+^X5U0dJS+}hqj9iN<@onKsDUH{941%Uns)_;-xZ(J1j zTo16ZLD+cza$!C2xmOScHV(T8E~V0QJZpC<4$+VJ)XHD7%UTFHpXwjc*mw*R(sGF{ zbEE!6`|o7`cVHp^Uu6FU_CL910Adi<{l^1Q01CkM;CXWWWxgAVQ{9Rf1GJhq(V&sS zZx={HCQPghPbP_cHjf@22l?(=X>X$)rfp7|CtWOV6B^_F-6!Q9`;iW(wT|ApFVCC3 zOoo(Cp4RuPiK@&f`7rg?>=5Gi18&35o*f5xV*ts5AuLrJ-+I%pZP(9?+&Q{Ck0<6L z1^}4v3hxoA?y?!h#aTZfAIvf1FT$xvW*e_wbrh zKBs|dxhf)(9rex7zcbXUa0?}s*o&1DLtoiLge&muW71!l>b;EW5Vg@x`N%J&$gXDS zQ3>It5lY5%T%LC~lfH3`eN609Sh&AInDVZA-tg5+NR-YPQ*^Nr7tRmTf>n#gyLLtf zW3L!E#akZm(bfl_8O@%spmW+iiee%SjA)=!5iy|&6R|5()1*vl-y&*)_xqAuN!@BE1Vo3M3A|KO^guO*2G zZZqTfeASe5xHGh(-FBAl)if^;!Y}Xc&3<-7rT=fiz-D%%q5^$FQ+sPwYCWv~RiF3F zF}Q4LNGIp@DYf*zl}^PgUxJ> z8xkw4{=56ONfwpDnn@_SHO&nTYq2n(1AV?xk0Y~CP-3lVPM5p>uz7o8%<9liAbbd! z3NUUMKKDIM+5Z`VoN9oj4xiL}e|SFAC=IJLkn+bruD80>MOp+ETWA^$aDYgPv$BLi zI2B;?gFAlRwhK0L!v(Lp@{zpu1CD^%Q0jix5Bj^5(xAy)##6#ab;(;zOJzNG1)Uh+ zWcdel$pr)4+NVugO3)8v{P;S1C+&^_DisE4CZ9j=U&CV%Sdie){^FDy#dvoA{F}Lk zf$PzYY(s(I#naDHa58eu74flC)nWLaU8!^E-H%EA@|qZ=iwl;H&VHl21q)j~^UOjw zscriUUzpqrbqmUcR%hI#rn$+)I*p>T>ixe`SJj(hhXlwKO)-vzhluhR!$rQARbOIN zeOOYvyH^?hijNGZna`MZ6YJvklxXH;qnIT=ze%6HG^q1bCnv7+ zz3I0F9xGa>7+W`M-iTO_pmLL+){=q6{l5|PH}ku>mUr7@`aoeZwX`c&@El8C!kFi+ z%u0Svu)KfG(5;2*vdLK-@5@PBSdd*^MS?xodUH`M=g=Y@6RX&d6hjplm@)cGl{sGph*0Dr2$=XD@S9^LM}4x1?9c~h-FIhZ_l<#Op$LE z2+dUoEx7%Zg#luXv{i9M3m(Z7iC-}5AmF~`6AKbC8kGq`Gz$z1>q!A$Si3Kviv|hq zD+$z{9LEn~ist;As_tQ%yljpokT*JVID!G+N85CC(8HNt7=VB`#&l;vCV<_a5mKHv zLFSnK&SSwL?LJ91K|DG2Q6k$p+gBK%GzJ5pqPJDq@`Y2Mw+$#9qtI+c{TRT}Hys^Z z2SpR7-@B%ljAjo&de#i@tsrb#HEo+6UNdRp;c}xN=9UCbYK}zzX1sZX0c36!x|jcW zWzm&yFTDL|M|)GWT1(^$^&($fuep+0hDw{UICoMCCBF3};%nIEHfylVnkytJO_;yH zf=VCY&`4j1TsL5V&DC4khIpPyQ&eD=Hk~xdcV}>#5C#|}I|v@=3(VN6m}syWamxG< z`Z`Lq?```2r<4?m^@KCqlKZ`loAH8ed=mpGur05zSzlV77&HwprJIx|=r+5~F2yVF z$lJ!hld<_RE>7Z4;ytr~gdplhGZzdKSF}T!2-N0_f(sas{-=X){pG*K`umS_8bNCK z-Z#HsYQ6B!I1jUvD05)wj!gT0tk;u|v){Nb2<3lMlJ8x-2`NFK3oF#$+X` z1)bjGz{hJMdZS>z6MXXqx6_PDpd=7UMkqu7<3NvbG5&t#MXQm6S^XRBWJLHCg`i^V zA4Qk9AK%xz&l#642eYZ~Q@gT$qZKv(Zd>w}zq5(q^7zK|GO5^c238W}<>M^4G3ze= zrGny5hwbq=wU&uqp$n{Kz&$f4AR{mV7hpHcU%4)&)k+LSUyf=BFe~PCGw=7pU*l}krfPgHa(rO zigm4eBzR_0IY_l#I<4YB_gNMez+gaM0q!G)C+f=mp33G=9c8 zO_G5r#0Vm!xbtBeKpPjg1~c%wt(#{IM$4+Y{j!>EStd%K)vzNVnXxkak>UMFuquTj zT%h@gad+znsd$6QifwQpg)dz#dZ-Emtn7Zp0AX>f48p>&RTXKz@TD%6h8flUU9nfh znj3$K9b}Kl-kk05fjTP}qbx=1=oH?Ju9l0;$-0Lhp?{)Zzq&1HMP)&?7LNww11$=j zewtj>KTuQFYWstXsOu zjnTac&Ke!%d{&hzI)3Y~TI&3*pB$7hy%jBqvWEvPZ+QvhK=PG>oW&-SN!~Ni#{c<9 z<;e9tocCy@kue$wGp>FYusS<>8+~jQmnlCM$mI7^v%tA@8cC%pkoJO0=^)2xRo$fr z8K!T9j3G7sr)3py>M?vhtZMDE>^Ta;MbgCk1w=o4)2p#Ggg2OMMJa2EB}6TD(YFP$~f>ICj6^4TkH zfz|ZB&+NzR>1)ilT^Di+o%tBx6WXW-5zQiaXlgiH-9J_SPUkR#!oAD;(4x9!`&xe= zRApAAHluPCaLLe8I`?Zt-=M?x)lWh(K>Wl}e!oLM z+q$&ex9fg1F7}6q^@%(5c|(Wr@e6w=VzU=OrgyDe*+_+}tX+W5T}Bq^j!01cS{%X; 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z0*X`~^vOMn$i%v1Lj`~i>8Ce@1b>=>_lrVtcIsEdrpknHILKo)qyi2F$xD|LhAux< zTmwojLE|R^2Z^*vP&}mC*18f-B(>ylSwC4(n0)cKb=5KJ*Z zI;$hUktkrDR>LvvjdBO%2OVKBgUE8mN~wq<#jJNJktzbsIsn{#f#~rXq$&yCBW-L~ zA26&;49OR_nfgjc9V}&XiIHIz6V3$Z9$8RL1#B1X<|*k(e?-7f0eU}3DKM-kjAa~J zTC$AhL$L$7ZKf#zNeKWgJWk@w;j1A|Oih>!X@gkS03(x=K$Kv})?o*SO8i^KOj_$f zjCX11$ya(peIn6sIzRgQ>jF(pPB*(YViGpB6kCLb9t;|BGyedgS?nZUMwn!dPp24b z1*i~IpdXe=U9tiJ&#SDlA!s(Uti-~_7`k{bC|1g0!3IZqV(wm*Oysq!!KgtsIE82~ z`!AfHsAiz%_zB5ABti#iXb_S(u@Xc`qzyPgd1G%h5MzX?Be;4nK(w(iX&sk(Cl0IP zP;nH$p<-%ORl7(OsxF*Lt^^9;~QF(W3~_a4ss| z@FEqWK1@g65N0Y!;sZ?Lp%0`X{ zDZ8!Y>3Fm}YQ$I=7R8IT0#n*H!MWZ5fKrLO_G+=rPK!m(f!o*7nmqrv~4zd|k z(vUDqz$NRF&{z^w_aOj*5fO#6sDZ@5lVt4)D9zp&f?HjH*LTa2(orC{8%GF0U}F&( zv$7DDXSuwE7;D86icuxu#v5V-$z_x+5+)cijCt)?vwKg0gTVk&g-gh`nkg?U%osp~ zNXpUIp@#s#fx&iSG|Ex zrY{qH><8G!gD}Ch0hE>fHbz;BpZsHTWA2ETmR6vNv>FwN$^rrjMI=q)-Lh~zJ3#0N z1=xu?L0LEszz$Me6-JJ$$pX^|Lfw?0R00aDd1Zwq9EpR5V1*JKE6}BJ6|h1ylb4@L zDZ8Zx&?u5SKDLbm%0c4=#ZKGT8(`yk!E44n?p#!2}@& WjDaS*5H`F>GXSXrrJ$h-@&DNh-JEOy literal 0 HcmV?d00001 From 981413beeb41bbb3def7ed5cde44636064b48dae Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Wed, 10 Apr 2024 02:32:01 +0100 Subject: [PATCH 093/140] add preliminary time to 30 min --- episodes/superspreading-estimate.Rmd | 2 +- episodes/superspreading-simulate.Rmd | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 20367f67..3dc019f4 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -1,6 +1,6 @@ --- title: 'Account for superspreading' -teaching: 10 +teaching: 30 exercises: 2 --- diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 6180fe32..d26025d5 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -1,6 +1,6 @@ --- title: 'Simulate transmission chains' -teaching: 10 +teaching: 30 exercises: 2 --- From b508e35cf68835c7178665d687e53bda9d6cd0a6 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Wed, 10 Apr 2024 03:06:37 +0100 Subject: [PATCH 094/140] use grammarly with simulate episode --- episodes/superspreading-simulate.Rmd | 228 +++++++++++++++++++++------ 1 file changed, 176 insertions(+), 52 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index d26025d5..9b6c53c9 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -20,7 +20,7 @@ exercises: 2 ## Prerequisites -Learners should familiarise themselves with following concept dependencies before working through this tutorial: +Learners should familiarise themselves with the following concept dependencies before working through this tutorial: **Statistics**: probability distributions. @@ -34,19 +34,139 @@ Learners should familiarise themselves with following concept dependencies befor Transmission heterogeneity affects epidemic establishment and the ease of control ([Cori et al., 2017](https://royalsocietypublishing.org/doi/10.1098/rstb.2016.0371)). -+ Greater heterogeneity reduces the chance of an outbreak emerging from single case. Individuals with more extreme amount of secondary cases are rare. ++ Greater heterogeneity reduces the chance of an outbreak emerging from a single case. Individuals with a more extreme amount of secondary cases are rare. + However, if the outbreak gets established, this heterogeneity can make an outbreak hard to control using *mass interventions* (which assumes transmission homogeneity), as a single uncontrolled case can generate a large number of secondary cases. -+ Conversely, heterogeneity in transmission may provide opportunities for *targeted interventions* if the individuals who contribute more to transmission (due to biological, environmental or behavioral factors) share socio-demographic or geographical characteristics that can be defined. ++ Conversely, heterogeneity in transmission may provide opportunities for *targeted interventions* if the individuals who contribute more to transmission (due to biological, environmental or behavioural factors) share socio-demographic or geographical characteristics that can be defined. -However, how can we have an early understanding of a disease epidemic potential from the mean reproduction number $R$ and dispersion $k$ of an offspring distribution? +However, how can we understand the potential of a disease epidemic early from the mean reproduction number $R$ and the dispersion $k$ of an offspring distribution? + +```{r,echo=FALSE,warning=FALSE,message=FALSE,fig.cap="Observed number of cumulative cases from the Middle East respiratory syndrome (MERS) outbreak in South Korea, 2015, alongside with simulated transmission chains given a known offspring distribution."} +library(epichains) +library(epiparameter) +library(tidyverse) +library(outbreaks) + +mers_cumcases <- mers_korea_2015$linelist %>% + # incidence2 workflow + incidence2::incidence(date_index = "dt_onset") %>% + incidence2::complete_dates() %>% + # wrangling using {dplyr} + mutate(count_cumsum = cumsum(count)) %>% + rownames_to_column(var = "day") %>% + mutate(day = as.numeric(day)) + +# offspring distribution +mers_offspring <- c(mean = 0.60, dispersion = 0.02) + +# generation time +serial_inverval <- epidist_db( + disease = "mers", + epi_dist = "serial", + single_epidist = TRUE +) + +# Set seed for random number generator +set.seed(33) +# Number of simulation runs +number_chains <- 1000 +# Number of initial cases +initial_cases <- 1 + +simulated_chains_map <- + # iterate one function across multiple numbers (chain IDs) + map( + # vector of numbers (chain IDs) + .x = seq_len(number_chains), + # function to iterate to each chain ID number + .f = function(sim) { + simulate_chains( + # simulation controls + index_cases = initial_cases, + statistic = "size", + # offspring + offspring_dist = rnbinom, + mu = mers_offspring["mean"], + size = mers_offspring["dispersion"], + # generation + generation_time = function(x) generate(x = serial_inverval, times = x) + ) %>% + # creates a column with the chain ID number + mutate(chain_id = sim) + } + ) %>% + # combine list outputs (for each chain ID) into a single data frame + list_rbind() + +# daily aggregate of cases +simulated_chains_day <- simulated_chains_map %>% + # use data.frame output from object + as_tibble() %>% + # transform chain ID column to factor (categorical variable) + mutate(chain_id = as_factor(chain_id)) %>% + # get the round number (day) of infection times + mutate(day = ceiling(time)) %>% + # count the daily number of cases each simulation (chain ID) + count(chain_id, day, name = "cases") %>% + # calculate the cumulative number of cases for each simulation (chain ID) + group_by(chain_id) %>% + mutate(cases_cumsum = cumsum(cases)) %>% + ungroup() + +# Summarise the chain duration and size +sim_chains_max <- + simulated_chains_day %>% + group_by(chain_id) %>% + summarise( + # duration + day_max = max(day), + # size + cases_total = max(cases_cumsum) + ) %>% + ungroup() + +# Observed cases vs Simulated transmission chains +mers_cumcases_type <- + mers_cumcases %>% + mutate(type = "Observed") +simulated_chains_day_type <- + simulated_chains_day %>% + mutate(type = "Simulated") + +ggplot() + + geom_line( + data = simulated_chains_day_type, + mapping = aes( + x = day, + y = cases_cumsum, + group = chain_id, + color = type + ) + ) + + geom_hline(aes(yintercept = 100), lty = 2) + + geom_line( + data = mers_cumcases_type, + mapping = aes( + x = day, + y = count_cumsum, + color = type + ), + linewidth = 1.5 + ) + + labs( + x = "Day since first report", + y = "Cumulative cases", + color = "Type" + ) +``` + -In this episode we are going to use the `{epichains}` package to simulate transmission chains to estimate the potential for explosive outbreaks. We are going to use it with functions from `{epiparameter}`, `{dplyr}` and `{purrr}`, so also loading the `{tidyverse}` package: +In this episode, we will use the `{epichains}` package to simulate transmission chains to estimate the potential for explosive outbreaks. We are going to use it with functions from `{epiparameter}`, `{dplyr}` and `{purrr}`, so also loading the `{tidyverse}` package: ```{r,message=FALSE,warning=FALSE} library(epichains) @@ -58,23 +178,23 @@ library(tidyverse) Infectious disease epidemics spread through populations when a chain of infected individuals transmit the infection to others. [Branching processes](https://epiverse-trace.github.io/epichains/articles/theoretical_background.html) can be used to model this process. A branching process is a stochastic process where each infectious individual in a generation gives rise to a random number of individuals in the next generation, starting with the index case in generation 1. The distribution of the number of offspring is called the offspring distribution. -`{epichains}` provides methods to analyse and simulate the *size* and *length* of branching processes with an arbitrary offspring distribution. `{epichains}` implements a rapid and low detail model to reconstruct transmission chains to assess epidemic risk, project cases into the future, and simulate interventions. +`{epichains}` provides methods to analyse and simulate the *size* and *length* of branching processes with an arbitrary offspring distribution. `{epichains}` implements a rapid and low-detail model to reconstruct transmission chains to assess epidemic risk, project cases into the future, and simulate interventions. ::::::::::::::::::: discussion ### chain size and length -- The **size** of the transmission chain is the total number of individuals infected by a single case, and +- The **size** of the transmission chain is the total number of individuals infected by a single case and - the **length** of the transmission chain is the number of generations from the first case to the last case they produced before the chain ended. -The *size* calculation includes the first case and the *length* calculation includes the first generation when the first case starts the chain (See figure below). +The *size* calculation includes the first case, and the *length* calculation contains the first generation when the first case starts the chain (See figure below). -![**An example of a transmission chain starting with a single case C1.** Cases are represented by blue circles and arrows indicate who infected whom. The chain grows through generations Gen 1, Gen 2, and Gen 3, producing cases C2, C3, C4, C5, and C6. The chain ends at generation Gen 3 with cases C4, C5, and C6. The size of C1’s chain is 6, including C1 (that is, the sum of all blue circles) and the length is 3, which includes Gen 1 (maximum number of generations reached by C1’s chain).](https://raw.githubusercontent.com/epiverse-trace/epichains/main/vignettes/img/transmission_chain_example.png) +![**An example of a transmission chain starting with a single case C1.** Cases are represented by blue circles and arrows indicating who infected whom. The chain grows through generations Gen 1, Gen 2, and Gen 3, producing cases C2, C3, C4, C5, and C6. The chain ends at generation Gen 3 with cases C4, C5, and C6. The size of C1’s chain is 6, including C1 (that is, the sum of all blue circles), and the length is 3, which includes Gen 1 (maximum number of generations reached by C1’s chain) ([Azam & Funk, 2024](https://epiverse-trace.github.io/epichains/articles/epichains.html)).](https://raw.githubusercontent.com/epiverse-trace/epichains/main/vignettes/img/transmission_chain_example.png) :::::::::::::::::::: -To use `{epichains}` we need two key delays: the offspring distribution and the generation time! +To use `{epichains}`, we need two key delays: the offspring distribution and the generation time! ## Get the offspring distribution @@ -88,7 +208,7 @@ mers_offspring <- c(mean = 0.60, dispersion = 0.02) ### offspring distribution for epichains -The way we input an offspring distribution to `{epichains}` is by defining the R function that generates random values. For example, for a negative binomial distribution we use `rnbinom` with its corresponding `mu` and `size` arguments: +We input an offspring distribution to `{epichains}` by defining the R function that generates random values. For example, for a negative binomial distribution, we use `rnbinom` with its corresponding `mu` and `size` arguments: ```r offspring_dist = rnbinom, @@ -96,7 +216,7 @@ The way we input an offspring distribution to `{epichains}` is by defining the R size = mers_offspring["dispersion"], ``` -The reference manual in `?rnbinom` tell us the specific arguments we require. +The reference manual in `?rnbinom` tells us our required specific arguments. :::::::::::::::::::::::::::: @@ -104,22 +224,22 @@ The reference manual in `?rnbinom` tell us the specific arguments we require. ### Poisson and other distributions -`{epichains}` can accept any R function that generates random numbers, so the specified arguments will change depending of the R function used. The way to know this is by accessing the function reference manual. +`{epichains}` can accept any R function that generates random numbers, so the specified arguments will change depending on the R function used. This can be learned by accessing the function reference manual. -For example, let's say that for the offspring distribution we want to use a Poisson distribution. First, read the argument required in the `?rpois` reference manual. Second, specify the `lambda` argument parameter, which is also known as rate or mean in the literature. In `{epichains}`, this can look like this: +For example, let's say we want to use a Poisson distribution for the offspring distribution. First, read the argument required in the `?rpois` reference manual. Second, specify the `lambda` argument parameter, also known as rate or mean in the literature. In `{epichains}`, this can look like this: ```r offspring_dist = rpois, lambda = mers_offspring["mean"], ``` -In this example we can specify `lambda = mers_offspring["mean"]` because in a negative binomial model, when the dispersion parameter $k$ approaches infinity ($k \rightarrow \infty$) the variance equals the mean. This makes the conventional Poisson model an special case of the negative binomial model. The mean of the negative binomial model (`mu`) can also be the mean of the poisson model (`lambda`). +In this example, we can specify `lambda = mers_offspring["mean"]` because in a negative binomial model, when the dispersion parameter $k$ approaches infinity ($k \rightarrow \infty$), the variance equals the mean. This makes the conventional Poisson model a special case of the negative binomial model. The mean of the negative binomial model (`mu`) can also be the mean of the Poisson model (`lambda`). :::::::::::::::::::::::::: ## Get generation time -The generation time distribution is often approximated by the [serial interval](../learners/reference.md#serialinterval) distribution. This approximation is frequent because it is easier to observe and measure the onset of symptoms than the onset of infectiousness. +The [serial interval](../learners/reference.md#serialinterval) distribution often approximates the generation time distribution. This approximation