From 064b32fde0027187997fb89003359aee453fa750 Mon Sep 17 00:00:00 2001 From: GitHub Actions Date: Tue, 2 Apr 2024 21:18:00 +0000 Subject: [PATCH] differences for PR #37 --- config.yaml | 1 + delays-functions.md | 455 ++++++------- delays-reuse.md | 229 +++---- ...-functions-rendered-unnamed-chunk-16-1.png | Bin 50914 -> 0 bytes ...-functions-rendered-unnamed-chunk-17-1.png | Bin 51598 -> 0 bytes ...-functions-rendered-unnamed-chunk-20-1.png | Bin 51704 -> 52059 bytes ...-functions-rendered-unnamed-chunk-21-1.png | Bin 33217 -> 0 bytes ...lays-reuse-rendered-unnamed-chunk-15-1.png | Bin 11595 -> 0 bytes ...issibility-rendered-unnamed-chunk-17-1.png | Bin 0 -> 31081 bytes ...issibility-rendered-unnamed-chunk-18-1.png | Bin 0 -> 31019 bytes ...issibility-rendered-unnamed-chunk-21-1.png | Bin 0 -> 84081 bytes ...missibility-rendered-unnamed-chunk-5-1.png | Bin 0 -> 5925 bytes ...missibility-rendered-unnamed-chunk-8-1.png | Bin 0 -> 10256 bytes md5sum.txt | 7 +- quantify-transmissibility.md | 608 ++++++++++++++++++ 15 files changed, 926 insertions(+), 374 deletions(-) delete mode 100644 fig/delays-functions-rendered-unnamed-chunk-16-1.png delete mode 100644 fig/delays-functions-rendered-unnamed-chunk-17-1.png delete mode 100644 fig/delays-functions-rendered-unnamed-chunk-21-1.png delete mode 100644 fig/delays-reuse-rendered-unnamed-chunk-15-1.png create mode 100644 fig/quantify-transmissibility-rendered-unnamed-chunk-17-1.png create mode 100644 fig/quantify-transmissibility-rendered-unnamed-chunk-18-1.png create mode 100644 fig/quantify-transmissibility-rendered-unnamed-chunk-21-1.png create mode 100644 fig/quantify-transmissibility-rendered-unnamed-chunk-5-1.png create mode 100644 fig/quantify-transmissibility-rendered-unnamed-chunk-8-1.png create mode 100644 quantify-transmissibility.md diff --git a/config.yaml b/config.yaml index cab81e68..615e9bfb 100644 --- a/config.yaml +++ b/config.yaml @@ -64,6 +64,7 @@ episodes: #- describe-cases.Rmd #- simple-analysis.Rmd - delays-reuse.Rmd +- quantify-transmissibility.Rmd - delays-functions.Rmd # Information for Learners diff --git a/delays-functions.md b/delays-functions.md index 2e4e5143..f021a8b7 100644 --- a/delays-functions.md +++ b/delays-functions.md @@ -1,5 +1,5 @@ --- -title: 'Use delay distributions in analysis' +title: 'Input delay data' teaching: 10 exercises: 2 editor_options: @@ -63,19 +63,44 @@ covid_serialint <- ) ``` -Now, we have an epidemiological parameter we can use in our analysis! In the chunk below we replaced one of the **summary statistics** inputs into `EpiNow2::dist_spec()` +```{.output} +Using Nishiura H, Linton N, Akhmetzhanov A (2020). "Serial interval of novel +coronavirus (COVID-19) infections." _International Journal of +Infectious Diseases_. doi:10.1016/j.ijid.2020.02.060 +.. +To retrieve the short citation use the 'get_citation' function +``` ```r -generation_time <- - EpiNow2::dist_spec( - mean = covid_serialint$summary_stats$mean, # we changed this line :) - sd = 2, - max = 20, - distribution = "gamma" - ) +covid_serialint ``` -In this episode, we will use the **distribution functions** that `{epiparameter}` provides to get a maximum value (`max`) for this and any other package downstream in your analysis pipeline! +```{.output} +Disease: COVID-19 +Pathogen: SARS-CoV-2 +Epi Distribution: serial interval +Study: Nishiura H, Linton N, Akhmetzhanov A (2020). "Serial interval of novel +coronavirus (COVID-19) infections." _International Journal of +Infectious Diseases_. doi:10.1016/j.ijid.2020.02.060 +. +Distribution: lnorm +Parameters: + meanlog: 1.386 + sdlog: 0.568 +``` + +Now, we have an epidemiological parameter we can reuse! We can replace the two out of three **summary statistics** into `EpiNow2::dist_spec()` + +```r +generation_time <- dist_spec( + mean = covid_serialint$summary_stats$mean, + sd = covid_serialint$summary_stats$sd, + max = 20, + distribution = "gamma" +) +``` + +In this episode, we will use the **distribution functions** that `{epiparameter}` provides to get a `max` value for this and any other package downstream in the pipeline! Let's load the `{epiparameter}` and `{EpiNow2}` package. For `{EpiNow2}`, we'll set 4 cores to be used in parallel computations. We'll use the pipe `%>%`, some `{dplyr}` verbs and `{ggplot2}`, so let's also call to the `{tidyverse}` package: @@ -150,8 +175,8 @@ generate(covid_serialint, times = 10) ``` ```{.output} - [1] 4.436411 4.079876 7.023633 16.692691 4.443053 2.929674 5.768319 - [8] 4.648662 6.260220 6.995987 + [1] 4.946173 1.848653 4.558656 4.051608 8.892126 3.296900 4.339645 5.280796 + [9] 6.350389 5.440831 ``` ::::::::: instructor @@ -268,7 +293,7 @@ Parameters: sdlog: 0.568 ``` -We identify this change in the `Distribution:` output line of the `` object. Double check this line: +We identify this change in the `Distribution:` output line of the `` object. Take a double check to this line: ``` Distribution: discrete lnorm @@ -410,24 +435,40 @@ quantile(covid_serialint_discrete, p = 0.999) %>% ::::::::::::::::::::::::::::::::::::::::::: +:::::::::::::::::::::::::::::: callout -## Plug-in `{epiparameter}` to `{EpiNow2}` - -Now we can plug everything into the `EpiNow2::dist_spec()` function! - -- the **summary statistics** `mean` and `sd` of the distribution, -- a maximum value `max`, -- the `distribution` name. +### Log normal distributions -But, before, in `EpiNow2::dist_spec()` for a **Lognormal** distribution we need the *distribution parameters* instead of the summary statistics: +If you need the log normal **distribution parameters** instead of the summary statistics, we can use `epiparameter::get_parameters()`: ```r covid_serialint_parameters <- epiparameter::get_parameters(covid_serialint) + +covid_serialint_parameters +``` + +```{.output} + meanlog sdlog +1.3862617 0.5679803 ``` -Then, we have: +This gets a vector of class `` ready to use as input for any other package! + +**BONUS TIP:** If we write the `[]` next to the last object create like in `covid_serialint_parameters[]`, within `[]` we can use the +Tab key ↹ +to use the [code completion feature](https://support.posit.co/hc/en-us/articles/205273297-Code-Completion-in-the-RStudio-IDE) and have a quick access to `covid_serialint_parameters["meanlog"]` and `covid_serialint_parameters["sdlog"]`. We invite you to try this out in code chunks and the R console! + +:::::::::::::::::::::::::::::: + +## Plug-in `{epiparameter}` to `{EpiNow2}` + +Now we can plug everything into the `EpiNow2::dist_spec()` function! + +- the **summary statistics** `mean` and `sd` of the distribution, +- a maximum value `max`, +- the `distribution` name. ```r @@ -447,53 +488,119 @@ serial_interval_covid Fixed distribution with PMF [0.0073 0.1 0.2 0.19 0.15 0.11 0.075 0.051 0.035 0.023 0.016 0.011 0.0076 0.0053 0.0037 0.0027 0.0019 0.0014 0.001 0.00074 0.00055 0.00041 