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mode 100644 links.md create mode 100644 md5sum.txt create mode 100644 network.html create mode 100644 quantify-transmissibility.md create mode 100644 reference.md create mode 100644 renv.lock create mode 100644 setup.md create mode 100644 severity-static.md create mode 100644 superspreading-estimate.md create mode 100644 superspreading-simulate.md create mode 100644 webshot.png diff --git a/CODE_OF_CONDUCT.md b/CODE_OF_CONDUCT.md new file mode 100644 index 00000000..13f72db7 --- /dev/null +++ b/CODE_OF_CONDUCT.md @@ -0,0 +1,15 @@ +--- +title: "Contributor Code of Conduct" +--- + +As contributors and maintainers of this project, +we pledge to follow the [The Epiverse-TRACE Code of Conduct][coc]. + + + +[coc-reporting]: https://forms.gle/guKqVXPk6K43jPn59 +[coc]: https://github.com/epiverse-trace/.github/blob/main/CODE_OF_CONDUCT.md + diff --git a/LICENSE.md b/LICENSE.md new file mode 100644 index 00000000..49a8cbdd --- /dev/null +++ b/LICENSE.md @@ -0,0 +1,74 @@ +--- +title: "Licenses" +--- + +## Instructional Material + +The tutorials in this repository are developed by Epiverse-TRACE, based on the [lesson template from the Carpentries](https://github.com/carpentries/workbench-template-rmd) (template under CC BY license). + +All Epiverse-TRACE +instructional material is made available under the [Creative Commons +Attribution license][cc-by-human]. The following is a human-readable summary of +(and not a substitute for) the [full legal text of the CC BY 4.0 +license][cc-by-legal]. + +You are free: + +- to **Share**---copy and redistribute the material in any medium or format +- to **Adapt**---remix, transform, and build upon the material + +for any purpose, even commercially. + +The licensor cannot revoke these freedoms as long as you follow the license +terms. + +Under the following terms: + +- **Attribution**---You must give appropriate credit (mentioning that your work + is derived from work that is Copyright (c) Epiverse-TRACE, where + practical, linking to ), provide a [link to the + license][cc-by-human], and indicate if changes were made. You may do so in + any reasonable manner, but not in any way that suggests the licensor endorses + you or your use. + +- **No additional restrictions**---You may not apply legal terms or + technological measures that legally restrict others from doing anything the + license permits. With the understanding that: + +Notices: + +* You do not have to comply with the license for elements of the material in + the public domain or where your use is permitted by an applicable exception + or limitation. +* No warranties are given. The license may not give you all of the permissions + necessary for your intended use. For example, other rights such as publicity, + privacy, or moral rights may limit how you use the material. + +## Software + +Except where otherwise noted, the example programs and other software provided +by Epiverse-TRACE are made available under the [OSI][osi]-approved [MIT +license][mit-license]. + +Permission is hereby granted, free of charge, to any person obtaining a copy of +this software and associated documentation files (the "Software"), to deal in +the Software without restriction, including without limitation the rights to +use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies +of the Software, and to permit persons to whom the Software is furnished to do +so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. + +[cc-by-human]: https://creativecommons.org/licenses/by/4.0/ +[cc-by-legal]: https://creativecommons.org/licenses/by/4.0/legalcode +[mit-license]: https://opensource.org/licenses/mit-license.html +[osi]: https://opensource.org diff --git a/config.yaml b/config.yaml new file mode 100644 index 00000000..8d92b971 --- /dev/null +++ b/config.yaml @@ -0,0 +1,86 @@ +#------------------------------------------------------------ +# Values for this lesson. +#------------------------------------------------------------ + +# Which carpentry is this (swc, dc, lc, or cp)? +# swc: Software Carpentry +# dc: Data Carpentry +# lc: Library Carpentry +# cp: Carpentries (to use for instructor training for instance) +# incubator: The Carpentries Incubator +carpentry: 'incubator' + +# Overall title for pages. +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: + +# Comma-separated list of keywords for the lesson +keywords: 'forecasts, epidemic models, interventions' + +# Life cycle stage of the lesson +# possible values: pre-alpha, alpha, beta, stable +life_cycle: 'pre-alpha' + +# License of the lesson materials (recommended CC-BY 4.0) +license: 'CC-BY 4.0' + +# Link to the source repository for this lesson +source: 'https://github.com/epiverse-trace/tutorials-middle' + +# Default branch of your lesson +branch: 'main' + +# Who to contact if there are any issues +contact: 'andree.valle-campos@lshtm.ac.uk' + +# Navigation ------------------------------------------------ +# +# Use the following menu items to specify the order of +# individual pages in each dropdown section. Leave blank to +# include all pages in the folder. +# +# Example ------------- +# +# episodes: +# - introduction.md +# - first-steps.md +# +# learners: +# - setup.md +# +# instructors: +# - instructor-notes.md +# +# profiles: +# - one-learner.md +# - another-learner.md + +# Order of episodes in your lesson +episodes: +- delays-access.Rmd +- quantify-transmissibility.Rmd +- delays-functions.Rmd +- create-forecast.Rmd +- severity-static.Rmd +- superspreading-estimate.Rmd +- superspreading-simulate.Rmd + +# Information for Learners +learners: + +# Information for Instructors +instructors: + +# Learner 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 +sandpaper: epiverse-trace/sandpaper@patch-renv-github-bug diff --git a/create-forecast.md b/create-forecast.md new file mode 100644 index 00000000..f8db5ffa --- /dev/null +++ b/create-forecast.md @@ -0,0 +1,639 @@ +--- +title: 'Create a short-term forecast' +teaching: 30 +exercises: 30 +editor_options: + chunk_output_type: inline +--- + + + + +:::::::::::::::::::::::::::::::::::::: questions + +- How do I create short-term forecasts from case data? +- How do I account for incomplete reporting in forecasts? + + +:::::::::::::::::::::::::::::::::::::::::::::::: + +::::::::::::::::::::::::::::::::::::: objectives + +- Learn how to make forecasts of cases using R package `EpiNow2` +- Learn how to include an observation process in estimation + +:::::::::::::::::::::::::::::::::::::::::::::::: + +::::::::::::::::::::::::::::::::::::: prereq + +## Prerequisites + ++ Complete tutorial [Quantifying transmission](../episodes/quantify-transmissibility.md) + +Learners should familiarise themselves with following concept dependencies before working through this tutorial: + +**Statistics** : probability distributions, principle of Bayesian analysis. + +**Epidemic theory** : Effective reproduction number. + +::::::::::::::::::::::::::::::::: + +## Introduction + +Given case data of an epidemic, we can create estimates of the current and future number of cases by accounting for both delays +in reporting and under reporting. To make statements about the future of th epidemic, we need to make an assumption of how +observations up to the present are related to what we expect to happen in the future. The simplest way of doing so is to assume "no change", i.e., the reproduction number remains the same in the future as last observed. In this tutorial we will create short-term [forecasts](../learners/reference.md#forecast) by assuming the reproduction number will remain the same as its estimate was on the final date for which data was available. + +In this tutorial we are going to learn how to use the `{EpiNow2}` package to forecast cases accounting for incomplete observations and forecast secondary observations like deaths. + +We’ll use the pipe `%>%` operator to connect functions, so let’s also call to the `{tidyverse}` package: + +```r +library(EpiNow2) +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. + +::::::::::::::::::: + +## Create a short-term forecast + +The function `epinow()` described in the [quantifying