is frequent because it is easier to observe and measure the onset of symptoms than the onset of infectiousness. :::::::::::::::::::::::::::::::: spoiler @@ -150,19 +270,19 @@ serial_summary <- serial_inverval$summary_stats %>% distinct(.keep_all = TRUE) ``` -The serial interval for MERS has a mean of `r serial_summary$mean` days and standard deviation `r serial_summary$sd` days. +The serial interval for MERS has a mean of `r serial_summary$mean` days and a standard deviation of `r serial_summary$sd` days. :::::::::::::::::::::::::::: callout ### generation time for epichains -In `{epichains}` we need to specify the generation time as a function that generates random numbers. Using `{epiparameter}` has the advantage of using the distribution function `epiparameter::generate()` for this input. This will look like this: +In `{epichains}`, we need to specify the generation time as a function that generates random numbers. Using `{epiparameter}` has the advantage of using the distribution function `epiparameter::generate()` for this input. This will look like this: ```r function(x) generate(x = serial_inverval, times = x) ``` -This interface is similar to the one used by `{cfr}` to link with `{epiparameter}`. For further context, read the [work with delay distributions](https://epiverse-trace.github.io/cfr/articles/delay_distributions.html) vignette. +This interface is similar to the one `{cfr}` uses to link with `{epiparameter}`. Read the [work with delay distributions](https://epiverse-trace.github.io/cfr/articles/delay_distributions.html) vignette for further context. :::::::::::::::::::::::::::: @@ -184,36 +304,36 @@ simulate_chains( ) ``` -`simulate_chains()` requires, at least, three sets of arguments: +`simulate_chains()` requires at least three sets of arguments: - simulation controls, - offspring distribution, and - generation time. -Lines above we described how to specify the offspring distribution and generation time. The **simulation controls** include, at least, two arguments: +In the lines above, we described how to specify the offspring distribution and generation time. The **simulation controls** include at least two arguments: -- `index_case`, which define the number of index cases to simulate transmission chains for, and -- `statistic`, which define a chain statistic to track (either `"size"` or `"length"`) as the stopping criteria for each chain being simulated. +- `index_case`, which defines the number of index cases to simulate transmission chains for and +- `statistic`, which defines a chain statistic to track (either `"size"` or `"length"`) as the stopping criteria for each chain being simulated. ::::::::::::::::::::::::::: callout ### Stopping criteria -This is an exclusive feature of `{epichains}`. Branching process simulations end when they have gone extinct, that is, no more offspring are being produced, or because of some stopping criterion. +This is an exclusive feature of `{epichains}`. Branching process simulations end when they have gone extinct. No more offspring are being produced because of some stopping criterion. ::::::::::::::::::::::::::: -The output of the `simulate_chains()` function creates a `` class object. +The `simulate_chains()` output creates a `` class object. ## Simulate multiple chains -We can use `simulate_chains()` to create multiple chains and increase the probability to simulate uncontrolled outbreaks projections given an overdispersed offspring distribution. +We can use `simulate_chains()` to create multiple chains and increase the probability of simulating uncontrolled outbreak projections given an overdispersed offspring distribution. We need to specify three additional elements: - `set.seed()`, which is a random number generator function with a specified seed value, the `` number, to ensure consistent results across different runs of the code. -- `number_chains`, which defines the number of simulation to run. -- `initial_cases`, which defines the number of initial cases to input to the `index_cases` argument explained lines above. +- `number_chains`, which defines the number of simulations to run. +- `initial_cases` defines the number of initial cases to input to the `index_cases` argument explained in the lines above. ```{r} # Set seed for random number generator @@ -224,30 +344,30 @@ number_chains <- 1000 initial_cases <- 1 ``` -`number_chains` and `initial_cases` are conveniently stored in objects to facilitate its reuse downstream in the workflow. +`number_chains` and `initial_cases` are conveniently stored in objects to facilitate downstream reuse in the workflow. :::::::::::::::::::::::::::::: checklist ### Iteration using purrr -[Iteration](https://r4ds.hadley.nz/iteration.html) aims to repeatedly perform the same action on different objects. +[Iteration](https://r4ds.hadley.nz/iteration.html) aims to perform the same action on different objects repeatedly. Learn how to use the core `{purrr}` functions like `map()` from the YouTube tutorial on [How to purrr](https://www.youtube.com/watch?v=nd-Y8b22YaQ) by Equitable Equations. -Or if you previously used the `*apply` family of functions, visit the package vignette on [purrr base R](https://purrr.tidyverse.org/articles/base.html) shares key differences, direct translations, and examples. +Or, if you previously used the `*apply` family of functions, visit the package vignette on [purrr base R](https://purrr.tidyverse.org/articles/base.html), which shares key differences, direct translations, and examples. :::::::::::::::::::::::::::::: -To get multiple chains, we need to apply the `simulate_chains()` function to each chain defined by a sequence of numbers from 1 to `number_chains`. +To get multiple chains, we must apply the `simulate_chains()` function to each chain defined by a sequence of numbers from 1 to `number_chains`. ::::::::::::::::::::::::::::::: callout ### purrr and epichains -First, let's make a minimal sketch of how we use `purrr::map()` with `epichains::simulate_chains()`. The `map()` function requires two arguments: +First, let's sketch how we use `purrr::map()` with `epichains::simulate_chains()`. The `map()` function requires two arguments: - `.x`, with a vector of numbers, and -- `.f`, a function to iterate to each value of the vector. +- `.f`, a function to iterate to each vector value. ```r map( @@ -357,7 +477,7 @@ Number of infectors (known): 3 Number of generations: 3 ``` -The simulated `chain_id` number `r chain_to_observe` has three known infector and three generations. These numbers are more visible when reading the `` objects as a data frame. +The simulated `chain_id` number `r chain_to_observe` has three known infectors and three generations. These numbers are more visible when reading the `` objects as a data frame. ::::::::::::::::::::::::: @@ -373,13 +493,13 @@ simulated_chains_map %>% as_tibble() ``` -Chain `r chain_to_observe` is telling us an **story**: "In the first transmission generation at `time = 0`, one index case infected the first case with `sim_id = 1`. Then, in the second transmission generation (between `time` 10 to 16), `sim_id = 1` infected five cases. Later, in the third transmission generation (between `time` 26 to 30), `sim_id = 2` infected three new cases." +Chain `r chain_to_observe` tells us a **story**: "In the first transmission generation at `time = 0`, one index case infected the first case with `sim_id = 1`. Then, in the second transmission generation (between `time` 10 to 16), `sim_id = 1` infected five cases. Later, in the third transmission generation (between `time` 26 to 30), `sim_id = 2` infected three new cases." ::::::::::::::::::::::::: ::::::::::::::::::::::::: solution -### an infectee data frame +### An infectee data frame The output data frame collects **infectees** as the observation unit: @@ -394,7 +514,11 @@ The output data frame collects **infectees** as the observation unit: ## Visualize multiple chains -To visualize the simulated chains, we need some pre-processing. First, let's use `{dplyr}` to get round time numbers, to resemble surveillance days. Second, count the daily number of cases in each simulation (by `chain_id`). Third, calculate the cumulative number of cases within simulation. +To visualize the simulated chains, we need some pre-processing: + +1. Let's use `{dplyr}` to get round time numbers to resemble surveillance days. +2. Count the daily cases in each simulation (by `chain_id`). +3. Calculate the cumulative number of cases within a simulation. ```{r} # daily aggregate of cases @@ -405,7 +529,7 @@ simulated_chains_day <- simulated_chains_map %>% mutate(chain_id = as_factor(chain_id)) %>% # get the round number (day) of infection times mutate(day = ceiling(time)) %>% - # count the daily number of cases each simulation (chain ID) + # count the daily number of cases in each simulation (chain ID) count(chain_id, day, name = "cases") %>% # calculate the cumulative number of cases for each simulation (chain ID) group_by(chain_id) %>% @@ -413,7 +537,7 @@ simulated_chains_day <- simulated_chains_map %>% ungroup() ``` -Previous to the plot, let's create a summary table with the total time duration and size of each chain. We can use the `{dplyr}` "combo" of `group_by()`, `summarise()` and `ungroup()`: +Before the plot, let's create a summary table with the total time duration and size of each chain. We can use the `{dplyr}` "combo" of `group_by()`, `summarise()` and `ungroup()`: ```{r} # Summarise the chain duration and size @@ -446,7 +570,7 @@ ggplot() + alpha = 0.25, show.legend = FALSE ) + - # create points to visualize the chain end point + # create points to visualize the chain endpoint geom_point( data = sim_chains_max, mapping = aes( @@ -519,7 +643,7 @@ plot(mers_cumcases) ::::::::::::::::::::::::::::::::::: -When plotting the observed number of cumulative cases from the Middle East respiratory syndrome (MERS) outbreak in South Korea in 2015, alongside the previously simulated chains, we identify that the observed cases followed a trajectory that resembled a simulated explosive outbreak. +When plotting the observed number of cumulative cases from the Middle East respiratory syndrome (MERS) outbreak in South Korea in 2015 alongside the previously simulated chains, we identify that the observed cases followed a trajectory that resembled a simulated explosive outbreak. ```{r,echo=FALSE} # Observed cases vs Simulated transmission chains @@ -557,15 +681,15 @@ ggplot() + ) ``` -Notice that when we increase the dispersion parameter from $k = 0.01$ to $k = \infty$, given a fixed reproduction number $R = 1.5$, the proportion of simulated outbreaks that reached the 100-case threshold increases. +When we increase the dispersion parameter from $k = 0.01$ to $k = \infty$, given a fixed reproduction number $R = 1.5$, the proportion of simulated outbreaks that reached the 100-case threshold increases. -![**Growth of simulated outbreaks with R = 1.5 and one initial case, conditional on non-extinction.** Boxes show median and interquartile range (IQR) of the first disease generation with 100 cases; whiskers show most extreme values within 1.5 × IQR of the boxes, and crosses show outliers. Percentages show the proportion of 10,000 simulated outbreaks that reached the 100-case threshold ([Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153)).](fig/see-nature04153_Fig2-c.jpg) +![**Growth of simulated outbreaks with R = 1.5 and one initial case, conditional on non-extinction.** Boxes show the median and interquartile range (IQR) of the first disease generation with 100 cases; whiskers show the most extreme values within 1.5 × IQR of the boxes, and crosses show outliers. Percentages show the proportion of 10,000 simulated outbreaks that reached the 100-case threshold ([Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153)).](fig/see-nature04153_Fig2-c.jpg) :::::::::::::::::::::: testimonial ### Early spread projections -In the initial phase of the epidemic you can use `{epichains}` to apply a branching process model to project the number of future cases. Validation analysis showed that this is a rapid and low detail model with forecast prediction intervals that are too certain ([Pearson et al., 2020](https://www.eurosurveillance.org/content/10.2807/1560-7917.ES.2020.25.18.2000543#validationofthemodel-1)). +In the epidemic's initial phase, you can use `{epichains}` to apply a branching process model to project the number of future cases. Validation analysis showed that this is a rapid and low-detail model with forecast prediction intervals that are too certain ([Pearson et al., 2020](https://www.eurosurveillance.org/content/10.2807/1560-7917.ES.2020.25.18.2000543#validationofthemodel-1)). We invite you to read the vignette on [Projecting infectious disease incidence: a COVID-19 example](https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html)! @@ -581,7 +705,7 @@ Evaluate the potential of Ebola to generate explosive outbreaks. Use the appropr :::::::::::::: hint -With `{epiparameter}` you can access and use delay distributions from previous outbreaks. +With `{epiparameter}`, you can access and use delay distributions from previous outbreaks. :::::::::::::: @@ -641,7 +765,7 @@ c0 %>% Remarkable, even with R0 less than 1 -with potentially explosive outbreaks. the observed variation in individual infectiousness in Ebola +with potentially explosive outbreaks. The observed variation in individual infectiousness in Ebola means that although the probability of extinction is high, new index cases also have the potential for explosive regrowth of the epidemic. ::::::::::: @@ -664,11 +788,11 @@ With `{epiparameter}` you can access and use delay distributions from previous o ### Epidemic Risk assessment accounting for superspreading -With `{superspreading}` you can get numerical solutions to processes that `{epichains}` solve using branching processes. We invite you to read the `{superspreading}` vignette on [Epidemic risk](https://epiverse-trace.github.io/superspreading/articles/epidemic_risk.html) and respond to: +With `{superspreading}`, you can get numerical solutions to processes that `{epichains}` solve using branching processes. We invite you to read the `{superspreading}` vignette on [Epidemic risk](https://epiverse-trace.github.io/superspreading/articles/epidemic_risk.html) and respond to: -- What is the probability of an pathogen to cause large outbreak? -- What is the probability of an outbreak to get extinct? -- What is the probability to contain the ongoing outbreak? +- What is the probability of a pathogen causing a large outbreak? +- What is the probability of an outbreak becoming extinct? +- What is the probability of containing the ongoing outbreak? Check how these estimates vary non-linearly with respect to the mean reproduction number $R$ and dispersion $k$ of a given disease. @@ -691,7 +815,7 @@ probability_contain( case_threshold = 100 ) -# Estimate probability of large outbreak +# Estimate the probability of a large outbreak # with 5 independent imported cases probability_epidemic( R = mers_offspring["mean"], From a7313ba904f5bb53fd515cbef171983e194746f9 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 15 Apr 2024 16:25:02 +0100 Subject: [PATCH 095/140] Clean writing of questions and objectives Co-authored-by: Adam Kucharski --- episodes/superspreading-estimate.Rmd | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 3dc019f4..7e09f106 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -13,15 +13,15 @@ webshot::install_phantomjs(force = TRUE) :::::::::::::::::::::::::::::::::::::: questions - How can we estimate individual-level variation in transmission (i.e. superspreading potential) from contact tracing data? -- How to account for transmission heterogeneity in decision-making? +- What are the implications for variation in transmission for decision-making? :::::::::::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::: objectives -- Create the offspring distribution from outbreak data using `{epicontacts}`. -- Estimate the dispersion parameter from the offspring distribution using `{fitdistrplus}`. -- Estimate the proportion of transmission accounting for superspreading events using `{superspreading}`. +- Estimate the distribution of onward transmission from infected individuals (i.e. offspring distribution) from outbreak data using `{epicontacts}`. +- Estimate the extent of individual-level variation (i.e. the dispersion parameter) of the offspring distribution using `{fitdistrplus}`. +- Estimate the proportion of transmission that is linked to 'superspreading events' using `{superspreading}`. :::::::::::::::::::::::::::::::::::::::::::::::: @@ -31,9 +31,9 @@ webshot::install_phantomjs(force = TRUE) Learners should familiarise themselves with following concept dependencies before working through this tutorial: -**Statistics**: probability distributions. +**Statistics**: common probability distributions, particularly Poisson and negative binomial. -**Epidemic theory**: Reproduction number. +**Epidemic theory**: The reproduction number, R. ::::::::::::::::::::::::::::::::: From 9f3e604340029c959dc81ef5e7898afec23578fb Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 15 Apr 2024 17:42:36 +0100 Subject: [PATCH 096/140] clean writing of introduction Co-authored-by: Adam Kucharski --- episodes/superspreading-estimate.Rmd | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 7e09f106..d33a50b7 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -41,23 +41,23 @@ Learners should familiarise themselves with following concept dependencies befor -From epidemics like Smallpox or the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), we know that some people spread disease more than others. Since disease transmission is caused by many physiological and social factors, we usually use population averages to assess the disease potential to spread. However, individual differences in infectiousness increase the tendency towards superspreading events (SSEs) which can ignite explosive epidemics and affect the ease of control. +From smallpox to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), some infected individuals spread infection to more people than others. Disease transmission is the result of a combination of biological and social factors, and these factors average out to some extent at the population level during a large epidemic. Hence researchers often use population averages to assess the potential for disease to spread. However, in the earlier or later phases of an outbreak, individual differences in infectiousness can be more important. In particular, they increase the chance of superspreading events (SSEs), which can ignite explosive epidemics and also influence the chances of controlling transmission ([Lloyd-Smith et al., 2005](https://wellcomeopenresearch.org/articles/5-83)).. ![**Chains of SARS-CoV-2 transmission in Hong Kong initiated by local or imported cases.