0.00031] ``` -:::::::::::::::::::::::::::::: callout - -### A code completion tip - -If we write the `[]` next to the object `covid_serialint_parameters[]`, within `[]` we can use the -Tab key ↹ -for [code completion feature](https://support.posit.co/hc/en-us/articles/205273297-Code-Completion-in-the-RStudio-IDE) +:::::::::: callout -This gives quick access to `covid_serialint_parameters["meanlog"]` and `covid_serialint_parameters["sdlog"]`. +### Warning -We invite you to try this out in code chunks and the R console! +Using the serial interval instead of the generation time is an alternative that can propagate bias in your estimates, even more so in diseases with reported pre-symptomatic transmission. ([Chung Lau et al., 2021](https://academic.oup.com/jid/article/224/10/1664/6356465)) -:::::::::::::::::::::::::::::: +:::::::::::::::::: Let's replace the `generation_time` input we used for `EpiNow2::epinow()`. ```r -epinow_estimates_cg <- epinow( +epinow_estimates <- epinow( # cases reported_cases = example_confirmed[1:60], # delays generation_time = generation_time_opts(serial_interval_covid) ) + +base::plot(epinow_estimates) +``` + +::::::::::::::::::::::::::::::::: challenge + +### Ebola's effective reproduction number + +Download and read the [Ebola dataset](data/ebola_cases.csv): + +- Reuse one epidemiological parameter to estimate the effective reproduction number for the Ebola dataset. +- Why did you choose that parameter? + +::::::::::::::::: hint + +To calculate the $R_t$, we need: + +- data set with confirmed cases per day and +- one key delay distribution + +Key functions we applied in this episode are: + +- `epidist_db()` +- `list_distributions()` +- `discretise()` +- probability functions for continuous and discrete distributions + +:::::::::::::::::::::: + +::::::::::::::::: solution + + + + +```r +# read data +# e.g.: if path to file is data/raw-data/ebola_cases.csv then: +ebola_confirmed <- + read_csv(here::here("data", "raw-data", "ebola_cases.csv")) + +# list distributions +epidist_db(disease = "ebola") %>% + list_distributions() +``` + + +```r +# subset one distribution +ebola_serial <- epidist_db( + disease = "ebola", + epi_dist = "serial", + single_epidist = TRUE +) + +# adapt epiparameter to epinow2 +ebola_serial_discrete <- discretise(ebola_serial) + +ebola_serial_discrete_max <- quantile(ebola_serial_discrete, p = 0.999) + +serial_interval_ebola <- + dist_spec( + mean = ebola_serial$summary_stats$mean, + sd = ebola_serial$summary_stats$sd, + max = ebola_serial_discrete_max, + distribution = "gamma" # don't forget! it's a must! + ) + +# run epinow +epinow_estimates <- epinow( + # cases + reported_cases = ebola_confirmed, + # delays + generation_time = generation_time_opts(serial_interval_ebola) +) ``` ```{.output} -WARN [2024-04-02 21:04:37] epinow: There were 3 divergent transitions after warmup. See +WARN [2024-03-28 20:46:51] epinow: There were 8 divergent transitions after warmup. See https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup to find out why this is a problem and how to eliminate them. - -WARN [2024-04-02 21:04:37] epinow: Examine the pairs() plot to diagnose sampling problems +WARN [2024-03-28 20:46:51] epinow: Examine the pairs() plot to diagnose sampling problems - ``` ```r -base::plot(epinow_estimates_cg) +plot(epinow_estimates) ``` - + -:::::::::: callout - -### Warning +`{EpiNow2}` can also include the uncertainty around each summary statistic. We invite you to read this discussion on: [How to adapt `{epiparameter}` uncertainty entries to `{EpiNow2}`](https://github.com/epiverse-trace/epiparameter/discussions/218)? -Using the serial interval instead of the generation time is an alternative that can propagate bias in your estimates, even more so in diseases with reported pre-symptomatic transmission. ([Chung Lau et al., 2021](https://academic.oup.com/jid/article/224/10/1664/6356465)) +:::::::::::::::::::::::::: -:::::::::::::::::: +::::::::::::::::::::::::::::::::::::::::::: ## Adjusting for reporting delays @@ -536,8 +643,6 @@ epinow_estimates <- epinow( ```r -# generation time --------------------------------------------------------- - # get covid serial interval covid_serialint <- epiparameter::epidist_db( @@ -546,7 +651,17 @@ covid_serialint <- author = "Nishiura", single_epidist = TRUE ) +``` + +```{.output} +Using Nishiura H, Linton N, Akhmetzhanov A (2020). "Serial interval of novel +coronavirus (COVID-19) infections." _International Journal of +Infectious Diseases_. doi:10.1016/j.ijid.2020.02.060 +.. +To retrieve the short citation use the 'get_citation' function +``` +```r # adapt epidist to epinow2 covid_serialint_discrete_max <- covid_serialint %>% @@ -564,8 +679,6 @@ covid_serial_interval <- distribution = "lognormal" ) -# incubation time --------------------------------------------------------- - # get covid incubation period covid_incubation <- epiparameter::epidist_db( disease = "covid", @@ -573,7 +686,19 @@ covid_incubation <- epiparameter::epidist_db( author = "Natalie", single_epidist = TRUE ) +``` +```{.output} +Using Linton N, Kobayashi T, Yang Y, Hayashi K, Akhmetzhanov A, Jung S, Yuan +B, Kinoshita R, Nishiura H (2020). "Incubation Period and Other +Epidemiological Characteristics of 2019 Novel Coronavirus Infections +with Right Truncation: A Statistical Analysis of Publicly Available +Case Data." _Journal of Clinical Medicine_. doi:10.3390/jcm9020538 +.. +To retrieve the short citation use the 'get_citation' function +``` + +```r # adapt epiparameter to epinow2 covid_incubation_discrete_max <- covid_incubation %>% @@ -591,10 +716,8 @@ covid_incubation_time <- distribution = "lognormal" # do not forget this! ) -# epinow ------------------------------------------------------------------ - # run epinow -epinow_estimates_cgi <- epinow( +epinow_estimates <- epinow( # cases reported_cases = example_confirmed[1:60], # delays @@ -604,66 +727,68 @@ epinow_estimates_cgi <- epinow( ``` ```{.output} -WARN [2024-04-02 21:06:28] epinow: There were 9 divergent transitions after warmup. See +Logging threshold set at INFO for the EpiNow2 logger +``` + +```{.output} +Writing EpiNow2 logs to the console and: /tmp/Rtmp0E3eaa/regional-epinow/2020-04-21.log +``` + +```{.output} +Logging threshold set at INFO for the EpiNow2.epinow logger +``` + +```{.output} +Writing EpiNow2.epinow logs to the console and: /tmp/Rtmp0E3eaa/epinow/2020-04-21.log +``` + +```{.output} +WARN [2024-03-28 20:48:37] epinow: There were 8 divergent transitions after warmup. See https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup to find out why this is a problem and how to eliminate them. - -WARN [2024-04-02 21:06:28] epinow: Examine the pairs() plot to diagnose sampling problems +WARN [2024-03-28 20:48:37] epinow: Examine the pairs() plot to diagnose sampling problems - -WARN [2024-04-02 