** (**a**), Transmission network of a cluster of cases traced back to a collection of four bars across Hong Kong (n = 106). (**b**), Transmission network associated with a wedding without clear infector–infectee pairs but linked back to a preceding social gathering and local source (n = 22). (**c**), Transmission network associated with a temple cluster of undetermined source (n = 19). (**d**), All other clusters of SARS-CoV-2 infections where the source and transmission chain could be determined ([Adam et al., 2020](https://www.nature.com/articles/s41591-020-1092-0)).](fig/see-intro-superspreading.png) -The [basic reproduction number](../learners/reference.md#basic), $R_0$, is the average number of cases caused by one infectious individual in a entirely susceptible population. Population estimates of $R_0$ can obscure considerable individual variation in infectiousness, as highlighted during the global emergence of SARS-CoV-2 by numerous ‘superspreading events’ in which certain individuals infected unusually large numbers of secondary cases ([Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153)). +The [basic reproduction number](../learners/reference.md#basic), $R_0$, measures the average number of cases caused by one infectious individual in a entirely susceptible population. Estimates of $R_0$ are useful for understanding the average dynamics of an epidemic at the population-level, but can obscure considerable individual variation in infectiousness. This was highlighted during the global emergence of SARS-CoV-2 by numerous ‘superspreading events’ in which certain infectious individuals generated unusually large numbers of secondary cases ([LeClerc et al, 2020](https://wellcomeopenresearch.org/articles/5-83)). ![**Observed offspring distribution of SARS-CoV-2 transmission in Hong Kong.** N = 91 SARS-CoV-2 infectors, N = 153 terminal infectees and N = 46 sporadic local cases. Histogram bars indicate the proportion of onward transmission per amount of secondary cases. Line corresponds to a fitted negative binomial distribution ([Adam et al., 2020](https://www.nature.com/articles/s41591-020-1092-0)).](fig/see-intro-secondary-cases-fig-b.png){alt='R = 0.58 and k = 0.43.'} -In this tutorial, we are going to estimate the individual variation in transmission and assess its heterogeneity, which often results in superspreading events. Also, we are going to use these estimates to account for superspreading in contact tracing interventions. +In this tutorial, we are going to quantify individual variation in transmission, and hence estimate the potential for superspreading events. Then we are going to use these estimates to explore the implications of superspreading for contact tracing interventions. -We are going to use data from the `{outbreaks}` package, manage linelist and contacts data using `{epicontacts}`, and estimate distribution parameters with `{fitdistrplus}`. Lastly, we are going to use `{superspreading}` to account for it in decision-making. +We are going to use data from the `{outbreaks}` package, manage the linelist and contacts data using `{epicontacts}`, and estimate distribution parameters with `{fitdistrplus}`. Lastly, we are going to use `{superspreading}` to explore the implications of variation in transmission for decision-making. -We’ll use the pipe `%>%` to connect some of their functions, so let’s also call to the `{tidyverse}` package: +We’ll use the pipe `%>%` to connect some of the functions from these packages, so let’s also call the `{tidyverse}` package: ```{r,message=FALSE,warning=FALSE} library(outbreaks) From 9a83061c03f950ceae8407541f1338f249b4ec3d Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 15 Apr 2024 17:46:26 +0100 Subject: [PATCH 097/140] clean contact data callout Co-authored-by: Adam Kucharski --- episodes/superspreading-estimate.Rmd | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index d33a50b7..baf5aee5 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -110,11 +110,11 @@ webshot::webshot( ### Is contact data tidy? -Contact data contains information of whom infected whom. We expect to have the infector (`from`) and the infectee (`to`) plus additional columns of variables related to their contact like location (`exposure`) and date of contact. +Contact data from a transmission chain can provide information on which infected individuals came into contact with others. We expect to have the infector (`from`) and the infectee (`to`) plus additional columns of variables related to their contact, such as location (`exposure`) and date of contact. -Following [tidy data](https://tidyr.tidyverse.org/articles/tidy-data.html#tidy-data) principles, in contact data the observation unit is the **infector-infectee** pair. Although one infector can infect multiple infectees, from contact tracing investigations we may record infectees contacts with more than one infector. But we should expect to have unique infector-infectee pairs. +Following [tidy data](https://tidyr.tidyverse.org/articles/tidy-data.html#tidy-data) principles, the observation unit in our contact dataset is the **infector-infectee** pair. Although one infector can infect multiple infectees, from contact tracing investigations we may record contacts linked to more than one infector (e.g. within a household). But we should expect to have unique infector-infectee pairs, because typically each infected person will have acquired the infection from one other. -We can check on replicates for infectees: +To ensure these unique pairs, we can check on replicates for infectees: ```{r} # no infector-infectee pairs are replicated From b6d287ebfd21f7f085ae8ce9f3d72f2a0527e602 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 15 Apr 2024 18:03:53 +0100 Subject: [PATCH 098/140] clean writing of questions and objectives Co-authored-by: Adam Kucharski --- episodes/superspreading-simulate.Rmd | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 9b6c53c9..8e39431f 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -6,13 +6,13 @@ exercises: 2 :::::::::::::::::::::::::::::::::::::: questions -- How to simulate transmission chains? +- How can we simulate transmission chains based on infection characteristics? :::::::::::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::: objectives -- Create a short term projection using branching process with `{epichains}`. +- Create a short term projection using a branching process with `{epichains}`. :::::::::::::::::::::::::::::::::::::::::::::::: @@ -22,9 +22,9 @@ exercises: 2 Learners should familiarise themselves with the following concept dependencies before working through this tutorial: -**Statistics**: probability distributions. +**Statistics**: Common probability distributions, including Poisson and negative binomial. -**Epidemic theory**: Reproduction number. +**Epidemic theory**: The reproduction number, $R$. ::::::::::::::::::::::::::::::::: From 38462e9b49dc5274bfe60bfb1f5e5b8631267c2a Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 15 Apr 2024 19:28:59 +0100 Subject: [PATCH 099/140] homogenize usage of individual-level variation --- episodes/superspreading-estimate.Rmd | 38 +++++++++++++++++----------- 1 file changed, 23 insertions(+), 15 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index baf5aee5..d883bbb7 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -71,7 +71,7 @@ library(tidyverse) The individual reproduction number is defined as the number of secondary cases caused by a particular infected individual. -Early in an outbreak we can use contact data to reconstruct transmission trees (whom infected whom) and calculate the number of secondary cases generated by each individual. Reconstruction of trees from contact data can provide an understanding of who contributes more to transmission and evaluate for heterogeneous distribution ([Cori et al., 2017](https://royalsocietypublishing.org/doi/10.1098/rstb.2016.0371)). +Early in an outbreak we can use contact data to reconstruct transmission chains (i.e. who infected whom) and calculate the number of secondary cases generated by each individual. This reconstruction of linked transmission events from contact data can provide an understanding about how different individuals have contributed to transmission during an epidemic ([Cori et al., 2017](https://royalsocietypublishing.org/doi/10.1098/rstb.2016.0371)). Let's practice this using the `mers_korea_2015` linelist and contact data from the `{outbreaks}` package and integrate them with the `{epicontacts}` package to calculate the distribution of secondary cases ([Campbell, 2022](https://community.appliedepi.org/t/estimating-the-degree-of-super-spreading-from-transmission-chain-data/103/2)): @@ -85,12 +85,12 @@ epi_contacts <- ``` ```{r,eval=FALSE} -# visualise contact tree +# visualise contact network epicontacts::vis_epicontacts(epi_contacts) ``` ```{r,echo=FALSE} -# visualise contact tree +# visualise contact network network <- vis_epicontacts(epi_contacts) %>% visNetwork::visPhysics(solver = "barnesHut") @@ -153,7 +153,7 @@ all_secondary <- epi_contacts %>% ) ``` -From a histogram of the `all_secondary` object, we can identify the **heterogeneity** in the number of secondary cases. Three cases were related to more than 20 secondary cases, while the complementary cases with less than five or zero secondary cases. +From a histogram of the `all_secondary` object, we can identify the **individual-level variation** in the number of secondary cases. Three cases were related to more than 20 secondary cases, while the complementary cases with less than five or zero secondary cases. ```{r,echo=FALSE,eval=FALSE} # arrange in descendant order of secondary cases @@ -178,7 +178,7 @@ The number of secondary cases can be used to _empirically_ estimate the **offspr - **Mean**, which represents the $R_{0}$, the average number of (secondary) cases produced by a single individual in an entirely susceptible population, and -- **Dispersion**, expressed as $k$, which represents the degree of heterogeneity in transmission by single individuals. +- **Dispersion**, expressed as $k$, which represents the degree of individual-level variation in transmission by single individuals. ```{r,echo=FALSE,message=FALSE,warning=FALSE} # Load parameters @@ -407,11 +407,11 @@ ggplot() + :::::::::::::::::::: callout -### Transmission heterogeneity +### Individual-level variation in transmission -Heterogeneity is defined by the relationship between the mean ($R_{0}$), dispersion ($k$), and the variance of a negative binomial distribution. +The individual-level variation in transmission is defined by the relationship between the mean ($R_{0}$), dispersion ($k$), and the variance of a negative binomial distribution. -The negative binomial model has $variance = R_{0}(1+\frac{R_{0}}{k})$, so smaller values of $k$ indicate greater variance and, consequently, greater **heterogeneity**. +The negative binomial model has $variance = R_{0}(1+\frac{R_{0}}{k})$, so smaller values of $k$ indicate greater variance and, consequently, greater **individual-level variation**. $$\uparrow variance = R_{0}(1+\frac{R_{0}}{\downarrow k})$$ @@ -425,7 +425,7 @@ Use the distribution of secondary cases from the `ebola_sim_clean` object from ` Fit a negative binomial distribution to estimate the mean and dispersion parameter of the offspring distribution. -Does the estimated dispersion parameter of Ebola provide evidence of transmission heterogeneity? +Does the estimated dispersion parameter of Ebola provide evidence of an individual-level variation in transmission? :::::::::::::: hint @@ -462,7 +462,7 @@ ebola_upper <- ebola_mid + ebola_offspring$sd[["size"]] * qnorm(0.975) From the number secondary cases distribution we estimated a dispersion parameter $k$ of `r round(ebola_mid, 3)`, with a 95% Confidence Interval from `r round(ebola_lower, 3)` to `r round(ebola_upper, 3)`. -For dispersion parameter estimates higher than one we get low distribution variance, hence, low heterogeneity. +For dispersion parameter estimates higher than one we get low distribution variance, hence, low individual-level variation in transmission. But does this mean that the secondary case distribution does not have superspreading events (SSEs)? You will later find one additional challenge: How do you define an SSE threshold for Ebola? @@ -482,11 +482,11 @@ We can use the maximum likelihood estimates from `{fitdistrplus}` to compare dif ### The dispersion parameter across diseases -[Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153) use a 20/80 rule to show how the core principle of heterogeneous transmission is supported. +[Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153) use a 20/80 rule to show how the core principle of individual-level variation in transmission is supported. -- When the 20% most infectious cases contribute to the 80% of transmission (or more), this is a highly heterogeneous offspring distribution ($k<0.3$), e.g., SARS. +- When the 20% most infectious cases contribute to the 80% of transmission (or more), there is a high individual-level variation in transmission, with a highly overdispersed offspring distribution ($k<0.3$), e.g., SARS. -- When the 20% most infectious cases contribute to the ~50% of transmission, this is a less heterogeneous offspring distribution ($k > 3$), e.g. Ebola. +- When the 20% most infectious cases contribute to the ~50% of transmission, there is a low individual-level variation in transmission, with a moderately dispersed offspring distribution ($k > 3$), e.g. Ebola. ```{r,message=FALSE,warning=FALSE,echo=FALSE} library(epiparameter) @@ -590,9 +590,9 @@ across_offspring %>% Contact tracing can be deployed in multiple strategies. Forward tracing targets downstream individuals who may be infected by index individual. Backward tracing targets the upstream primary case who infected the index case (or a setting or event at which the index case was infected) by retracing history of contact to the likely point of exposure up to the upper bound of the incubation period. -In the presence of heterogeneous transmission, i.e., with an overdispersed offspring distribution, if this primary case is identified, a larger fraction of the transmission chain can be detected by forward tracing each of the contacts of this primary case ([Endo et al., 2020](https://wellcomeopenresearch.org/articles/5-239/v3)). +In the presence of individual-level variation in transmission, i.e., with an overdispersed offspring distribution, if this primary case is identified, a larger fraction of the transmission chain can be detected by forward tracing each of the contacts of this primary case ([Endo et al., 2020](https://wellcomeopenresearch.org/articles/5-239/v3)). -![Schematic representation of contact tracing strategies. Black arrows indicate the directions of transmission, blue and Orange arrows, a successful or failed contact tracing, respectivelly. When there is evidence of individual-level transmission heterogeneity, often resulting in superspreading, backward contact tracing from the index case (blue circle) increase the probability to find the primary case (green circle) or clusters with a larger fraction of cases, potentially increasing the number of quarentined cases (yellow circles). [Claire Blackmore, 2021](https://www.paho.org/sites/default/files/backward_contact_tracing_v3_0.pdf)](fig/contact-tracing-strategies.png) +![Schematic representation of contact tracing strategies. Black arrows indicate the directions of transmission, blue and Orange arrows, a successful or failed contact tracing, respectivelly. When there is evidence of individual-level variation in transmission, often resulting in superspreading, backward contact tracing from the index case (blue circle) increase the probability to find the primary case (green circle) or clusters with a larger fraction of cases, potentially increasing the number of quarentined cases (yellow circles). [Claire Blackmore, 2021](https://www.paho.org/sites/default/files/backward_contact_tracing_v3_0.pdf)](fig/contact-tracing-strategies.png) When there is evidence of individual-level variation (i.e. overdispersion), often resulting in so-called superspreading events, a large proportion of infections may be linked to a small proportion of original clusters. As a result, finding and targeting originating clusters in combination with reducing onwards infection may substantially enhance the effectiveness of tracing methods ([Endo et al., 2020](https://wellcomeopenresearch.org/articles/5-239/v3)). @@ -807,6 +807,14 @@ The dispersion parameter $k$ can be expressed differently across the literature. ::::::::::::::::: +:::::::::::::::::::::::::::: callout + +### heterogeneity? + +The individual-level variation in transmission is also referred as the heterogeneity in the transmission or degree of heterogeneity in [Lloyd-Smith et al., 2005](https://wellcomeopenresearch.org/articles/5-83), heterogeneous infectiousness in [Campbell et al., 2018](https://bmcbioinformatics.biomedcentral.com/articles/10.1186/s12859-018-2330-z) when introducing the `{outbreaker2}` package. Similarly, a contact network can store heterogeneous epidemiological contacts as in the documentation of the `{epicontacts}` package ([Nagraj et al., 2018](https://www.repidemicsconsortium.org/epicontacts/articles/epicontacts.html)). + +:::::::::::::::::::::::::::: + ::::::::::::::::::::::::::::: testimonial ### Read these blog posts From 061ebd747f7b653ffc86679d6ea3a53c435ddaf3 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 15 Apr 2024 20:43:33 +0100 Subject: [PATCH 100/140] add detail on mers data --- episodes/superspreading-estimate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index d883bbb7..136bbe39 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -73,7 +73,7 @@ The individual reproduction number is defined as the number of secondary cases c Early in an outbreak we can use contact data to reconstruct transmission chains (i.e. who infected whom) and calculate the number of secondary cases generated by each individual. This reconstruction of linked transmission events from contact data can provide an understanding about how different individuals have contributed to transmission during an epidemic ([Cori et al., 2017](https://royalsocietypublishing.org/doi/10.1098/rstb.2016.0371)). -Let's practice this using the `mers_korea_2015` linelist and contact data from the `{outbreaks}` package and integrate them with the `{epicontacts}` package to calculate the distribution of secondary cases ([Campbell, 2022](https://community.appliedepi.org/t/estimating-the-degree-of-super-spreading-from-transmission-chain-data/103/2)): +Let's practice this using the `mers_korea_2015` linelist and contact data from the `{outbreaks}` package and integrate them with the `{epicontacts}` package to calculate the distribution of secondary cases during the 2015 MERS-CoV outbreak in South Korea ([Campbell, 2022](https://community.appliedepi.org/t/estimating-the-degree-of-super-spreading-from-transmission-chain-data/103/2)): ```{r} ## first, make an epicontacts object From 06731447d8152d33b5a31c00b39e875fec282940 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 15 Apr 2024 20:48:54 +0100 Subject: [PATCH 101/140] rewrite for clarity --- episodes/superspreading-estimate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 136bbe39..ec843caa 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -126,7 +126,7 @@ epi_contacts %>% ::::::::::::::::::::::::::: -When each infector-infectee row is unique, the number of entries per infector corresponds to their number of secondary cases. +When each infector-infectee row is unique, the number of entries per infector corresponds to the number of secondary cases generated by that individual. ```{r} # count secondary cases per infector From 36dc1d42f4cc08955fe968b416b8a080b9ccc6b9 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 15 Apr 2024 20:49:07 +0100 Subject: [PATCH 102/140] homogenize usage of r nut --- episodes/superspreading-estimate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index ec843caa..8bdfd0dc 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -47,7 +47,7 @@ From smallpox to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), s -The [basic reproduction number](../learners/reference.md#basic), $R_0$, measures the average number of cases caused by one infectious individual in a entirely susceptible population. Estimates of $R_0$ are useful for understanding the average dynamics of an epidemic at the population-level, but can obscure considerable individual variation in infectiousness. This was highlighted during the global emergence of SARS-CoV-2 by numerous ‘superspreading events’ in which certain infectious individuals generated unusually large numbers of secondary cases ([LeClerc et al, 2020](https://wellcomeopenresearch.org/articles/5-83)). +The [basic reproduction number](../learners/reference.md#basic), $R_{0}$, measures the average number of cases caused by one infectious individual in a entirely susceptible population. Estimates of $R_{0}$ are useful for understanding the average dynamics of an epidemic at the population-level, but can obscure considerable individual variation in infectiousness. This was highlighted during the global emergence of SARS-CoV-2 by numerous ‘superspreading events’ in which certain infectious individuals generated unusually large numbers of secondary cases ([LeClerc et al, 2020](https://wellcomeopenresearch.org/articles/5-83)). ![**Observed offspring distribution of SARS-CoV-2 transmission in Hong Kong.** N = 91 SARS-CoV-2 infectors, N = 153 terminal infectees and N = 46 sporadic local cases. Histogram bars indicate the proportion of onward transmission per amount of secondary cases. Line corresponds to a fitted negative binomial distribution ([Adam et al., 2020](https://www.nature.com/articles/s41591-020-1092-0)).](fig/see-intro-secondary-cases-fig-b.png){alt='R = 0.58 and k = 0.43.'} From 0fd212b792e9d8109b40360a1135f0098e13a953 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 15 Apr 2024 20:52:50 +0100 Subject: [PATCH 103/140] add R0 context for individual reproduction number --- episodes/superspreading-estimate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 8bdfd0dc..710c3c69 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -235,7 +235,7 @@ From the histogram and density plot, we can identify that the offspring distribu ### Terminology recap - From linelist and contact data, we calculate the **number of secondary cases** caused by the observed infected individuals. -- The **individual reproduction number** is a random variable representing the _expected_ number of secondary cases caused by a infected individual. +- Whereas $R_{0}$ captures the average transmission in the population, we can define the **individual reproduction number** as a random variable representing the _expected_ number of secondary cases caused by a infected individual. - From the stochastic effects in transmission, the number of secondary _infections_ caused by each case is described by an **offspring distribution**. - An _empirical_ offspring distribution can be modeled by the **negative-binomial** distribution with mean $R_{0}$ and dispersion parameter $k$. From d9d7226678d22c25df342e60cfde98c0e5ddac5e Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 15 Apr 2024 20:58:52 +0100 Subject: [PATCH 104/140] add explanation on the right-hand tail --- episodes/superspreading-estimate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 710c3c69..78514823 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -228,7 +228,7 @@ ggplot() + ) ``` -From the histogram and density plot, we can identify that the offspring distribution is highly skewed or **overdispersed**. In this framework, the superspreading events (SSEs) are realizations from the right-hand tail of the offspring distribution ([Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153)). +From the histogram and density plot, we can identify that the offspring distribution is highly skewed or **overdispersed**. In this framework, the superspreading events (SSEs) are not arbitrary or exceptional, but simply realizations from the right-hand tail of the offspring distribution, which we can quantify and analyse ([Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153)). ::::::::::::::::::::::::::: callout From 34a50265aa9ce7ac81ae4860351b1b4aa5138c36 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 15 Apr 2024 21:12:47 +0100 Subject: [PATCH 105/140] add biological and environmental details --- episodes/superspreading-estimate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 78514823..1177338c 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -253,7 +253,7 @@ In a Poisson distribution, mean is equal to variance. But when variance is highe **Negative binomial** distribution is specially useful for discrete data over an unbounded positive range whose sample variance exceeds the sample mean. In such terms, the observations are overdispersed with respect to a Poisson distribution, for which the mean is equal to the variance. -In epidemiology, [negative binomial](https://en.wikipedia.org/wiki/Negative_binomial_distribution) have being used to model disease transmission for infectious diseases where the likely number of onward infections may vary considerably from individual to individual and from setting to setting. +In epidemiology, [negative binomial](https://en.wikipedia.org/wiki/Negative_binomial_distribution) have being used to model disease transmission for infectious diseases where the likely number of onward infections may vary considerably from individual to individual and from setting to setting, capturing all variation in infectious histories of individuals, including properties of the biological (i.e. degree of viral shedding) and environmental circumstances (e.g. type and location of contact). ::::::::::::::::::::::::::::: From c0e3822b75186be6730172bb9be7c7905c2167d4 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 15 Apr 2024 21:17:58 +0100 Subject: [PATCH 106/140] expand sentence on individual level of transmission --- episodes/superspreading-estimate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 1177338c..ede94ddd 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -411,7 +411,7 @@ ggplot() + The individual-level variation in transmission is defined by the relationship between the mean ($R_{0}$), dispersion ($k$), and the variance of a negative binomial distribution. -The negative binomial model has $variance = R_{0}(1+\frac{R_{0}}{k})$, so smaller values of $k$ indicate greater variance and, consequently, greater **individual-level variation**. +The negative binomial model has $variance = R_{0}(1+\frac{R_{0}}{k})$, so smaller values of $k$ indicate greater variance and, consequently, greater **individual-level variation** in transmission. $$\uparrow variance = R_{0}(1+\frac{R_{0}}{\downarrow k})$$ From 0bc169a5cd5cdfe49669ded8486fce92f4ee9509 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 15 Apr 2024 21:23:41 +0100 Subject: [PATCH 107/140] use potential for superspreading --- episodes/superspreading-estimate.Rmd | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index ede94ddd..6b6ab6df 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -178,7 +178,7 @@ The number of secondary cases can be used to _empirically_ estimate the **offspr - **Mean**, which represents the $R_{0}$, the average number of (secondary) cases produced by a single individual in an entirely susceptible population, and -- **Dispersion**, expressed as $k$, which represents the degree of individual-level variation in transmission by single individuals. +- **Dispersion**, expressed as $k$, which represents the individual-level variation in transmission by single individuals. ```{r,echo=FALSE,message=FALSE,warning=FALSE} # Load parameters @@ -352,7 +352,7 @@ upper <- mid + offspring_fit$sd[["size"]] * qnorm(0.975) ``` From the number secondary cases distribution we estimated a dispersion parameter $k$ of -`r round(mid, 3)`, with a 95% Confidence Interval from `r round(lower, 3)` to `r round(upper, 3)`. As the value of $k$ is significantly lower than one, we can conclude that the degree of superspreading is high. +`r round(mid, 3)`, with a 95% Confidence Interval from `r round(lower, 3)` to `r round(upper, 3)`. As the value of $k$ is significantly lower than one, we can conclude that there is considerable potential for superspreading events. We can overlap the estimated density values of the fitted negative binomial distribution and the histogram of the number of secondary cases: From d30729997ae9ed779dfa3dc867671b872f87062c Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 15 Apr 2024 21:30:38 +0100 Subject: [PATCH 108/140] add explanation on the 20/80 rule --- episodes/superspreading-estimate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 6b6ab6df..5d0a7ee4 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -482,7 +482,7 @@ We can use the maximum likelihood estimates from `{fitdistrplus}` to compare dif ### The dispersion parameter across diseases -[Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153) use a 20/80 rule to show how the core principle of individual-level variation in transmission is supported. +Research into sexually transmitted and vector-borne diseases has previously suggested a '20/80' rule, with 20% of individuals contributing at least 80% of the transmission potential ([Woolhouse et al](https://www.pnas.org/doi/10.1073/pnas.94.1.338)). On its own, the dispersion parameter $k$ is hard to interpret intuitively, and hence converting into proportional summary can enable easier comparison. When we consider a wider range of pathogens, we can see there is no hard and fast rule for the percentage that generates 80% of transmission, but variation does emerge as a common feature of infectious diseases - When the 20% most infectious cases contribute to the 80% of transmission (or more), there is a high individual-level variation in transmission, with a highly overdispersed offspring distribution ($k<0.3$), e.g., SARS. From 381abd0a714cfdb30c8b7220dd6ee322d768de79 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 15 Apr 2024 21:33:50 +0100 Subject: [PATCH 109/140] fix one dot --- episodes/superspreading-estimate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 5d0a7ee4..c636cb41 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -41,7 +41,7 @@ Learners should familiarise themselves with following concept dependencies befor -From smallpox to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), some infected individuals spread infection to more people than others. Disease transmission is the result of a combination of biological and social factors, and these factors average out to some extent at the population level during a large epidemic. Hence researchers often use population averages to assess the potential for disease to spread. However, in the earlier or later phases of an outbreak, individual differences in infectiousness can be more important. In particular, they increase the chance of superspreading events (SSEs), which can ignite explosive epidemics and also influence the chances of controlling transmission ([Lloyd-Smith et al., 2005](https://wellcomeopenresearch.org/articles/5-83)).. +From smallpox to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), some infected individuals spread infection to more people than others. Disease transmission is the result of a combination of biological and social factors, and these factors average out to some extent at the population level during a large epidemic. Hence researchers often use population averages to assess the potential for disease to spread. However, in the earlier or later phases of an outbreak, individual differences in infectiousness can be more important. In particular, they increase the chance of superspreading events (SSEs), which can ignite explosive epidemics and also influence the chances of controlling transmission ([Lloyd-Smith et al., 2005](https://wellcomeopenresearch.org/articles/5-83)). ![**Chains of SARS-CoV-2 transmission in Hong Kong initiated by local or imported cases.** (**a**), Transmission network of a cluster of cases traced back to a collection of four bars across Hong Kong (n = 106). (**b**), Transmission network associated with a wedding without clear infector–infectee pairs but linked back to a preceding social gathering and local source (n = 22). (**c**), Transmission network associated with a temple cluster of undetermined source (n = 19). (**d**), All other clusters of SARS-CoV-2 infections where the source and transmission chain could be determined ([Adam et al., 2020](https://www.nature.com/articles/s41591-020-1092-0)).](fig/see-intro-superspreading.png) From f2dfd8dc8b54d0678426b42d65e4384bbffe2b3e Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 15 Apr 2024 21:35:00 +0100 Subject: [PATCH 110/140] rewrite intro on SSE definition --- episodes/superspreading-estimate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index c636cb41..55db2d21 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -665,7 +665,7 @@ The probability of having clusters of five people is 1.8%. At this stage, given ### Does Ebola have any superspreading event? -[Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153) propose a general protocol for defining a superspreading event (SSE). If the number of secondary infections caused by each case, $Z$, follows a negative binomial distribution ($R, k$): +'Superspreading events' can mean different things to different people, so [Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153) proposed a general protocol for defining a superspreading event (SSE). If the number of secondary infections caused by each case, $Z$, follows a negative binomial distribution ($R, k$): - We define an SSE as any infected individual who infects more than $Z(n)$ others, where $Z(n)$ is the nth percentile of the $Poisson(R)$ distribution. - A 99th-percentile SSE is then any case causing more infections than would occur in 99% of infectious histories in a homogeneous population From f0618293a9182c3c4d95a63ddd9c1e46c87df158 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 15 Apr 2024 21:40:43 +0100 Subject: [PATCH 111/140] add suggested edit on backward contact strategy --- episodes/superspreading-estimate.Rmd | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 55db2d21..7467cedb 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -588,7 +588,7 @@ across_offspring %>% ## Backward and forward contact tracing -Contact tracing can be deployed in multiple strategies. Forward tracing targets downstream individuals who may be infected by index individual. Backward tracing targets the upstream primary case who infected the index case (or a setting or event at which the index case was infected) by retracing history of contact to the likely point of exposure up to the upper bound of the incubation period. +During an outbreak, it is common to try and reduce transmission by identifying people who have come into contact with an infected person, then quarantine them in case they subsequently turn out to be infected. Such contact tracing can be deployed in multiple ways. 