21:06:29] epinow: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable. -Running the chains for more iterations may help. See -https://mc-stan.org/misc/warnings.html#bulk-ess - ``` ```r -base::plot(epinow_estimates_cgi) +base::plot(epinow_estimates) ``` - + :::::::::::::::::::::::::: -::::::::::::::::::::::::::::::::::::::::::: - -:::::::::::::::::::::::::::::::::::::::::::::::::::::::: discussion +:::::::::::::: solution ### How much has it changed? After adding the incubation period, discuss: -- Does the trend of the model fit in the "Estimate" section change? +- Does the retrospective trend of forecast change? - Has the uncertainty changed? - How would you explain or interpret any of these changes? -Compare the `{EpiNow2}` figures generated previously. +:::::::::::::::::::::::::::: -:::::::::::::::::::::::::::::::::::::::::::::::::::::::: +::::::::::::::::::::::::::::::::::::::::::: -## Challenges ::::::::::::::::::::::::::::::::: challenge -### Ebola's effective reproduction number adjusted by reporting delays +### Ebola's effective reproduction number was adjusted by reporting delays -Download and read the [Ebola dataset](data/ebola_cases.csv): +Using the same [Ebola dataset](data/ebola_cases.csv): -- Estimate the effective reproduction number using `{EpiNow2}` -- Adjust the estimate by the available reporting delays in `{epiparameter}` +- Reuse one additional epidemiological parameter for the `delays` argument in `EpiNow2::epinow()`. +- Estimate the effective reproduction number using `EpiNow2::epinow()`. - Why did you choose that parameter? ::::::::::::::::: hint -To calculate the $R_t$ using `{EpiNow2}`, we need: - -- Aggregated incidence `data`, with confirmed cases per day, and -- The `generation` time distribution. -- Optionally, reporting `delays` distributions when available (e.g., incubation period). +We can use two complementary delay distributions to estimate the $R_t$ at time $t$. -To get delay distribution using `{epiparameter}` we can use functions like: - -- `epidist_db()` -- `list_distributions()` -- `discretise()` -- `quantile()` +- generation time. +- incubation period and reporting delays. :::::::::::::::::::::: @@ -685,8 +810,6 @@ epidist_db(disease = "ebola") %>% ```r -# generation time --------------------------------------------------------- - # subset one distribution for the generation time ebola_serial <- epidist_db( disease = "ebola", @@ -705,8 +828,6 @@ serial_interval_ebola <- distribution = "gamma" ) -# incubation time --------------------------------------------------------- - # subset one distribution for delay of the incubation period ebola_incubation <- epidist_db( disease = "ebola", @@ -725,10 +846,8 @@ incubation_period_ebola <- distribution = "gamma" ) -# epinow ------------------------------------------------------------------ - # run epinow -epinow_estimates_egi <- epinow( +epinow_estimates <- epinow( # cases reported_cases = ebola_confirmed, # delays @@ -738,173 +857,18 @@ epinow_estimates_egi <- epinow( ``` ```{.output} -WARN [2024-04-02 21:09:53] epinow: There were 2 divergent transitions after warmup. See +WARN [2024-03-28 20:52:04] epinow: There were 10 divergent transitions after warmup. See https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup to find out why this is a problem and how to eliminate them. - -WARN [2024-04-02 21:09:53] epinow: Examine the pairs() plot to diagnose sampling problems +WARN [2024-03-28 20:52:04] epinow: Examine the pairs() plot to diagnose sampling problems - ``` ```r -plot(epinow_estimates_egi) -``` - - - -:::::::::::::::::::::::::: - -::::::::::::::::::::::::::::::::::::::::::: - - -::::::::::::::::::::::::::::::::: challenge - -### What to do with Weibull distributions? - -Use the `influenza_england_1978_school` dataset from the `{outbreaks}` package to calculate the effective reproduction number using `{EpiNow2}` adjusting by the available reporting delays in `{epiparameter}`. - -::::::::::::::::: hint - -`EpiNow2::dist_spec()` also accepts Probability Mass Functions (PMF) from any distribution family. Read the reference guide on [Specify a distribution](https://epiforecasts.io/EpiNow2/reference/dist_spec.html). - -:::::::::::::::::::::: - -::::::::::::::::: solution - - -```r -# What parameters are available for Influenza? -epidist_db(disease = "influenza") %>% - list_distributions() %>% - as_tibble() %>% - count(epi_distribution) -``` - -```{.output} -# A tibble: 3 × 2 - epi_distribution n - -1 generation time 1 -2 incubation period 15 -3 serial interval 1 -``` - -```r -# generation time --------------------------------------------------------- - -# Read the generation time -influenza_generation <- - epidist_db( - disease = "influenza", - epi_dist = "generation" - ) - -influenza_generation -``` - -```{.output} -Disease: Influenza -Pathogen: Influenza-A-H1N1 -Epi Distribution: generation time -Study: Lessler J, Reich N, Cummings D, New York City Department of Health and -Mental Hygiene Swine Influenza Investigation Team (2009). "Outbreak of -2009 Pandemic Influenza A (H1N1) at a New York City School." _The New -England Journal of Medicine_. doi:10.1056/NEJMoa0906089 -. -Distribution: weibull -Parameters: - shape: 2.360 - scale: 3.180 -``` - -```r -# EpiNow2 currently accepts Gamma or LogNormal -# other can pass the PMF function - -influenza_generation_discrete <- - epiparameter::discretise(influenza_generation) - -influenza_generation_max <- - quantile(influenza_generation_discrete, p = 0.999) - -influenza_generation_pmf <- - density( - influenza_generation_discrete, - at = 1:influenza_generation_max - ) - -influenza_generation_pmf -``` - -```{.output} -[1] 0.063123364 0.221349877 0.297212205 0.238968280 0.124851641 0.043094538 -[7] 0.009799363 -``` - -```r -# EpiNow2::dist_spec() can also accept the PMF values -generation_time_influenza <- - dist_spec( - pmf = influenza_generation_pmf - ) - -# incubation period ------------------------------------------------------- - -# Read the incubation period -influenza_incubation <- - epidist_db( - disease = "influenza", - epi_dist = "incubation", - single_epidist = TRUE - ) - -# Discretize incubation period -influenza_incubation_discrete <- - epiparameter::discretise(influenza_incubation) - -influenza_incubation_max <- - quantile(influenza_incubation_discrete, p = 0.999) - -influenza_incubation_pmf <- - density( - influenza_incubation_discrete, - at = 1:influenza_incubation_max - ) - -influenza_incubation_pmf +plot(epinow_estimates) ``` -```{.output} -[1] 0.057491512 0.166877052 0.224430917 0.215076318 0.161045462 0.097466092 -[7] 0.048419279 0.019900259 0.006795222 -``` - -```r -# EpiNow2::dist_spec() can also accept the PMF values -incubation_time_influenza <- - dist_spec( - pmf = influenza_incubation_pmf - ) - -# epinow ------------------------------------------------------------------ - -# Read data -influenza_cleaned <- - outbreaks::influenza_england_1978_school %>% - select(date, confirm = in_bed) - -# Run epinow() -epinow_estimates_igi <- epinow( - # cases - reported_cases = influenza_cleaned, - # delays - generation_time = generation_time_opts(generation_time_influenza), - delays = delay_opts(incubation_time_influenza) -) - -plot(epinow_estimates_igi) -``` - - + :::::::::::::::::::::::::: @@ -918,7 +882,7 @@ plot(epinow_estimates_igi) How to get the mean and standard deviation from a generation time with *only* distribution parameters but no summary statistics like `mean` or `sd` for `EpiNow2::dist_spec()`? -Look at the `{epiparameter}` vignette on [parameter extraction and conversion](https://epiverse-trace.github.io/epiparameter/articles/extract_convert.html) and its [use cases](https://epiverse-trace.github.io/epiparameter/articles/extract_convert.html#use-cases)! +Look at the `{epiparameter}` vignette on [parameter extraction and conversion](https://epiverse-trace.github.io/epiparameter/articles/extract_convert.html)! ::::::::::::::::::::::::::::: @@ -935,7 +899,6 @@ Refer to this excellent tutorial on estimating the serial interval and incubatio ::::::::::::::::::::::::::::: - @@ -100,21 +99,6 @@ epinow_estimates <- epinow( ``` --> -## Find a Generation time - -The generation time, jointly with the $R$, can inform about the speed of spread and its feasibility of control. Given a $R>1$, with a shorter generation time, cases can appear more quickly. - -![Video from the MRC Centre for Global Infectious Disease Analysis, Ep 76. Science In Context - Epi Parameter Review Group with Dr Anne Cori (27-07-2023) at ](fig/reproduction-generation-time.png) - -In calculating the effective reproduction number ($R_{t}$), the *generation time* distribution is often approximated by the [serial interval](../learners/reference.md#serialinterval) distribution. -This frequent approximation is because it is easier to observe and measure the onset of symptoms than the onset of infectiousness. - -![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 of a pre-symptomatic transmission ([Nishiura et al., 2020](https://www.ijidonline.com/article/S1201-9712(20)30119-3/fulltext#gr2)). - -Additionally, even if the *generation time* and *serial interval* have the same mean, their variance usually differs, propagating bias to the $R_{t}$ estimation. $R_{t}$ estimates are sensitive not only to the mean generation time but also to the variance and form of the generation interval distribution [(Gostic et al., 2020)](https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1008409). - ::::::::::::::::: callout ### From time periods to probability distributions. @@ -150,6 +134,21 @@ Table: Serial interval estimates using Gamma, Weibull, and Log normal distributi ::::::::::::::::::::::::: +## Find a Generation time + +The generation time, jointly with the $R$, can inform about the speed of spread and its feasibility of control. Given a $R>1$, with a shorter generation time, cases can appear more quickly. + +![Video from the MRC Centre for Global Infectious Disease Analysis, Ep 76. Science In Context - Epi Parameter Review Group with Dr Anne Cori (27-07-2023) at ](fig/reproduction-generation-time.png) + +In calculating the effective reproduction number ($R_{t}$), the *generation time* distribution is often approximated by the [serial interval](../learners/reference.md#serialinterval) distribution. +This frequent approximation is because it is easier to observe and measure the onset of symptoms than the onset of infectiousness. + +![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 of a pre-symptomatic transmission ([Nishiura et al., 2020](https://www.ijidonline.com/article/S1201-9712(20)30119-3/fulltext#gr2)). + +Additionally, even if the *generation time* and *serial interval* have the same mean, their variance usually differs, propagating bias to the $R_{t}$ estimation. $R_{t}$ estimates are sensitive not only to the mean generation time but also to the variance and form of the generation interval distribution [(Gostic et al., 2020)](https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1008409). + ::::::::::::::::::::::::::::::::: challenge ### Serial interval @@ -300,7 +299,7 @@ In the `epiparameter::list_distributions()` output, we can also find different t ::::::::::::::::: spoiler -### Why do we have a 'NA' entry? +### Why do we have a `` entry? Entries with a missing value (``) in the `prob_distribution` column are *non-parameterised* entries. They have summary statistics but no probability distribution. Compare these two outputs: @@ -342,48 +341,34 @@ distribution[[4]]$metadata$inference_method ::::::::::::::::::::::::::::::::: challenge -### Find your delay distributions! - -Take 2 minutes to explore the `{epiparameter}` library. - -**Choose** a disease of interest (e.g., Influenza, Measles, etc.) and a delay distribution (e.g., the incubation period, onset to death, etc.). +### Ebola's incubation periods -Find: +Take 5 minutes to explore the `{epiparameter}` library. -- How many delay distributions are for that disease? +First, search for Ebola disease delay distributions. Find: -- How many types of probability distribution (e.g., gamma, lognormal) are for a given delay in that disease? +- How many delay distributions are for the Ebola disease? -Ask: - -- Do you recognise the papers? - -- Should `{epiparameter}` literature review consider any other paper? +- How many types of delay distributions are for the incubation period of Ebola? ::::::::::::::::: hint -The `epidist_db()` function with `disease` alone counts the number of entries like: +`epidist_db()` and `list_distributions()` give us different and complementary summary outputs. + +The `epidist_db()` function alone counts for us the number of entries like: - studies, and - delay distributions. -The `epidist_db()` function with `disease` and `epi_dist` gets a list of all entries with: +On the other hand, the `{epiparameter}` combo of `epidist_db()` plus `list_distributions()` lists all the entries in a data frame with columns like: -- the complete citation, -- the **type** of a probability distribution, and -- distribution parameter values. - -The combo of `epidist_db()` plus `list_distributions()` gets a data frame of all entries with columns like: - -- the **type** of the probability distribution per delay, and +- the type of the probability distribution per delay, and - author and year of the study. :::::::::::::::::::::: ::::::::::::::::: solution -We choose to explore Ebola's delay distributions: - ```r # we expect 16 delays distributions for ebola @@ -409,18 +394,6 @@ List of objects Now, from the output of `epiparameter::epidist_db()`, What is an [offspring distribution](../learners/reference.md#offspringdist)? -We choose to find Ebola's incubation periods. This output list all the papers