'Forward' contact tracing targets downstream contacts who may have been infected by a newly identifed infection (i.e. the 'index case'). 'Backward' tracing instead tracks the upstream primary case who infected the index case (or a setting or event at which the index case was infected), for example by retracing history of contact to the likely point of exposure. This makes it possible to identify others who were also potentially infected by this earlier primary case. In the presence of individual-level variation in transmission, i.e., with an overdispersed offspring distribution, if this primary case is identified, a larger fraction of the transmission chain can be detected by forward tracing each of the contacts of this primary case ([Endo et al., 2020](https://wellcomeopenresearch.org/articles/5-239/v3)). @@ -601,7 +601,7 @@ Empirical evidence focused on evaluating the efficiency of backward tracing lead ## Probability of cases in a given cluster -Using `{superspreading}`, we can calculate the probability of having a cluster of secondary infections caused by a primary case identified by backward tracing of size $X$ or larger ([Endo et al., 2020](https://wellcomeopenresearch.org/articles/5-239/v3)). +Using `{superspreading}`, we can estimate the probability of having a cluster of secondary infections caused by a primary case identified by backward tracing of size $X$ or larger ([Endo et al., 2020](https://wellcomeopenresearch.org/articles/5-239/v3)). ```{r} # estimate the probability of @@ -617,7 +617,7 @@ proportion_cluster_size( ``` -Even though we have an $R<1$, given a highly overdispersed offspring distribution ($k=0.02$) we have a 46.9% probability to find a cluster of 25 people or larger. Then, by following a backwards strategy, contact tracing efforts will increase their probability to find the primary case and successfully contain and quarantine an increased proportion of contacts. +Even though we have an $R<1$, a highly overdispersed offspring distribution ($k=0.02$) means that if we detect a new case, there is a 47% probability they originated from a cluster of 25 infections or more. Hence, by following a backwards strategy, contact tracing efforts will increase the probability of successfully contain and quarantining this large number of earlier infected individuals, rather than simply focusing on the new case, who is likely to have infected nobody (because $k$ is very small). We can also use this number to prevent gathering of certain sized to reduce the epidemic by preventing potential superspreading events. Interventions can target to reduce the reproduction number in order to reduce the probability of having clusters of secondary cases. From ce3dda2c665914c3f1cfdd87571ceeb5f83665c1 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 15 Apr 2024 21:54:56 +0100 Subject: [PATCH 112/140] use SARS-1 to differenciate it from SARS-CoV-2 --- episodes/superspreading-estimate.Rmd | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 7467cedb..bd08ebe5 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -484,7 +484,7 @@ We can use the maximum likelihood estimates from `{fitdistrplus}` to compare dif Research into sexually transmitted and vector-borne diseases has previously suggested a '20/80' rule, with 20% of individuals contributing at least 80% of the transmission potential ([Woolhouse et al](https://www.pnas.org/doi/10.1073/pnas.94.1.338)). On its own, the dispersion parameter $k$ is hard to interpret intuitively, and hence converting into proportional summary can enable easier comparison. When we consider a wider range of pathogens, we can see there is no hard and fast rule for the percentage that generates 80% of transmission, but variation does emerge as a common feature of infectious diseases -- When the 20% most infectious cases contribute to the 80% of transmission (or more), there is a high individual-level variation in transmission, with a highly overdispersed offspring distribution ($k<0.3$), e.g., SARS. +- When the 20% most infectious cases contribute to the 80% of transmission (or more), there is a high individual-level variation in transmission, with a highly overdispersed offspring distribution ($k<0.3$), e.g., SARS-1. - When the 20% most infectious cases contribute to the ~50% of transmission, there is a low individual-level variation in transmission, with a moderately dispersed offspring distribution ($k > 3$), e.g. Ebola. @@ -708,7 +708,7 @@ Compare this values with the ones reported by [Lloyd-Smith et al., 2005](https:/ What is the proportion of cases that are responsible of the 80% of transmission? -Use `{superspreading}` and compare the estimates for **MERS** using the offspring distributions parameters from this tutorial episode, with **SARS** and **Ebola** offspring distributions parameter accessible via the `{epiparameter}` R package. +Use `{superspreading}` and compare the estimates for **MERS** using the offspring distributions parameters from this tutorial episode, with **SARS-1** and **Ebola** offspring distributions parameter accessible via the `{epiparameter}` R package. ::::::::::::::::::::: hint @@ -727,7 +727,7 @@ epidist_string <- epidist_db( paste(collapse = ", ") ``` -Currently, `{epiparameter}` have offspring distributions for `r epidist_string`. Let's access the offspring distribution `mean` and `dispersion` parameters for SARS: +Currently, `{epiparameter}` have offspring distributions for `r epidist_string`. Let's access the offspring distribution `mean` and `dispersion` parameters for SARS-1: ```{r,message=FALSE,warning=FALSE} # Load parameters From 0fee33ee11e9d4d20fd5769c5d29b241b422f1d6 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 15 Apr 2024 23:14:06 +0100 Subject: [PATCH 113/140] apply suggestions for introduction Co-authored-by: Adam Kucharski --- episodes/superspreading-simulate.Rmd | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 8e39431f..f1fe1f93 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -34,17 +34,17 @@ Learners should familiarise themselves with the following concept dependencies b Transmission heterogeneity affects epidemic establishment and the ease of control ([Cori et al., 2017](https://royalsocietypublishing.org/doi/10.1098/rstb.2016.0371)). -+ Greater heterogeneity reduces the chance of an outbreak emerging from a single case. Individuals with a more extreme amount of secondary cases are rare. ++ Greater heterogeneity reduces the overall probably of a single new case causing a large local outbreak, because most cases infect few others and individuals that generate a large number of secondary cases are relatively rare. -+ However, if the outbreak gets established, this heterogeneity can make an outbreak hard to control using *mass interventions* (which assumes transmission homogeneity), as a single uncontrolled case can generate a large number of secondary cases. ++ However, if a 'superspreading event' does occur and the outbreak gets established, this heterogeneity can make an outbreak harder to control using *mass interventions* (i.e. blanket interventions that implicitly assume everyone contributes equally to transmission), because some cases contribute disproportionality: a single uncontrolled case may generate a large number of secondary cases. -+ Conversely, heterogeneity in transmission may provide opportunities for *targeted interventions* if the individuals who contribute more to transmission (due to biological, environmental or behavioural factors) share socio-demographic or geographical characteristics that can be defined. ++ Conversely, heterogeneity in transmission may provide opportunities for *targeted interventions* if the individuals who contribute more to transmission (due to biological or behavioural factors), or the settings in which 'superspreading events' occur, share socio-demographic, environmental or geographical characteristics that can be defined. -However, how can we understand the potential of a disease epidemic early from the mean reproduction number $R$ and the dispersion $k$ of an offspring distribution? +How can we quantify the potential of a new infection to cause a large outbreak based on its reproduction number $R$ and the dispersion $k$ of its offspring distribution? -```{r,echo=FALSE,warning=FALSE,message=FALSE,fig.cap="Observed number of cumulative cases from the Middle East respiratory syndrome (MERS) outbreak in South Korea, 2015, alongside with simulated transmission chains given a known offspring distribution."} +```{r,echo=FALSE,warning=FALSE,message=FALSE,fig.cap="Observed number of cumulative cases from the Middle East respiratory syndrome (MERS) outbreak in South Korea, 2015, alongside with simulated transmission chains assuming an offspring distribution with $R=0.6$ and $k=0.02$."} library(epichains) library(epiparameter) library(tidyverse) @@ -166,7 +166,7 @@ ggplot() + -In this episode, we will use the `{epichains}` package to simulate transmission chains to estimate the potential for explosive outbreaks. We are going to use it with functions from `{epiparameter}`, `{dplyr}` and `{purrr}`, so also loading the `{tidyverse}` package: +In this episode, we will use the `{epichains}` package to simulate transmission chains and estimate the potential for large outbreaks following the introduction of a new case. We are going to use it with functions from `{epiparameter}`, `{dplyr}` and `{purrr}`, so also loading the `{tidyverse}` package: ```{r,message=FALSE,warning=FALSE} library(epichains) From c87cbdc5ce716c9d1bfbfc3222cead4e82c0862e Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 15 Apr 2024 23:35:22 +0100 Subject: [PATCH 114/140] apply suggestions for branching intro Co-authored-by: Adam Kucharski --- episodes/superspreading-simulate.Rmd | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index f1fe1f93..202ee8af 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -176,17 +176,17 @@ library(tidyverse) ## Simulation of uncontrolled outbreaks -Infectious disease epidemics spread through populations when a chain of infected individuals transmit the infection to others. [Branching processes](https://epiverse-trace.github.io/epichains/articles/theoretical_background.html) can be used to model this process. A branching process is a stochastic process where each infectious individual in a generation gives rise to a random number of individuals in the next generation, starting with the index case in generation 1. The distribution of the number of offspring is called the offspring distribution. +Infectious disease epidemics spread through populations when a chain of infected individuals transmit the infection to others. [Branching processes](https://epiverse-trace.github.io/epichains/articles/theoretical_background.html) can be used to model this transmission. A branching process is a stochastic process (i.e. a random process that can be described by a known probability distribution), where each infectious individual gives rise to a random number of individuals in the next generation of infection, starting with the index case in generation 1. The distribution of the number of secondary cases each individual generates is called the offspring distribution ([Azam & Funk, 2024](https://epiverse-trace.github.io/epichains/articles/epichains.html)). -`{epichains}` provides methods to analyse and simulate the *size* and *length* of branching processes with an arbitrary offspring distribution. `{epichains}` implements a rapid and low-detail model to reconstruct transmission chains to assess epidemic risk, project cases into the future, and simulate interventions. +`{epichains}` provides methods to analyse and simulate the *size* and *length* of branching processes with an given offspring distribution. `{epichains}` implements a rapid and simple model to simulate transmission chains to assess epidemic risk, project cases into the future, and evaluate interventions that change $R$. ::::::::::::::::::: discussion ### chain size and length -- The **size** of the transmission chain is the total number of individuals infected by a single case and +- The **size** of the transmission chain is defined as the total number of individuals infected across all generations of infection, and -- the **length** of the transmission chain is the number of generations from the first case to the last case they produced before the chain ended. +- the **length** of the transmission chain is the number of generations from the first case to the last case in the outbreak before the chain ended. The *size* calculation includes the first case, and the *length* calculation contains the first generation when the first case starts the chain (See figure below). @@ -194,7 +194,7 @@ The *size* calculation includes the first case, and the *length* calculation con :::::::::::::::::::: -To use `{epichains}`, we need two key delays: the offspring distribution and the generation time! +To use `{epichains}`, we need to know (or assume) two key epidemiological values: the offspring distribution and the generation time. ## Get the offspring distribution From a1db806804d899ab8992d822f5982a78d20e44c2 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 15 Apr 2024 23:41:52 +0100 Subject: [PATCH 115/140] homogenise to use individual level variation --- episodes/superspreading-simulate.Rmd | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 202ee8af..bb8c6073 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -32,13 +32,13 @@ Learners should familiarise themselves with the following concept dependencies b -Transmission heterogeneity affects epidemic establishment and the ease of control ([Cori et al., 2017](https://royalsocietypublishing.org/doi/10.1098/rstb.2016.0371)). +Individual variation in transmission can affects both the potential for an epidemic to establish in a population and the ease of control ([Cori et al., 2017](https://royalsocietypublishing.org/doi/10.1098/rstb.2016.0371)). -+ Greater heterogeneity reduces the overall probably of a single new case causing a large local outbreak, because most cases infect few others and individuals that generate a large number of secondary cases are relatively rare. ++ Greater variation reduces the overall probably of a single new case causing a large local outbreak, because most cases infect few others and individuals that generate a large number of secondary cases are relatively rare. -+ However, if a 'superspreading event' does occur and the outbreak gets established, this heterogeneity can make an outbreak harder to control using *mass interventions* (i.e. blanket interventions that implicitly assume everyone contributes equally to transmission), because some cases contribute disproportionality: a single uncontrolled case may generate a large number of secondary cases. ++ However, if a 'superspreading event' does occur and the outbreak gets established, this variation can make an outbreak harder to control using *mass interventions* (i.e. blanket interventions that implicitly assume everyone contributes equally to transmission), because some cases contribute disproportionality: a single uncontrolled case may generate a large number of secondary cases. -+ Conversely, heterogeneity in transmission may provide opportunities for *targeted interventions* if the individuals who contribute more to transmission (due to biological or behavioural factors), or the settings in which 'superspreading events' occur, share socio-demographic, environmental or geographical characteristics that can be defined. ++ Conversely, variation in transmission may provide opportunities for *targeted interventions* if the individuals who contribute more to transmission (due to biological or behavioural factors), or the settings in which 'superspreading events' occur, share socio-demographic, environmental or geographical characteristics that can be defined. From 77fe7e22f351154c85528e141082d3b39b49e768 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 15 Apr 2024 23:51:05 +0100 Subject: [PATCH 116/140] clear get offspring distribution section Co-authored-by: Adam Kucharski --- episodes/superspreading-simulate.Rmd | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index bb8c6073..ca86f362 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -198,7 +198,7 @@ To use `{epichains}`, we need to know (or assume) two key epidemiological values ## Get the offspring distribution -The MERS offspring distribution will follow a negative binomial distribution with mean (reproduction number $R$) and dispersion $k$ values estimated from the linelist and contact data of `mers_korea_2015` in the `{outbreaks}` R package in the previous episode. +Here we assume the MERS offspring distribution follows a negative binomial distribution, with mean (reproduction number $R$) and dispersion $k$ values estimated from the linelist and contact data of `mers_korea_2015` in the `{outbreaks}` R package in