and parameters found. Run this locally if needed: - - -```r -epiparameter::epidist_db( - disease = "ebola", - epi_dist = "incubation" -) -``` - -We use `list_distributions()` to get a summary display of all: - ```r # we expect 2 different types of delay distributions @@ -449,6 +422,12 @@ To retrieve the short citation for each use the 'get_citation' function We find two types of probability distributions for this query: _lognormal_ and _gamma_. +Now, search for delay distributions of your disease of interest! Ask: + +- Do you recognise the papers? + +- Should it consider any other paper? + How does `{epiparameter}` do the collection and review of peer-reviewed literature? We invite you to read the vignette on ["Data Collation and Synthesis Protocol"](https://epiverse-trace.github.io/epiparameter/articles/data_protocol.html)! :::::::::::::::::::::::::: @@ -518,7 +497,7 @@ Parameters: ::::::::::::::::: callout -### How does 'single_epidist' works? +### How does `single_epidist` works? Looking at the help documentation for `?epiparameter::epidist_db()`: @@ -545,6 +524,32 @@ covid_serialint <- ) ``` +```{.output} +Using Nishiura H, Linton N, Akhmetzhanov A (2020). "Serial interval of novel +coronavirus (COVID-19) infections." _International Journal of +Infectious Diseases_. doi:10.1016/j.ijid.2020.02.060 +.. +To retrieve the short citation use the 'get_citation' function +``` + +```r +covid_serialint +``` + +```{.output} +Disease: COVID-19 +Pathogen: SARS-CoV-2 +Epi Distribution: serial interval +Study: Nishiura H, Linton N, Akhmetzhanov A (2020). "Serial interval of novel +coronavirus (COVID-19) infections." _International Journal of +Infectious Diseases_. doi:10.1016/j.ijid.2020.02.060 +. +Distribution: lnorm +Parameters: + meanlog: 1.386 + sdlog: 0.568 +``` + nG)i#XIobp~T<`@ucZ0Doppy7RAIZ>YE{sZO^Gv12kK~^iu~cqcF9>JKbU` zrYCoAwCrFQN)%Pk*N_;Wr}oJa--~~?y^5q#T8fJC;bTiydKqeRj0N_>_Ltv(kut_y zdGGSyh1{}7B^NC82OGK zpg^09XNi*o+6dLEC13-}nWQWQiJ_?U`_C>U z*fPM}1m#9!l49`9SiyHu9D1ORAuOBpHP~k}7@>ZL^E#QGZMX_gAH91+nOZ|a50G^@ zALz?ILM7KvNg&D;slBv92UdqNV{RGbcRYjeu8FyRqHafU1Kxe2S_%h>f*vJ$XY+v zt(L-ErF;B@*zy9r<9Lc!&^$N^W1(5NiC<-ARH?>&!?V*IT|33F{bV++pQ5%mr5K>v z^6T4U3NKxvo?H052rr+pYX-72B`6=;9QqE~jkQ;qai+`wm))ZaS;m)Y!K5YaybZX* z3TC&3H*@Wn*X#2%<=Uz&a8gi}7BdmYo`0C~0t7EL<)Bqi%rE5*H|BxLjz@s-=SVRQ z^jOiEyOa>u`nIq^Csc~_pS%g)Ikf}u^hBJyEae8}f|mrBBDX7Q&fGVln`5B}M$xXE z6T3f5`wJoUP@H#vhoH3Jy-v$cid|hROU`SI&Lr2t(3Sua_<$iO$-v3DQ0sE?9i?s#6-#5l}&ce%73fN`vXD8pGs^>!x zh8`4YW(^aKqhoHd_moO#-G;IQ`4K+V#;T*617jt_F6u&RBL{AJ= 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"f0f01aa200908903fd18ca72cff0eac7" "site/built/delays-reuse.md" "2024-03-28" +"episodes/quantify-transmissibility.Rmd" "f552d70266c0967dc2a4203599b3ad25" "site/built/quantify-transmissibility.md" "2024-04-02" +"episodes/delays-functions.Rmd" "1b8c594905ee34befa02f1912256b37f" "site/built/delays-functions.md" "2024-03-28" "instructors/instructor-notes.md" "ca3834a1b0f9e70c4702aa7a367a6bb5" "site/built/instructor-notes.md" "2024-03-28" "learners/reference.md" "e030f09656b2233a643e7aa2727e4fab" "site/built/reference.md" "2024-03-28" "learners/setup.md" "3720bb4d00b8f9bf1af6b0b582ff36c3" "site/built/setup.md" "2024-03-30" diff --git a/quantify-transmissibility.md b/quantify-transmissibility.md new file mode 100644 index 00000000..87ac51dc --- /dev/null +++ b/quantify-transmissibility.md @@ -0,0 +1,608 @@ +--- +title: 'Quantifying transmission' +teaching: 30 +exercises: 0 +--- + + + +:::::::::::::::::::::::::::::::::::::: questions + +- How can I estimate the time-varying reproduction number ($Rt$) and growth rate from a time series of case data? +- How can I quantify geographical heterogeneity from these transmission metrics? + + +:::::::::::::::::::::::::::::::::::::::::::::::: + +::::::::::::::::::::::::::::::::::::: objectives + +- Learn how to estimate transmission metrics from a time series of case data using the R package `EpiNow2` + +:::::::::::::::::::::::::::::::::::::::::::::::: + +::::::::::::::::::::::::::::::::::::: prereq + +## Prerequisites + +Learners should familiarise themselves with following concepts before working through this tutorial: + +**Statistics**: probability distributions, principle of Bayesian analysis. + +**Epidemic theory**: Effective reproduction number. + +::::::::::::::::::::::::::::::::: + + + +::::::::::::::::::::::::::::::::::::: callout +### Reminder: the Effective Reproduction Number, $R_t$ + +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. + +But in an ongoing outbreak, the population does not remain entirely susceptible as those that recover from infection are typically immune. Moreover, there can be changes in behaviour or other factors that affect transmission. When we are interested in monitoring changes in transmission we are therefore more interested in the value of the **effective reproduction number**, $R_t$, the average number of cases caused by one infectious individual in the population at time $t$. + +:::::::::::::::::::::::::::::::::::::::::::::::: + + +## Introduction + +The transmission intensity of an outbreak is quantified using two key metrics: the reproduction number, which informs on the strength of the transmission by indicating how many new cases are expected from each existing case; and the [growth rate](../learners/reference.md#growth), which informs on the speed of the transmission by indicating how rapidly the outbreak is spreading or declining (doubling/halving time) within a population. To estimate these key metrics using case data we must account for delays between the date of infections and date of reported cases. In an outbreak situation, data are usually available on reported dates only, therefore we must use estimation methods to account for these delays when trying to understand changes in transmission over time. For more details on the distinction between speed and strength of transmission and implications for control, see [Dushoff & Park, 2021](https://royalsocietypublishing.org/doi/full/10.1098/rspb.2020.1556). + +In the next tutorials we will focus on how to use the functions in `{EpiNow2}` to estimate transmission metrics of case data. We will not cover the theoretical background of the models or inference framework, for details on these concepts see the [vignette](https://epiforecasts.io/EpiNow2/dev/articles/estimate_infections.html). + + +::::::::::::::::::::::::::::::::::::: callout +### Bayesian inference + +The R package `EpiNow2` uses a [Bayesian inference](../learners/reference.md#bayesian) framework to estimate reproduction numbers and infection times based on reporting dates. + +In Bayesian inference, we use prior knowledge (prior distributions) with data (in a likelihood function) to find the posterior probability. + +

Posterior probability $\propto$ likelihood $\times$ prior probability +

+ +:::::::::::::::::::::::::::::::::::::::::::::::: + +:::::::::::::::::::::::::::::::::::::::::::::::: instructor + +Refer to the prior probability distribution and the [posterior probability](https://en.wikipedia.org/wiki/Posterior_probability) distribution. + +In the ["`Expected change in daily cases`" callout](#expected-change-in-daily-cases), by "the posterior probability that $R_t < 1$", we refer specifically to the [area under the posterior probability distribution curve](https://www.nature.com/articles/nmeth.3368/figures/1). + +:::::::::::::::::::::::::::::::::::::::::::::::: + + +The first step is to load the `{EpiNow2}` package: + + +```r +library(EpiNow2) +``` + +:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: instructor + +This tutorial illustrates the usage of `epinow()` to estimate the time-varying reproduction number and infection times. Learners should understand the necessary inputs to the model and the limitations of the model output. + +:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: + + +## Delay distributions and case data +### Case data + +To illustrate the functions of `EpiNow2` we will use outbreak data of the start of the COVID-19 pandemic from the United Kingdom. The data are available in the R package `{incidence2}`. + + +```r +dplyr::as_tibble(incidence2::covidregionaldataUK) +``` + +```{.output} +# A tibble: 6,370 × 13 + date region region_code cases_new cases_total deaths_new deaths_total + + 1 2020-01-30 East Mi… E12000004 NA NA NA NA + 2 2020-01-30 East of… E12000006 NA NA NA NA + 3 2020-01-30 England E92000001 2 2 NA NA + 4 2020-01-30 London E12000007 NA NA NA NA + 5 2020-01-30 North E… E12000001 NA NA NA NA + 6 2020-01-30 North W… E12000002 NA NA NA NA + 7 2020-01-30 Norther… N92000002 NA NA NA NA + 8 2020-01-30 Scotland S92000003 NA NA NA NA + 9 2020-01-30 South E… E12000008 NA NA NA NA +10 2020-01-30 South W… E12000009 NA NA NA NA +# ℹ 6,360 more rows +# ℹ 6 more variables: recovered_new , recovered_total , +# hosp_new , hosp_total , tested_new , tested_total +``` + +To use the data, we must format the data to have two columns: + ++ `date`: the date (as a date object see `?is.Date()`), ++ `confirm`: number of confirmed cases on that date. + +Let's use `{dplyr}` for this: + + +```r +library(dplyr) + +cases <- incidence2::covidregionaldataUK %>% + select(date, cases_new) %>% + group_by(date) %>% + summarise(confirm = sum(cases_new, na.rm = TRUE)) %>% + ungroup() +``` + +::::::::::::::::::::::::: spoiler + +### When to use incidence2? + +We can also use the `{incidence2}` package to aggregate cases. However, if you ever need to aggregate you data in a different time **interval** (i.e., days, weeks or months) or per **group** categories, we recommend you to explore the `incidence2::incidence()` function: + + +```r +library(tidyr) +library(dplyr) + +incidence2::covidregionaldataUK %>% + # preprocess missing values + tidyr::replace_na(list(cases_new = 0)) %>% + # compute the daily incidence + incidence2::incidence( + date_index = "date", + counts = "cases_new", + groups = "region", + interval = "week" + ) +``` + +You can also estimate transmission metrics from {incidence2} objects using the `{i2extras}` package. Read further in the [Fitting curves](https://www.reconverse.org/i2extras/articles/fitting_epicurves.html) vignette! + +::::::::::::::::::::::::: + +There are case data available for 490 days, but in an outbreak situation it is likely we would only have access to the beginning of this data set. Therefore we assume we only have the first 90 days of this data. + + + + + +### Delay distributions +We assume there are delays from the time of infection until the time a case is reported. We specify these delays as distributions to account for the uncertainty in individual level differences. The delay can consist of multiple types of delays/processes. A typical delay from time of infection to case reporting may consist of: + +

**time from infection to symptom onset** (the [incubation period](../learners/reference.md#incubation)) + **time from symptom onset to case notification** (the reporting time) +.

+ +The delay distribution for each of these processes can either estimated from data or obtained from the literature. We can express uncertainty about what the correct parameters of the distributions by assuming the distributions have **fixed** parameters or whether they have **variable** parameters. To understand the difference between **fixed** and **variable** distributions, let's consider the incubation period. + +::::::::::::::::::::::::::::::::::::: callout +### Delays and data +The number of delays and type of delay are a flexible input that depend on the data. The examples below highlight how the delays can be specified for different data sources: + +
+ +| Data source | Delay(s) | +| ------------- |-------------| +|Time of symptom onset |Incubation period | +|Time of case report |Incubation period + time from symptom onset to case notification | +|Time of hospitalisation |Incubation period + time from symptom onset to hospitalisation | + +
+ + +:::::::::::::::::::::::::::::::::::::::::::::::: + + + +#### Incubation period distribution + +The distribution of incubation period for many diseases can usually be obtained from the literature. The package `{epiparameter}` contains a library of epidemiological parameters for different diseases obtained from the literature. + +We specify a (fixed) gamma distribution with mean $\mu = 4$ and standard deviation $\sigma= 2$ (shape = $4$, scale = $1$) using the function `dist_spec()` as follows: + + +```r +incubation_period_fixed <- dist_spec( + mean = 4, sd = 2, + max = 20, distribution = "gamma" +) +incubation_period_fixed +``` + +```{.output} + + Fixed distribution with PMF [0.019 0.12 0.21 0.21 0.17 0.11 0.069 0.039 0.021 0.011 0.0054 0.0026 0.0012 0.00058 0.00026 0.00012 5.3e-05 2.3e-05 1e-05 4.3e-06] +``` + +The argument `max` is the maximum value the distribution can take, in this example 20 days. + +::::::::::::::::::::::::::::::::::::: callout +### Why a gamma distrubution? + +The incubation period has to be positive in value. Therefore we must specific a distribution in `dist_spec` which is for positive values only. + +`dist_spec()` supports log normal and gamma distributions, which are distributions for positive values only. + +For all types of delay, we will need to use distributions for positive values only - we don't want to include delays of negative days in our analysis! + +:::::::::::::::::::::::::::::::::::::::::::::::: + + + +#### Including distribution uncertainty + +To specify a **variable** distribution, we include uncertainty around the mean $\mu$ and standard deviation $\sigma$ of our gamma distribution. If our incubation period distribution has a mean $\mu$ and standard deviation $\sigma$, then we assume the mean ($\mu$) follows a Normal distribution with standard deviation $\sigma_{\mu}$: + +$$\mbox{Normal}(\mu,\sigma_{\mu}^2)$$ + +and a standard deviation ($\sigma$) follows a Normal distribution with standard deviation $\sigma_{\sigma}$: + +$$\mbox{Normal}(\sigma,\sigma_{\sigma}^2).