the previous episode. ```{r} mers_offspring <- c(mean = 0.60, dispersion = 0.02) @@ -208,7 +208,7 @@ mers_offspring <- c(mean = 0.60, dispersion = 0.02) ### offspring distribution for epichains -We input an offspring distribution to `{epichains}` by defining the R function that generates random values. For example, for a negative binomial distribution, we use `rnbinom` with its corresponding `mu` and `size` arguments: +We input an offspring distribution to `{epichains}` by referring to the R function that generates random values from the distribution we want. For a negative binomial distribution, we use `rnbinom` with its corresponding `mu` and `size` arguments: ```r offspring_dist = rnbinom, @@ -224,7 +224,7 @@ The reference manual in `?rnbinom` tells us our required specific arguments. ### Poisson and other distributions -`{epichains}` can accept any R function that generates random numbers, so the specified arguments will change depending on the R function used. This can be learned by accessing the function reference manual. +`{epichains}` can accept any R function that generates random numbers, so the specified arguments will change depending on the R function used. For more details on the range of possible options, see the function reference manual. For example, let's say we want to use a Poisson distribution for the offspring distribution. First, read the argument required in the `?rpois` reference manual. Second, specify the `lambda` argument parameter, also known as rate or mean in the literature. In `{epichains}`, this can look like this: @@ -233,7 +233,7 @@ For example, let's say we want to use a Poisson distribution for the offspring d lambda = mers_offspring["mean"], ``` -In this example, we can specify `lambda = mers_offspring["mean"]` because in a negative binomial model, when the dispersion parameter $k$ approaches infinity ($k \rightarrow \infty$), the variance equals the mean. This makes the conventional Poisson model a special case of the negative binomial model. The mean of the negative binomial model (`mu`) can also be the mean of the Poisson model (`lambda`). +In this example, we can specify `lambda = mers_offspring["mean"]` because the mean number of secondary cases generated (i.e. $R$) should be the same regardless of the distribution we assume. What changes is the variance of the distribution, and hence the level of individual-level variation in transmission. When the dispersion parameter $k$ approaches infinity ($k \rightarrow \infty$) in a negative binomial distribution, the variance equals the mean. This makes the conventional Poisson distribution a special case of the negative binomial distribution. :::::::::::::::::::::::::: From 3a476c643f143961bb69e3cd23dc6c494f131c62 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 15 Apr 2024 23:53:24 +0100 Subject: [PATCH 117/140] clear simulate single chain section Co-authored-by: Adam Kucharski --- episodes/superspreading-simulate.Rmd | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index ca86f362..b03291f2 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -239,7 +239,7 @@ In this example, we can specify `lambda = mers_offspring["mean"]` because the me ## Get generation time -The [serial interval](../learners/reference.md#serialinterval) distribution often approximates the generation time distribution. This approximation is frequent because it is easier to observe and measure the onset of symptoms than the onset of infectiousness. +The [serial interval](../learners/reference.md#serialinterval) distribution is often used to approximate the generation time distribution. This approximation is commonly used because it is easier to observe and measure the onset of symptoms in each case than the precise time of infection. :::::::::::::::::::::::::::::::: spoiler @@ -304,7 +304,7 @@ simulate_chains( ) ``` -`simulate_chains()` requires at least three sets of arguments: +`simulate_chains()` requires three sets of arguments as a minimum: - simulation controls, - offspring distribution, and @@ -323,7 +323,7 @@ This is an exclusive feature of `{epichains}`. Branching process simulations end ::::::::::::::::::::::::::: -The `simulate_chains()` output creates a `` class object. +The `simulate_chains()` output creates a `` class object, which we can then analyse further in R. ## Simulate multiple chains From 18af963b6dc211dc5b40b13679bc48af1db403bd Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Mon, 15 Apr 2024 23:57:55 +0100 Subject: [PATCH 118/140] fix number_chains typo --- episodes/superspreading-simulate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index b03291f2..9611d4c2 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -358,7 +358,7 @@ Or, if you previously used the `*apply` family of functions, visit the package v :::::::::::::::::::::::::::::: -To get multiple chains, we must apply the `simulate_chains()` function to each chain defined by a sequence of numbers from 1 to `number_chains`. +To get multiple chains, we must apply the `simulate_chains()` function to each chain defined by a sequence of numbers from 1 to `r number_chains`. ::::::::::::::::::::::::::::::: callout From 7d42cbe07e09098d73f07532efa8d50a6ca9551b Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 16 Apr 2024 00:01:11 +0100 Subject: [PATCH 119/140] add chunk to make visible the number of chain --- episodes/superspreading-simulate.Rmd | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 9611d4c2..8f828d15 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -463,6 +463,10 @@ To explore the output format of the `` class object of name `simulate Let's use `dplyr::filter()` for this: +```r +chain_to_observe <- 806 +``` + ```{r} #### get epichain summary ---------------------------------------------------- From 2c94e3252094397668f013f84d8429f2a07abb85 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 16 Apr 2024 00:04:16 +0100 Subject: [PATCH 120/140] clear mention to number of chains Co-authored-by: Adam Kucharski --- episodes/superspreading-simulate.Rmd | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 8f828d15..6ae2a39b 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -388,7 +388,7 @@ The `sim` element is placed to register the iteration number (**chain ID**) as a ::::::::::::::::::::::::::::::: -Now, we are prepared to use `map()` to iterate `simulate_chains()` in a vector from 1 to `r number_chains`: +Now, we are prepared to use `map()` to repeatedly simulate from `simulate_chains()` and store in a vector from 1 to `number_chains`: ```{r} simulated_chains_map <- @@ -453,7 +453,7 @@ chain_to_observe <- simulated_chains_map %>% pull(chain_id) ``` -To explore the output format of the `` class object of name `simulated_chains_map`, let's observe closely the simulated `chain_id` number `r chain_to_observe`. +To explore the output format of the `` class object of name `simulated_chains_map`, let's look at the simulated `chain_id` number `r chain_to_observe`. ::::::::::::::::::::::::::::::::: From 9ccde6eb22a5e4b7ab74d5a326f2546226339420 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 16 Apr 2024 00:08:20 +0100 Subject: [PATCH 121/140] fix print of number_chains --- episodes/superspreading-simulate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 6ae2a39b..db47f278 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -388,7 +388,7 @@ The `sim` element is placed to register the iteration number (**chain ID**) as a ::::::::::::::::::::::::::::::: -Now, we are prepared to use `map()` to repeatedly simulate from `simulate_chains()` and store in a vector from 1 to `number_chains`: +Now, we are prepared to use `map()` to repeatedly simulate from `simulate_chains()` and store in a vector from 1 to `r number_chains`: ```{r} simulated_chains_map <- From 7ea4815eb143c9659a62a41e81cd9486103ca00e Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 16 Apr 2024 00:14:09 +0100 Subject: [PATCH 122/140] fix capitalization in solution subtitle --- episodes/superspreading-simulate.Rmd | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index db47f278..590d25a7 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -459,7 +459,7 @@ To explore the output format of the `` class object of name `simulate ::::::::::::::::::::::::: solution -### the epichains object +### The epichains object Let's use `dplyr::filter()` for this: @@ -487,7 +487,7 @@ The simulated `chain_id` number `r chain_to_observe` has three known infectors a ::::::::::::::::::::::::: solution -### the epichains data frame +### The epichains data frame ```{r} #### infector-infectee data frame -------------------------------------------- From 1574c33b706e2e81b59bb1a101711add962ab9d6 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 16 Apr 2024 00:23:02 +0100 Subject: [PATCH 123/140] collect suggestions across text Co-authored-by: Adam Kucharski --- episodes/superspreading-simulate.Rmd | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 590d25a7..15145fbd 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -474,7 +474,7 @@ simulated_chains_map %>% filter(chain_id == chain_to_observe) ``` -Key elements exclusive from this output are in the **footer**: +Key elements from this output are in the footer, the piece of text that appears at the bottom: ```output Number of infectors (known): 3 @@ -623,7 +623,7 @@ Although most introductions of `r initial_cases` index case do not generate seco ### Observed cases vs simulated chains -Let's overlap the cumulative number of observed cases using the linelist object from the `mers_korea_2015` dataset of the `{outbreaks}` R package. To prepare the dataset we use `{incidence2}` to convert the linelist to an `` object, complete the missing dates of the time series with `complete_dates()` +Let's overlap the cumulative number of observed cases using the linelist object from the `mers_korea_2015` dataset of the `{outbreaks}` R package. To prepare the dataset so we can plot daily total cases over time, we use `{incidence2}` to convert the linelist to an `` object, complete the missing dates of the time series with `complete_dates()` ```{r,warning=FALSE,message=FALSE} library(outbreaks) @@ -647,7 +647,7 @@ plot(mers_cumcases) ::::::::::::::::::::::::::::::::::: -When plotting the observed number of cumulative cases from the Middle East respiratory syndrome (MERS) outbreak in South Korea in 2015 alongside the previously simulated chains, we identify that the observed cases followed a trajectory that resembled a simulated explosive outbreak. +When plotting the observed number of cumulative cases from the Middle East respiratory syndrome (MERS) outbreak in South Korea in 2015 alongside the previously simulated chains, we see that the observed cases followed a trajectory that is consistent with the simulated explosive outbreak dynamics (which makes sense, given the simulation uses parameters based on this specific outbreak). ```{r,echo=FALSE} # Observed cases vs Simulated transmission chains @@ -685,7 +685,7 @@ ggplot() + ) ``` -When we increase the dispersion parameter from $k = 0.01$ to $k = \infty$, given a fixed reproduction number $R = 1.5$, the proportion of simulated outbreaks that reached the 100-case threshold increases. +When we increase the dispersion parameter from $k = 0.01$ to $k = \infty$ - and hence reduce individual-level variation in transmission - and assume a fixed reproduction number $R = 1.5$, the proportion of simulated outbreaks that reached the 100-case threshold increases. This is because the simulated outbreaks now have more of a consistent, clockwise dynamic, rather than the high level of variability seen previously. ![**Growth of simulated outbreaks with R = 1.5 and one initial case, conditional on non-extinction.** Boxes show the median and interquartile range (IQR) of the first disease generation with 100 cases; whiskers show the most extreme values within 1.5 × IQR of the boxes, and crosses show outliers. Percentages show the proportion of 10,000 simulated outbreaks that reached the 100-case threshold ([Lloyd-Smith et al., 2005](https://www.nature.com/articles/nature04153)).](fig/see-nature04153_Fig2-c.jpg) From 04e894f96276fa476b9f21e63779b0254acf3fcc Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 16 Apr 2024 00:24:22 +0100 Subject: [PATCH 124/140] add discussion context to readers Co-authored-by: Adam Kucharski --- episodes/superspreading-simulate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 15145fbd..3f55b5ee 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -693,7 +693,7 @@ When we increase the dispersion parameter from $k = 0.01$ to $k = \infty$ - and ### Early spread projections -In the epidemic's initial phase, you can use `{epichains}` to apply a branching process model to project the number of future cases. Validation analysis showed that this is a rapid and low-detail model with forecast prediction intervals that are too certain ([Pearson et al., 2020](https://www.eurosurveillance.org/content/10.2807/1560-7917.ES.2020.25.18.2000543#validationofthemodel-1)). +In the epidemic's initial phase, you can use `{epichains}` to apply a branching process model to project the number of future cases. Even though the model accounts for randomness in transmission and variation in the number of secondary cases, there may be additional local features we have not considered. Analysis of early forecasts made for COVID in different countries using this model structure found that predictions were often overconfident ([Pearson et al., 2020](https://www.eurosurveillance.org/content/10.2807/1560-7917.ES.2020.25.18.2000543#validationofthemodel-1)). This is likely because the real-time model did not include all the changes in the offspring distribution that were happening at the local level as a result of behaviour change and control measures. You can read more about the importance of local context in COVID-19 models in [Eggo et al. (2020)](https://www.nature.com/articles/s43588-020-00014-7). We invite you to read the vignette on [Projecting infectious disease incidence: a COVID-19 example](https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html)! From 0d50b8796d11a666dc37b80bba3f84b0ea04ce06 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 16 Apr 2024 00:26:38 +0100 Subject: [PATCH 125/140] collect edits in viz and challenge Co-authored-by: Adam Kucharski --- episodes/superspreading-simulate.Rmd | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 3f55b5ee..655563c1 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -695,7 +695,7 @@ When we increase the dispersion parameter from $k = 0.01$ to $k = \infty$ - and In the epidemic's initial phase, you can use `{epichains}` to apply a branching process model to project the number of future cases. Even though the model accounts for randomness in transmission and variation in the number of secondary cases, there may be additional local features we have not considered. Analysis of early forecasts made for COVID in different countries using this model structure found that predictions were often overconfident ([Pearson et al., 2020](https://www.eurosurveillance.org/content/10.2807/1560-7917.ES.2020.25.18.2000543#validationofthemodel-1)). This is likely because the real-time model did not include all the changes in the offspring distribution that were happening at the local level as a result of behaviour change and control measures. You can read more about the importance of local context in COVID-19 models in [Eggo et al. (2020)](https://www.nature.com/articles/s43588-020-00014-7). -We invite you to read the vignette on [Projecting infectious disease incidence: a COVID-19 example](https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html)! +We invite you to read the vignette on [Projecting infectious disease incidence: a COVID-19 example](https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html)! for more on making predictions using `{epichains}`. :::::::::::::::::::::: @@ -705,11 +705,11 @@ We invite you to read the vignette on [Projecting infectious disease incidence: ### Ebola's large outbreak potential -Evaluate the potential of Ebola to generate explosive outbreaks. Use the appropriate package to access delay data from previous outbreaks. +Evaluate the potential for a new Ebola case to generate an explosive large outbreak. Use the appropriate package to access delay data from previous outbreaks. :::::::::::::: hint -With `{epiparameter}`, you can access and use delay distributions from previous outbreaks. +With `{epiparameter}`, you can access and use offspring and delay distributions from previous Ebola outbreaks. :::::::::::::: From 139244bc9b32febbd07eceeb25451c4bb4afb629 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 16 Apr 2024 00:33:08 +0100 Subject: [PATCH 126/140] collect edits on questions --- episodes/superspreading-simulate.Rmd | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 655563c1..b2392016 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -794,9 +794,9 @@ With `{epiparameter}` you can access and use delay distributions from previous o With `{superspreading}`, you can get numerical solutions to processes that `{epichains}` solve using branching processes. We invite you to read the `{superspreading}` vignette on [Epidemic risk](https://epiverse-trace.github.io/superspreading/articles/epidemic_risk.html) and respond to: -- What is the probability of a pathogen causing a large outbreak? -- What is the probability of an outbreak becoming extinct? -- What is the probability of containing the ongoing outbreak? +- What is the probability that a newly introduced pathogen will cause a large outbreak? +- What is the probability that an infection will, by chance, fail to establish following initial introduction(s)? +- What is the probability the outbreak will be contained? Check how