$$ + +We specify this using `dist_spec` with the additional arguments `mean_sd` ($\sigma_{\mu}$) and `sd_sd` ($\sigma_{\sigma}$). + + +```r +incubation_period_variable <- dist_spec( + mean = 4, sd = 2, + mean_sd = 0.5, sd_sd = 0.5, + max = 20, distribution = "gamma" +) +incubation_period_variable +``` + +```{.output} + + Uncertain gamma distribution with (untruncated) mean 4 (SD 0.5) and SD 2 (SD 0.5) +``` + + + +#### Reporting delays + +After the incubation period, there will be an additional delay of time from symptom onset to case notification: the reporting delay. We can specify this as a fixed or variable distribution, or estimate a distribution from data. + +When specifying a distribution, it is useful to visualise the probability density to see the peak and spread of the distribution, in this case we will use a log normal distribution. We can use the functions `convert_to_logmean()` and `convert_to_logsd()` to convert the mean and standard deviation of a normal distribution to that of a log normal distribution. + +If we want to assume that the mean reporting delay is 2 days (with a standard deviation of 1 day), the log normal distribution will look like: + + +```r +log_mean <- convert_to_logmean(2, 1) +log_sd <- convert_to_logsd(2, 1) +x <- seq(from = 0, to = 10, length = 1000) +df <- data.frame(x = x, density = dlnorm(x, meanlog = log_mean, sdlog = log_sd)) +ggplot(df) + + geom_line( + aes(x, density) + ) + + theme_grey( + base_size = 15 + ) +``` + + + +Using the mean and standard deviation for the log normal distribution, we can specify a fixed or variable distribution using `dist_spec()` as before: + + +```r +reporting_delay_variable <- dist_spec( + mean = log_mean, sd = log_sd, + mean_sd = 0.5, sd_sd = 0.5, + max = 10, distribution = "lognormal" +) +``` + +If data is available on the time between symptom onset and reporting, we can use the function `estimate_delay()` to estimate a log normal distribution from a vector of delays. The code below illustrates how to use `estimate_delay()` with synthetic delay data. + + +```r +delay_data <- rlnorm(500, log(5), 1) # synthetic delay data +reporting_delay <- estimate_delay( + delay_data, + samples = 1000, + bootstraps = 10 +) +``` + + +#### Generation time + +We also must specify a distribution for the generation time. Here we will use a log normal distribution with mean 3.6 and standard deviation 3.1 ([Ganyani et al. 2020](https://doi.org/10.2807/1560-7917.ES.2020.25.17.2000257)). + + + +```r +generation_time_variable <- dist_spec( + mean = 3.6, sd = 3.1, + mean_sd = 0.5, sd_sd = 0.5, + max = 20, distribution = "lognormal" +) +``` + + +## Finding estimates + +The function `epinow()` is a wrapper for the function `estimate_infections()` used to estimate cases by date of infection. The generation time distribution and delay distributions must be passed using the functions ` generation_time_opts()` and `delay_opts()` respectively. + +There are numerous other inputs that can be passed to `epinow()`, see `EpiNow2::?epinow()` for more detail. +One optional input is to specify a log normal prior for the effective reproduction number $R_t$ at the start of the outbreak. We specify a mean and standard deviation as arguments of `prior` within `rt_opts()`: + + +```r +rt_log_mean <- convert_to_logmean(2, 1) +rt_log_sd <- convert_to_logsd(2, 1) +rt <- rt_opts(prior = list(mean = rt_log_mean, sd = rt_log_sd)) +``` + +::::::::::::::::::::::::::::::::::::: callout +### Bayesian inference using Stan + +The Bayesian inference is performed using MCMC methods with the program [Stan](https://mc-stan.org/). There are a number of default inputs to the Stan functions including the number of chains and number of samples per chain (see `?EpiNow2::stan_opts()`). + +To reduce computation time, we can run chains in parallel. To do this, we must set the number of cores to be used. By default, 4 MCMC chains are run (see `stan_opts()$chains`), so we can set an equal number of cores to be used in parallel as follows: + + +```r +withr::local_options(list(mc.cores = 4)) +``` + +To find the maximum number of available cores on your machine, use `parallel::detectCores()`. + +:::::::::::::::::::::::::::::::::::::::::::::::: + + + +*Note: in the code below fixed distributions are used instead of variable. This is to speed up computation time. It is generally recommended to use variable distributions that account for additional uncertainty.* + +::::::::::::::::::::::::::::::::: spoiler + +### On reducing computation time + +Using an appropriate number of samples and chains is crucial for ensuring convergence and obtaining reliable estimates in Bayesian computations using Stan. Inadequate sampling or insufficient chains may lead to issues such as divergent transitions, impacting the accuracy and stability of the inference process. + +For the purpose of this tutorial, we can add more configuration details to get an useful output in less time. You can specify a fixed number of `samples` and `chains` to the `stan` argument using the `stan_opts()` function: + +The code in the proposed code chunk can take around 10 minutes. We expect this alternative code chunk below using `stan_opts()` to take approximately 3 minutes: + + +```r +estimates <- epinow( + # same code as previous chunk + reported_cases = reported_cases, + generation_time = generation_time_opts(generation_time_fixed), + delays = delay_opts( + incubation_period_fixed + reporting_delay_fixed + ), + rt = rt_opts( + prior = list(mean = rt_log_mean, sd = rt_log_sd) + ), + # [new] set a fixed number of samples and chains + stan = stan_opts(samples = 1000, chains = 3) +) +``` + +::::::::::::::::::::::::::::::::: + + +```r +reported_cases <- cases[1:90, ] + +estimates <- epinow( + reported_cases = reported_cases, + generation_time = generation_time_opts(generation_time_fixed), + delays = delay_opts( + incubation_period_fixed + reporting_delay_fixed + ), + rt = rt_opts( + prior = list(mean = rt_log_mean, sd = rt_log_sd) + ) +) +``` + +```{.output} +WARN [2024-04-02 20:30:27] epinow: There were 5 divergent transitions after warmup. See +https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup +to find out why this is a problem and how to eliminate them. - +WARN [2024-04-02 20:30:27] epinow: Examine the pairs() plot to diagnose sampling problems + - +``` + +### Results + +We can extract and visualise estimates of the effective reproduction number through time: + + +```r +estimates$plots$R +``` + + + +The uncertainty in the estimates increases through time. This is because estimates are informed by data in the past - within the delay