these estimates vary non-linearly with respect to the mean reproduction number $R$ and dispersion $k$ of a given disease. From e243368d1b28e54b9af6153cef5d1012817daf32 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 30 Apr 2024 12:46:12 +0100 Subject: [PATCH 127/140] apply suggestions from code review Co-authored-by: Abdoelnaser M Degoot Co-authored-by: James Azam --- episodes/superspreading-estimate.Rmd | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index bd08ebe5..6c486789 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -57,7 +57,7 @@ In this tutorial, we are going to quantify individual variation in transmission, We are going to use data from the `{outbreaks}` package, manage the linelist and contacts data using `{epicontacts}`, and estimate distribution parameters with `{fitdistrplus}`. Lastly, we are going to use `{superspreading}` to explore the implications of variation in transmission for decision-making. -We’ll use the pipe `%>%` to connect some of the functions from these packages, so let’s also call the `{tidyverse}` package: +We’ll use the pipe `%>%` to connect some of the functions from these packages, so let’s also call the `{tidyverse}` package. ```{r,message=FALSE,warning=FALSE} library(outbreaks) @@ -79,8 +79,8 @@ Let's practice this using the `mers_korea_2015` linelist and contact data from t ## first, make an epicontacts object epi_contacts <- epicontacts::make_epicontacts( - linelist = mers_korea_2015$linelist, - contacts = mers_korea_2015$contacts + linelist = outbreaks::mers_korea_2015$linelist, + contacts = outbreaks::mers_korea_2015$contacts ) ``` @@ -261,7 +261,7 @@ In epidemiology, [negative binomial](https://en.wikipedia.org/wiki/Negative_bino Calculate the distribution of secondary cases for Ebola using the `ebola_sim_clean` object from `{outbreaks}` package. -Does the offspring distribution of Ebola is skewed or overdispersed? +Is the offspring distribution of Ebola skewed or overdispersed? :::::::::::::::::: hint @@ -315,7 +315,7 @@ From a visual inspection, the distribution of secondary cases for the Ebola data ## Estimate the dispersion parameter -To empirically estimate the dispersion parameter $k$, we can to fit a negative binomial distribution to the number of secondary cases. +To empirically estimate the dispersion parameter $k$, we could fit a negative binomial distribution to the number of secondary cases. We can fit distributions to data using the `{fitdistrplus}` package, which provides maximum likelihood estimates. @@ -706,7 +706,7 @@ Compare this values with the ones reported by [Lloyd-Smith et al., 2005](https:/ ### Expected proportion of transmission -What is the proportion of cases that are responsible of the 80% of transmission? +What is the proportion of cases responsible for 80% of transmission? Use `{superspreading}` and compare the estimates for **MERS** using the offspring distributions parameters from this tutorial episode, with **SARS-1** and **Ebola** offspring distributions parameter accessible via the `{epiparameter}` R package. @@ -727,7 +727,7 @@ epidist_string <- epidist_db( paste(collapse = ", ") ``` -Currently, `{epiparameter}` have offspring distributions for `r epidist_string`. Let's access the offspring distribution `mean` and `dispersion` parameters for SARS-1: +Currently, `{epiparameter}` has offspring distributions for `r epidist_string`. Let's access the offspring distribution `mean` and `dispersion` parameters for SARS-1: ```{r,message=FALSE,warning=FALSE} # Load parameters From 0d7e4355360a2ae45a920df509d109dcaa22e0eb Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 30 Apr 2024 12:50:21 +0100 Subject: [PATCH 128/140] apply suggestions from code review Co-authored-by: James Azam --- episodes/superspreading-simulate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index b2392016..79e2eae2 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -32,7 +32,7 @@ Learners should familiarise themselves with the following concept dependencies b -Individual variation in transmission can affects both the potential for an epidemic to establish in a population and the ease of control ([Cori et al., 2017](https://royalsocietypublishing.org/doi/10.1098/rstb.2016.0371)). +Individual variation in transmission can affect both the potential for an epidemic to establish in a population and the ease of control ([Cori et al., 2017](https://royalsocietypublishing.org/doi/10.1098/rstb.2016.0371)). + Greater variation reduces the overall probably of a single new case causing a large local outbreak, because most cases infect few others and individuals that generate a large number of secondary cases are relatively rare. From ff35dc84c6df86825faeeee2c02d1936e9d24395 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 30 Apr 2024 12:51:59 +0100 Subject: [PATCH 129/140] fix serial interval object naming --- episodes/superspreading-simulate.Rmd | 16 ++++++++-------- 1 file changed, 8 insertions(+), 8 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 79e2eae2..ed36d6f6 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -63,7 +63,7 @@ mers_cumcases <- mers_korea_2015$linelist %>% mers_offspring <- c(mean = 0.60, dispersion = 0.02) # generation time -serial_inverval <- epidist_db( +serial_interval <- epidist_db( disease = "mers", epi_dist = "serial", single_epidist = TRUE @@ -92,7 +92,7 @@ simulated_chains_map <- mu = mers_offspring["mean"], size = mers_offspring["dispersion"], # generation - generation_time = function(x) generate(x = serial_inverval, times = x) + generation_time = function(x) generate(x = serial_interval, times = x) ) %>% # creates a column with the chain ID number mutate(chain_id = sim) @@ -254,17 +254,17 @@ However, using the *serial interval* as an approximation of the *generation time Let's use the `{epiparameter}` package to access and use the available serial interval for MERS disease: ```{r,message=FALSE,warning=FALSE} -serial_inverval <- epidist_db( +serial_interval <- epidist_db( disease = "mers", epi_dist = "serial", single_epidist = TRUE ) -plot(serial_inverval, day_range = 0:25) +plot(serial_interval, day_range = 0:25) ``` ```{r,echo=FALSE} -serial_summary <- serial_inverval$summary_stats %>% +serial_summary <- serial_interval$summary_stats %>% as_tibble() %>% select(mean, sd) %>% distinct(.keep_all = TRUE) @@ -279,7 +279,7 @@ The serial interval for MERS has a mean of `r serial_summary$mean` days and a st In `{epichains}`, we need to specify the generation time as a function that generates random numbers. Using `{epiparameter}` has the advantage of using the distribution function `epiparameter::generate()` for this input. This will look like this: ```r -function(x) generate(x = serial_inverval, times = x) +function(x) generate(x = serial_interval, times = x) ``` This interface is similar to the one `{cfr}` uses to link with `{epiparameter}`. Read the [work with delay distributions](https://epiverse-trace.github.io/cfr/articles/delay_distributions.html) vignette for further context. @@ -300,7 +300,7 @@ simulate_chains( mu = mers_offspring["mean"], size = mers_offspring["dispersion"], # generation - generation_time = function(x) generate(x = serial_inverval, times = x) + generation_time = function(x) generate(x = serial_interval, times = x) ) ``` @@ -407,7 +407,7 @@ simulated_chains_map <- mu = mers_offspring["mean"], size = mers_offspring["dispersion"], # generation - generation_time = function(x) generate(x = serial_inverval, times = x) + generation_time = function(x) generate(x = serial_interval, times = x) ) %>% # creates a column with the chain ID number mutate(chain_id = sim) From 3ca57f3319a9c21125a8a80467385528474eece5 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 30 Apr 2024 12:57:07 +0100 Subject: [PATCH 130/140] replace exclusive with customizable --- episodes/superspreading-simulate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index ed36d6f6..1a636d16 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -319,7 +319,7 @@ In the lines above, we described how to specify the offspring distribution and g ### Stopping criteria -This is an exclusive feature of `{epichains}`. Branching process simulations end when they have gone extinct. No more offspring are being produced because of some stopping criterion. +This is an customisable feature of `{epichains}`. Branching process simulations end when they have gone extinct. No more offspring are being produced because of some stopping criterion. ::::::::::::::::::::::::::: From abdbec0aac52036cc91a9539d507d508cbb3d001 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 30 Apr 2024 13:02:22 +0100 Subject: [PATCH 131/140] add double colon checklist in introduction (#49) --- episodes/superspreading-estimate.Rmd | 12 ++++++++++++ episodes/superspreading-simulate.Rmd | 12 ++++++++++++ 2 files changed, 24 insertions(+) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 6c486789..b18eec75 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -67,6 +67,18 @@ library(superspreading) library(tidyverse) ``` +::::::::::::::::::: checklist + +### The double-colon + +The double-colon `::` in R let you call a specific function from a package without loading the entire package into the current environment. + +For example, `dplyr::filter(data, condition)` uses `filter()` from the `{dplyr}` package. + +This help us remember package functions and avoid namespace conflicts. + +::::::::::::::::::: + ## The individual reprodution number The individual reproduction number is defined as the number of secondary cases caused by a particular infected individual. diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 1a636d16..77b371e3 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -174,6 +174,18 @@ library(epiparameter) library(tidyverse) ``` +::::::::::::::::::: checklist + +### The double-colon + +The double-colon `::` in R let you call a specific function from a package without loading the entire package into the current environment. + +For example, `dplyr::filter(data, condition)` uses `filter()` from the `{dplyr}` package. + +This help us remember package functions and avoid namespace conflicts. + +::::::::::::::::::: + ## Simulation of uncontrolled outbreaks Infectious disease epidemics spread through populations when a chain of infected individuals transmit the infection to others. [Branching processes](https://epiverse-trace.github.io/epichains/articles/theoretical_background.html) can be used to model this transmission. A branching process is a stochastic process (i.e. a random process that can be described by a known probability distribution), where each infectious individual gives rise to a random number of individuals in the next generation of infection, starting with the index case in generation 1. The distribution of the number of secondary cases each individual generates is called the offspring distribution ([Azam & Funk, 2024](https://epiverse-trace.github.io/epichains/articles/epichains.html)). From dcfa576811013f39a8be0176addd85b620900589 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 30 Apr 2024 13:10:06 +0100 Subject: [PATCH 132/140] add book link to the dot prefix --- episodes/superspreading-simulate.Rmd | 2 ++ 1 file changed, 2 insertions(+) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 77b371e3..7ff6eb7a 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -398,6 +398,8 @@ map( The `sim` element is placed to register the iteration number (**chain ID**) as a new column in the `` output. The `purrr::list_rbind()` function aims to combine all the list outputs from `map()`. +**Why a dot (`.`) as a prefix?** In the [tidy design principles](https://design.tidyverse.org/dots-prefix.html) book we have a chapter on the dot prefix! + ::::::::::::::::::::::::::::::: Now, we are prepared to use `map()` to repeatedly simulate from `simulate_chains()` and store in a vector from 1 to `r number_chains`: From fa8742fc4ede24b5b76dd99802d0d5e5c315d43f Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 30 Apr 2024 13:22:52 +0100 Subject: [PATCH 133/140] remove covidregional from setup --- learners/setup.md | 1 - 1 file changed, 1 deletion(-) diff --git a/learners/setup.md b/learners/setup.md index b2e982a8..a88922f6 100644 --- a/learners/setup.md +++ b/learners/setup.md @@ -213,7 +213,6 @@ library(EpiNow2) library(cfr) library(epiparameter) library(incidence2) -library(covidregionaldata) library(outbreaks) library(tidyverse) ``` From 2679788c061c063b3f26fbfffad770621fe57f6c Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 30 Apr 2024 20:25:23 +0100 Subject: [PATCH 134/140] rename subtitle on backward strategy --- episodes/superspreading-estimate.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index b18eec75..cb660e6b 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -598,7 +598,7 @@ across_offspring %>% :::::::::::::::::::::::::::::::::: -## Backward and forward contact tracing +## Controlling superspreading with contact tracing During an outbreak, it is common to try and reduce transmission by identifying people who have come into contact with an infected person, then quarantine them in case they subsequently turn out to be infected. Such contact tracing can be deployed in multiple ways. 'Forward' contact tracing targets downstream contacts who may have been infected by a newly identifed infection (i.e. the 'index case'). 'Backward' tracing instead tracks the upstream primary case who infected the index case (or a setting or event at which the index case was infected), for example by retracing history of contact to the likely point of exposure. This makes it possible to identify others who were also potentially infected by this earlier primary case. From bf0da27f938ce4602496b98fc91f3fbf6ed28571 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 30 Apr 2024 20:25:41 +0100 Subject: [PATCH 135/140] connect number output with text --- episodes/superspreading-estimate.Rmd | 14 +++++++++++++- 1 file changed, 13 insertions(+), 1 deletion(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index cb660e6b..98529589 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -626,10 +626,22 @@ proportion_cluster_size( k = offspring_fit$estimate["size"], cluster_size = c(5, 10, 25) ) +``` + +```{r,echo=FALSE,message=FALSE,warning=FALSE} +cluster_probability <- proportion_cluster_size( + R = offspring_fit$estimate["mu"], + k = offspring_fit$estimate["size"], + cluster_size = c(5, 10, 25) +) +cluster_probability_percent <- cluster_probability %>% + select(prop_25) %>% + pull(prop_25) ``` -Even though we have an $R<1$, a highly overdispersed offspring distribution ($k=0.02$) means that if we detect a new case, there is a 47% probability they originated from a cluster of 25 infections or more. Hence, by following a backwards strategy, contact tracing efforts will increase the probability of successfully contain and quarantining this large number of earlier infected individuals, rather than simply focusing on the new case, who is likely to have infected nobody (because $k$ is very small). + +Even though we have an $R<1$, a highly overdispersed offspring distribution ($k=0.02$) means that if we detect a new case, there is a `r cluster_probability_percent` probability they originated from a cluster of 25 infections or more. Hence, by following a backwards strategy, contact tracing efforts will increase the probability of successfully contain and quarantining this large number of earlier infected individuals, rather than simply focusing on the new case, who is likely to have infected nobody (because $k$ is very small). We can also use this number to prevent gathering of certain sized to reduce the epidemic by preventing potential superspreading events. Interventions can target to reduce the reproduction number in order to reduce the probability of having clusters of secondary cases. From 9d76ddf29e2e413cdc8d1122f8f2625c0508e748 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 30 Apr 2024 20:34:33 +0100 Subject: [PATCH 136/140] add set seed for same result always --- episodes/superspreading-estimate.Rmd | 8 ++++++++ 1 file changed, 8 insertions(+) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 98529589..c80b5a05 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -616,6 +616,9 @@ Empirical evidence focused on evaluating the efficiency of backward tracing lead Using `{superspreading}`, we can estimate the probability of having a cluster of secondary infections caused by a primary case identified by backward tracing of size $X$ or larger ([Endo et al., 2020](https://wellcomeopenresearch.org/articles/5-239/v3)). ```{r} +# Set seed for random number generator +set.seed(33) + # estimate the probability of # having a cluster size of 5, 10, or 25 # secondary cases from a primary case, @@ -629,6 +632,9 @@ proportion_cluster_size( ``` ```{r,echo=FALSE,message=FALSE,warning=FALSE} +# Set seed for random number generator +set.seed(33) + cluster_probability <- proportion_cluster_size( R = offspring_fit$estimate["mu"], k = offspring_fit$estimate["size"], @@ -638,6 +644,8 @@ cluster_probability <- proportion_cluster_size( cluster_probability_percent <- cluster_probability %>% select(prop_25) %>% pull(prop_25) + +# cluster_probability_percent ``` From a6cb3c33a4b036624c7eadfeaead15579662fc38 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 30 Apr 2024 20:41:31 +0100 Subject: [PATCH 137/140] annotate code and use simulation TRUE --- episodes/superspreading-estimate.Rmd | 26 ++++++++++++++++++++------ 1 file changed, 20 insertions(+), 6 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index c80b5a05..424b07c4 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -502,16 +502,21 @@ Research into sexually transmitted and vector-borne diseases has previously sugg ```{r,message=FALSE,warning=FALSE,echo=FALSE} library(epiparameter) +library(superspreading) library(tidyverse) +# list of diseases with offspring distribution epidist_string <- epidist_db( epi_dist = "offspring distribution" ) %>% list_distributions() %>% dplyr::select(disease) %>% - distinct() + distinct() %>% + as_tibble() +# get percent of cases that cause percent of transmission across_offspring <- epidist_string %>% + # add column list of epidist objects mutate( epidist_out = map( @@ -521,6 +526,7 @@ across_offspring <- epidist_string %>% single_epidist = TRUE ) ) %>% + # get parameters mutate( epidist_params = map( @@ -528,18 +534,23 @@ across_offspring <- epidist_string %>% .f = epiparameter::get_parameters ) ) %>% + # unnest parameters unnest_wider(col = epidist_params) %>% - expand_grid(percent_transmission = seq(0.01, 1, 0.01)) %>% - # mutate(percent_transmission = 0.8) %>% + # to each disease, add sequence from 0.01 to 1 (proportion of transmission) + expand_grid(percent_transmission = seq(from = 0.01, to = 1, by = 0.01)) %>% + # estimate proportion of cases responsible of proportion of transmission (row) mutate( transmission_output = pmap( .l = select(., R = mean, k = dispersion, percent_transmission), .f = superspreading::proportion_transmission, - format_prop = FALSE + format_prop = FALSE, + simulate = TRUE # use a numerical simulation ) ) %>% + # unnest proportion of cases results unnest_wider(col = transmission_output) %>% + # move each result to one column rowwise() %>% mutate( percent_cases = @@ -548,8 +559,10 @@ across_offspring <- epidist_string %>% na.rm = TRUE ) ) %>% - select(-starts_with("prop_")) + select(-starts_with("prop_")) %>% + ungroup() +# get a position to the ggplot text annotation across_offspring_tip <- across_offspring %>% group_by(disease) %>% filter(percent_transmission < 0.98, percent_transmission > 0.85) %>% @@ -561,6 +574,7 @@ across_offspring_tip <- across_offspring %>% TRUE ~ disease )) +# plot x: proportion of cases, y: proportion of transmission across_offspring %>% ggplot() + geom_line( @@ -584,7 +598,7 @@ across_offspring %>% size = 3 ) + scale_y_continuous(breaks = scales::breaks_pretty(n = 5)) + - colorspace::scale_color_continuous_diverging(trans = "log10") + + colorspace::scale_color_continuous_diverging(trans = "log10", rev = TRUE) + labs( x = "Proportion of infectious cases (ranked)", y = "Expected proportion of transmission", From 60ceb9f801222656f8bc3ecaf7a72132096e3256 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 30 Apr 2024 23:12:48 +0100 Subject: [PATCH 138/140] add solutions to challenges --- episodes/superspreading-simulate.Rmd | 301 +++++++++++++++++++++------ 1 file changed, 233 insertions(+), 68 deletions(-) diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index 7ff6eb7a..f0b9ebc8 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -717,36 +717,193 @@ We invite you to read the vignette on [Projecting infectious disease incidence: :::::::::::::::::::::::::: challenge -### Ebola's large outbreak potential +### Monkeypox large outbreak potential -Evaluate the potential for a new Ebola case to generate an explosive large outbreak. Use the appropriate package to access delay data from previous outbreaks. +Evaluate the potential for a new Monkey pox (Mpox) case to generate an explosive large outbreak. + +- Simulate 1000 transmission chains with 1 initial case each. +- Use the appropriate package to access delay data from previous outbreaks. +- How many simulated trajectories reach more than 100 infected cases? :::::::::::::: hint With `{epiparameter}`, you can access and use offspring and delay distributions from previous Ebola outbreaks. +```{r,warning=FALSE,message=FALSE} +library(epiparameter) +library(tidyverse) + +epidist_db(epi_dist = "offspring") %>% + list_distributions() %>% + count(disease, epi_distribution) + +epidist_db(epi_dist = "serial interval") %>% + list_distributions() %>% + count(disease, epi_distribution) +``` + :::::::::::::: :::::::::::::: solution ```{r,message=FALSE,warning=FALSE} -ebola_offspring <- epidist_db( - disease = "ebola", +# load packages ----------------------------------------------------------- + +library(epiparameter) +library(epichains) +library(tidyverse) + +# delays ------------------------------------------------------------------ + +mpox_offspring_epidist <- epidist_db( + disease = "mpox", epi_dist = "offspring", single_epidist = TRUE ) -ebola_serial <- epidist_db( - disease = "ebola", +mpox_offspring <- get_parameters(mpox_offspring_epidist) + +mpox_serialint <- epidist_db( + disease = "mpox", epi_dist = "serial interval", single_epidist = TRUE ) + +# iterate ----------------------------------------------------------------- + +# Set seed for random number generator +set.seed(33) +# Number of simulation runs +number_chains <- 1000 +# Number of initial cases +initial_cases <- 1 + +simulated_chains_mpox <- + # iterate one function across multiple numbers (chain IDs) + map( + # vector of numbers (chain IDs) + .x = seq_len(number_chains), + # function to iterate to each chain ID number + .f = function(sim) { + simulate_chains( + # simulation controls + index_cases = initial_cases, + statistic = "size", + # offspring + offspring_dist = rnbinom, + mu = mpox_offspring["mean"], + size = mpox_offspring["dispersion"], + # generation + generation_time = function(x) generate(x = mpox_serialint, times = x) + ) %>% + # creates a column with the chain ID number + mutate(chain_id = sim) + } + ) %>% + # combine list outputs (for each chain ID) into a single data frame + list_rbind() + +# visualize --------------------------------------------------------------- + +# daily aggregate of cases +simulated_chains_mpox_day <- simulated_chains_mpox %>% + # use data.frame output from object + as_tibble() %>% + # transform chain ID column to factor (categorical variable) + mutate(chain_id = as_factor(chain_id)) %>% + # get the round number (day) of infection times + mutate(day = ceiling(time)) %>% + # count the daily number of cases in each simulation (chain ID) + count(chain_id, day, name = "cases") %>% + # calculate the cumulative number of cases for each simulation (chain ID) + group_by(chain_id) %>% + mutate(cases_cumsum = cumsum(cases)) %>% + ungroup() + +# Visualize transmission chains by cumulative cases +ggplot() + + # create grouped chain trajectories + geom_line( + data = simulated_chains_mpox_day, + mapping = aes( + x = day, + y = cases_cumsum, + group = chain_id + ), + color = "black", + alpha = 0.25, + show.legend = FALSE + ) + + # define a 100-case threshold + geom_hline(aes(yintercept = 100), lty = 2) + + labs( + x = "Day", + y = "Cumulative cases" + ) ``` - +Assuming a Monkey pox outbreak with $R$ = 0.32 and $k$ = 0.58, there is no trajectory among 1000 simulations that reach more than 100 infected cases. Compared to MERS ($R$ = 0.6 and $k$ = 0.02). :::::::::::::: +::::::::::::::::::: hint + +### Epidemic Risk assessment accounting for superspreading + +With `{superspreading}`, you can get numerical solutions to processes that `{epichains}` solve using branching processes. We invite you to read the `{superspreading}` vignette on [Epidemic risk](https://epiverse-trace.github.io/superspreading/articles/epidemic_risk.html) and respond to: + +- What is the probability that a newly introduced pathogen will cause a large outbreak? +- What is the probability that an infection will, by chance, fail to establish following initial introduction(s)? +- What is the probability the outbreak will be contained? + +Check how these estimates vary non-linearly with respect to the mean reproduction number $R$ and dispersion $k$ of a given disease. + + + + + +```{r,message=FALSE,warning=FALSE,echo=FALSE,eval=FALSE} +library(superspreading) + +# estimate probability to contain +probability_contain( + R = mers_offspring["mean"], + k = mers_offspring["dispersion"], + num_init_infect = 1, + case_threshold = 100 +) + +# Estimate the probability of a large outbreak +# with 5 independent imported cases +probability_epidemic( + R = mers_offspring["mean"], + k = mers_offspring["dispersion"], + num_init_infect = 5 +) +``` + +```{r,message=FALSE,warning=FALSE,echo=FALSE,eval=FALSE} +library(superspreading) + +# estimate probability to contain +probability_contain( + R = mpox_offspring_epidist["mean"], + k = mpox_offspring_epidist["dispersion"], + num_init_infect = 1, + case_threshold = 100 +) + +# Estimate the probability of a large outbreak +# with 5 independent imported cases +probability_epidemic( + R = mpox_offspring_epidist["mean"], + k = mpox_offspring_epidist["dispersion"], + num_init_infect = 5 +) +``` + +:::::::::::::::::: + ::::::::::::::::::::::::: :::::::::::::::::::::::::: challenge @@ -780,82 +937,90 @@ c0 %>% ::::::::::: solution - - -Remarkable, even with R0 less than 1 -with potentially explosive outbreaks. The observed variation in individual infectiousness in Ebola -means that although the probability of extinction is high, new index cases also have the potential for explosive regrowth of the epidemic. - -::::::::::: - -::::::::::::::::::::::::::::: - -:::::::::::::::::::: challenge - -### Probability to contain an epidemic - -Calculate probabilities for Ebola of a large outbreak and to contain an epidemic. Use the appropriate package to access delay data from previous outbreaks. - -:::::::::::::::::: hint - -With `{epiparameter}` you can access and use delay distributions from previous outbreaks. - -::::::::::::::::::::: - -::::::::::::::::::: hint - -### Epidemic Risk assessment accounting for superspreading - -With `{superspreading}`, you can get numerical solutions to processes that `{epichains}` solve using branching processes. We invite you to read the `{superspreading}` vignette on [Epidemic risk](https://epiverse-trace.github.io/superspreading/articles/epidemic_risk.html) and respond to: - -- What is the probability that a newly introduced pathogen will cause a large outbreak? -- What is the probability that an infection will, by chance, fail to establish following initial introduction(s)? -- What is the probability the outbreak will be contained? +```{r,message=FALSE,warning=FALSE} +# load packages --------------------------- +library(fitdistrplus) +library(epiparameter) +library(epichains) +library(tidyverse) -Check how these estimates vary non-linearly with respect to the mean reproduction number $R$ and dispersion $k$ of a given disease. +# fit a negative binomial distribution ------------------------------------ -:::::::::::::::::: +# Fitting a negative binomial distribution to the number of secondary cases +fit.cases <- fitdist(c0, "nbinom") +fit.cases -::::::::::::::::::::: hint +# serial interval parameters ---------------------------------------------- -Here is an example with the MERS offspring distribution estimates: +ebola_serialinter <- epidist_db( + disease = "ebola", + epi_dist = "serial interval", + single_epidist = T +) -```{r,message=FALSE,warning=FALSE} -library(superspreading) -``` +# simulate outbreak trajectories ------------------------------------------ -```{r} -# estimate probability to contain -probability_contain( - R = mers_offspring["mean"], - k = mers_offspring["dispersion"], - num_init_infect = 1, - case_threshold = 100 -) +# Set seed for random number generator +set.seed(645) +# Number of simulation runs +number_chains <- 1e2 +# Number of initial cases +initial_cases <- 1 -# Estimate the probability of a large outbreak -# with 5 independent imported cases -probability_epidemic( - R = mers_offspring["mean"], - k = mers_offspring["dispersion"], - num_init_infect = 5 -) -``` +sim_multiple_chains <- + map( + .x = seq_len(number_chains), + .f = function(sim) { + simulate_chains( + index_cases = initial_cases, + # stopping + statistic = "size", + # offspring + offspring_dist = rnbinom, + mu = fit.cases$estimate["mu"], + size = fit.cases$estimate["size"], + # generation + generation_time = function(x) generate(x = ebola_serialinter, times = x) + ) %>% + mutate(simulation_n = sim) + } + ) %>% + # combine list outputs (for each chain ID) into a single data frame + list_rbind() -:::::::::::::::::: +# visualize ---------------------------------------- -:::::::::::::::::: solution +sim_chains_aggregate <- + sim_multiple_chains %>% + as_tibble() %>% + mutate(simulation_n = as_factor(simulation_n)) %>% + mutate(day = ceiling(time)) %>% + count(simulation_n, day, name = "cases") %>% + group_by(simulation_n) %>% + mutate(cases_cumsum = cumsum(cases)) %>% + ungroup() -```{r} -#' get ebola params +ggplot() + + geom_line( + data = sim_chains_aggregate, + mapping = aes( + x = day, + y = cases_cumsum, + group = simulation_n#, + # color = simulation_n + ), + show.legend = FALSE + ) + + # define a 100-case threshold + geom_hline(aes(yintercept = 100), lty = 2) ``` - -:::::::::::::::::: +Remarkably, even with R0 less than 1 (R = 0.95) we can have potentially explosive outbreaks. The observed variation in individual infectiousness in Ebola means that although the probability of extinction is high, new index cases also have the potential for explosive regrowth of the epidemic. -::::::::::::::::::::::::::::::::::::: +::::::::::: +::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::: keypoints From 189cd0276bf5151c922a5bcf31bd6e7bcb762521 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Tue, 30 Apr 2024 23:43:41 +0100 Subject: [PATCH 139/140] protect from conflicts --- episodes/superspreading-estimate.Rmd | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index 424b07c4..a9900989 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -542,7 +542,7 @@ across_offspring <- epidist_string %>% mutate( transmission_output = pmap( - .l = select(., R = mean, k = dispersion, percent_transmission), + .l = dplyr::select(., R = mean, k = dispersion, percent_transmission), .f = superspreading::proportion_transmission, format_prop = FALSE, simulate = TRUE # use a numerical simulation @@ -559,7 +559,7 @@ across_offspring <- epidist_string %>% na.rm = TRUE ) ) %>% - select(-starts_with("prop_")) %>% + dplyr::select(-starts_with("prop_")) %>% ungroup() # get a position to the ggplot text annotation From 488b88713f15837fcaa97a5d2a510609aed72344 Mon Sep 17 00:00:00 2001 From: Andree Valle Campos Date: Wed, 1 May 2024 00:46:03 +0100 Subject: [PATCH 140/140] fix lintr checks --- episodes/superspreading-estimate.Rmd | 10 ++++----- episodes/superspreading-simulate.Rmd | 33 ++++++++++++++-------------- 2 files changed, 21 insertions(+), 22 deletions(-) diff --git a/episodes/superspreading-estimate.Rmd b/episodes/superspreading-estimate.Rmd index a9900989..5ec417ad 100644 --- a/episodes/superspreading-estimate.Rmd +++ b/episodes/superspreading-estimate.Rmd @@ -511,7 +511,7 @@ epidist_string <- epidist_db( ) %>% list_distributions() %>% dplyr::select(disease) %>% - distinct() %>% + distinct() %>% as_tibble() # get percent of cases that cause percent of transmission @@ -544,7 +544,7 @@ across_offspring <- epidist_string %>% pmap( .l = dplyr::select(., R = mean, k = dispersion, percent_transmission), .f = superspreading::proportion_transmission, - format_prop = FALSE, + format_prop = FALSE, simulate = TRUE # use a numerical simulation ) ) %>% @@ -559,7 +559,7 @@ across_offspring <- epidist_string %>% na.rm = TRUE ) ) %>% - dplyr::select(-starts_with("prop_")) %>% + dplyr::select(-starts_with("prop_")) %>% ungroup() # get a position to the ggplot text annotation @@ -655,8 +655,8 @@ cluster_probability <- proportion_cluster_size( cluster_size = c(5, 10, 25) ) -cluster_probability_percent <- cluster_probability %>% - select(prop_25) %>% +cluster_probability_percent <- cluster_probability %>% + select(prop_25) %>% pull(prop_25) # cluster_probability_percent diff --git a/episodes/superspreading-simulate.Rmd b/episodes/superspreading-simulate.Rmd index f0b9ebc8..7a94c077 100644 --- a/episodes/superspreading-simulate.Rmd +++ b/episodes/superspreading-simulate.Rmd @@ -734,11 +734,11 @@ library(epiparameter) library(tidyverse) epidist_db(epi_dist = "offspring") %>% - list_distributions() %>% + list_distributions() %>% count(disease, epi_distribution) epidist_db(epi_dist = "serial interval") %>% - list_distributions() %>% + list_distributions() %>% count(disease, epi_distribution) ``` @@ -955,7 +955,7 @@ fit.cases ebola_serialinter <- epidist_db( disease = "ebola", epi_dist = "serial interval", - single_epidist = T + single_epidist = TRUE ) # simulate outbreak trajectories ------------------------------------------ @@ -967,9 +967,9 @@ number_chains <- 1e2 # Number of initial cases initial_cases <- 1 -sim_multiple_chains <- +sim_multiple_chains <- map( - .x = seq_len(number_chains), + .x = seq_len(number_chains), .f = function(sim) { simulate_chains( index_cases = initial_cases, @@ -981,7 +981,7 @@ sim_multiple_chains <- size = fit.cases$estimate["size"], # generation generation_time = function(x) generate(x = ebola_serialinter, times = x) - ) %>% + ) %>% mutate(simulation_n = sim) } ) %>% @@ -990,24 +990,23 @@ sim_multiple_chains <- # visualize ---------------------------------------- -sim_chains_aggregate <- - sim_multiple_chains %>% - as_tibble() %>% - mutate(simulation_n = as_factor(simulation_n)) %>% +sim_chains_aggregate <- + sim_multiple_chains %>% + as_tibble() %>% + mutate(simulation_n = as_factor(simulation_n)) %>% mutate(day = ceiling(time)) %>% - count(simulation_n, day, name = "cases") %>% - group_by(simulation_n) %>% - mutate(cases_cumsum = cumsum(cases)) %>% + count(simulation_n, day, name = "cases") %>% + group_by(simulation_n) %>% + mutate(cases_cumsum = cumsum(cases)) %>% ungroup() ggplot() + geom_line( data = sim_chains_aggregate, mapping = aes( - x = day, - y = cases_cumsum, - group = simulation_n#, - # color = simulation_n + x = day, + y = cases_cumsum, + group = simulation_n ), show.legend = FALSE ) +