periods. This difference in uncertainty is categorised into **Estimate** (green) utilises all data and **Estimate based on partial data** (orange) estimates that are based on less data (because infections that happened at the time are more likely to not have been observed yet) and therefore have increasingly wider intervals towards the date of the last data point. Finally, the **Forecast** (purple) is a projection ahead of time. + +We can also visualise the growth rate estimate through time: + +```r +estimates$plots$growth_rate +``` + + + +To extract a summary of the key transmission metrics at the *latest date* in the data: + + +```r +summary(estimates) +``` + +```{.output} + measure estimate + +1: New confirmed cases by infection date 7146 (4029 -- 12540) +2: Expected change in daily cases Likely decreasing +3: Effective reproduction no. 0.89 (0.57 -- 1.3) +4: Rate of growth -0.015 (-0.064 -- 0.039) +5: Doubling/halving time (days) -46 (18 -- -11) +``` + +As these estimates are based on partial data, they have a wide uncertainty interval. + ++ From the summary of our analysis we see that the expected change in daily cases is Likely decreasing with the estimated new confirmed cases 7146 (4029 -- 12540). + ++ The effective reproduction number $R_t$ estimate (on the last date of the data) is 0.89 (0.57 -- 1.3). + ++ The exponential growth rate of case numbers is -0.015 (-0.064 -- 0.039). + ++ The doubling time (the time taken for case numbers to double) is -46 (18 -- -11). + +::::::::::::::::::::::::::::::::::::: callout +### `Expected change in daily cases` + +A factor describing expected change in daily cases based on the posterior probability that $R_t < 1$. + +
+| Probability ($p$) | Expected change | +| ------------- |-------------| +|$p < 0.05$ |Increasing | +|$0.05 \leq p< 0.4$ |Likely increasing | +|$0.4 \leq p< 0.6$ |Stable | +|$0.6 \leq p < 0.95$ |Likely decreasing | +|$0.95 \leq p \leq 1$ |Decreasing | +
+ +:::::::::::::::::::::::::::::::::::::::::::::::: + + + + +## Quantify geographical heterogeneity + +The outbreak data of the start of the COVID-19 pandemic from the United Kingdom from the R package `{incidence2}` includes the region in which the cases were recorded. To find regional estimates of the effective reproduction number and cases, we must format the data to have three columns: + ++ `date`: the date, ++ `region`: the region, ++ `confirm`: number of confirmed cases for a region on a given date. + + +```r +regional_cases <- + incidence2::covidregionaldataUK[, c("date", "cases_new", "region")] +colnames(regional_cases) <- c("date", "confirm", "region") + +# extract the first 90 dates for all regions +dates <- sort(unique(regional_cases$date))[1:90] +regional_cases <- regional_cases[which(regional_cases$date %in% dates), ] + +head(regional_cases) +``` + +```{.output} + date confirm region +1 2020-01-30 NA East Midlands +2 2020-01-30 NA East of England +3 2020-01-30 2 England +4 2020-01-30 NA London +5 2020-01-30 NA North East +6 2020-01-30 NA North West +``` + +To find regional estimates, we use the same inputs as `epinow()` to the function `regional_epinow()`: + + +```r +estimates_regional <- regional_epinow( + reported_cases = regional_cases, + generation_time = generation_time_opts(generation_time_fixed), + delays = delay_opts( + incubation_period_fixed + reporting_delay_fixed + ), + rt = rt_opts( + prior = list(mean = rt_log_mean, sd = rt_log_sd) + ) +) +``` + +```{.output} +INFO [2024-04-02 20:30:32] Producing following optional outputs: regions, summary, samples, plots, latest +INFO [2024-04-02 20:30:32] Reporting estimates using data up to: 2020-04-28 +INFO [2024-04-02 20:30:32] No target directory specified so returning output +INFO [2024-04-02 20:30:32] Producing estimates for: East Midlands, East of England, England, London, North East, North West, Northern Ireland, Scotland, South East, South West, Wales, West Midlands, Yorkshire and The Humber +INFO [2024-04-02 20:30:32] Regions excluded: none +INFO [2024-04-02 21:17:16] Completed regional estimates +INFO [2024-04-02 21:17:16] Regions with estimates: 13 +INFO [2024-04-02 21:17:16] Regions with runtime errors: 0 +INFO [2024-04-02 21:17:16] Producing summary +INFO [2024-04-02 21:17:16] No summary directory specified so returning summary output +INFO [2024-04-02 21:17:16] No target directory specified so returning timings +``` + +```r +estimates_regional$summary$summarised_results$table +``` + +```{.output} + Region New confirmed cases by infection date + + 1: East Midlands 337 (212 -- 546) + 2: East of England 531 (326 -- 838) + 3: England 3533 (2275 -- 5680) + 4: London 295 (189 -- 455) + 5: North East 249 (145 -- 415) + 6: North West 556 (328 -- 873) + 7: Northern Ireland 43 (22 -- 82) + 8: Scotland 287 (163 -- 533) + 9: South East 598 (361 -- 1025) +10: South West 427 (292 -- 605) +11: Wales 94 (66 -- 136) +12: West Midlands 270 (144 -- 475) +13: Yorkshire and The Humber 482 (296 -- 794) + Expected change in daily cases Effective reproduction no. + + 1: Likely increasing 1.2 (0.85 -- 1.6) + 2: Likely increasing 1.2 (0.82 -- 1.6) + 3: Likely decreasing 0.91 (0.65 -- 1.3) + 4: Likely decreasing 0.79 (0.55 -- 1.1) + 5: Likely decreasing 0.9 (0.61 -- 1.3) + 6: Likely decreasing 0.86 (0.57 -- 1.2) + 7: Likely decreasing 0.64 (0.37 -- 1) + 8: Likely decreasing 0.91 (0.59 -- 1.4) + 9: Stable 0.99 (0.69 -- 1.4) +10: Increasing 1.4 (1.1 -- 1.8) +11: Decreasing 0.56 (0.42 -- 0.75) +12: Likely decreasing 0.7 (0.42 -- 1.1) +13: Stable 1 (0.72 -- 1.4) + Rate of growth Doubling/halving time (days) + + 1: 0.022 (-0.021 -- 0.067) 32 (10 -- -33) + 2: 0.021 (-0.024 -- 0.066) 33 (11 -- -29) + 3: -0.012 (-0.051 -- 0.034) -58 (21 -- -14) + 4: -0.029 (-0.068 -- 0.0099) -24 (70 -- -10) + 5: -0.013 (-0.057 -- 0.035) -53 (20 -- -12) + 6: -0.018 (-0.064 -- 0.024) -38 (29 -- -11) + 7: -0.051 (-0.1 -- 0.005) -13 (140 -- -6.8) + 8: -0.012 (-0.061 -- 0.044) -57 (16 -- -11) + 9: -0.00069 (-0.045 -- 0.052) -1000 (13 -- -15) +10: 0.049 (0.013 -- 0.085) 14 (8.1 -- 54) +11: -0.065 (-0.092 -- -0.035) -11 (-20 -- -7.5) +12: -0.042 (-0.092 -- 0.01) -17 (69 -- -7.6) +13: 0.0034 (-0.04 -- 0.052) 210 (13 -- -17) +``` + +```r +estimates_regional$summary$plots$R +``` + + + + +## Summary + +`EpiNow2` can be used to estimate transmission metrics from case data at any time in the course of an outbreak. The reliability of these estimates depends on the quality of the data and appropriate choice of delay distributions. In the next tutorial we will learn how to make forecasts and investigate some of the additional inference options available in `EpiNow2`. + +::::::::::::::::::::::::::::::::::::: keypoints + +- Transmission metrics can be estimated from case data after accounting for delays +- Uncertainty can be accounted for in delay distributions + +::::::::::::::::::::::::::::::::::::::::::::::::