transmission](../episodes/quantify-transmissibility.md) episode is a wrapper for the functions: + +- `estimate_infections()` used to estimate cases by date of infection. +- `forecast_infections()` used to simulate infections using an existing fit (estimate) to observed cases. + +Let's use the same code used in [quantifying transmission](../episodes/quantify-transmissibility.md) episode to get the input data, delays and priors: + + +``` r +# Read cases dataset +cases <- incidence2::covidregionaldataUK %>% + # use {tidyr} to preprocess missing values + tidyr::replace_na(base::list(cases_new = 0)) %>% + # use {incidence2} to compute the daily incidence + incidence2::incidence( + date_index = "date", + counts = "cases_new", + count_values_to = "confirm", + date_names_to = "date", + complete_dates = TRUE + ) %>% + dplyr::select(-count_variable) + +# Incubation period +incubation_period_fixed <- EpiNow2::Gamma( + mean = 4, + sd = 2, + max = 20 +) + +# Log-tranformed mean +log_mean <- EpiNow2::convert_to_logmean(mean = 2, sd = 1) + +# Log-transformed std +log_sd <- EpiNow2::convert_to_logsd(mean = 2, sd = 1) + +# Reporting dalay +reporting_delay_fixed <- EpiNow2::LogNormal( + mean = log_mean, + sd = log_sd, + max = 10 +) + +# Generation time +generation_time_fixed <- EpiNow2::LogNormal( + mean = 3.6, + sd = 3.1, + max = 20 +) + +# define Rt prior distribution +rt_prior <- EpiNow2::rt_opts(prior = base::list(mean = 2, sd = 2)) +``` + +Now we can extract the short-term forecast using: + + +``` r +# Assume we only have the first 90 days of this data +reported_cases <- cases %>% + dplyr::slice(1:90) + +# Estimate and forecast +estimates <- EpiNow2::epinow( + data = reported_cases, + generation_time = EpiNow2::generation_time_opts(generation_time_fixed), + delays = EpiNow2::delay_opts(incubation_period_fixed + reporting_delay_fixed), + rt = rt_prior +) +``` + +``` output +WARN [2024-09-24 03:12:10] epinow: There were 3 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 [2024-09-24 03:12:10] epinow: Examine the pairs() plot to diagnose sampling problems + - +``` + +::::::::::::::::::::::::::::::::: callout + +### Do not wait for this to complete! + +This last chunk may take 10 minutes to run. Keep reading this tutorial episode while this runs in the background. For more information on computing time, read the "Bayesian inference using Stan" section within the [quantifying transmission](../episodes/quantify-transmissibility.md) episode. + +::::::::::::::::::::::::::::::::: + +We can visualise the estimates of the effective reproduction number and the estimated number of cases using `plot()`. The estimates are split into three categories: + ++ **Estimate** (green): utilises all data, + ++ **Estimate based on partial data** (orange): contains a higher degree of uncertainty because such estimates are based on less data, + ++ **Forecast** (purple): forecasts into the future. + + + +``` r +plot(estimates) +``` + + + +### Forecasting with incomplete observations + +In the [quantifying transmission](../episodes/quantify-transmissibility.md) episode we accounted for delays in reporting.In `EpiNow2` we also can account for incomplete observations as in reality, 100% of cases are not reported. +We will pass another argument into `epinow()` function called `obs` to define an observation model. The format of `obs` is defined by the `obs_opt()` function (see `?EpiNow2::obs_opts` for more detail). + +Let's say we believe the COVID-19 outbreak data in the `cases` object do not include all reported cases. We believe that we only observe 40% of cases. To specify this in the observation model, we must pass a scaling factor with a mean and standard deviation. If we assume that 40% of cases are in the case data (with standard deviation 1%), then we specify the `scale` input to `obs_opts()` as follows: + + +``` r +obs_scale <- base::list(mean = 0.4, sd = 0.01) +``` + +To run the inference framework with this observation process, we add `obs = obs_opts(scale = obs_scale)` to the input arguments of `epinow()`: + + +``` r +# Define observation model +obs_scale <- base::list(mean = 0.4, sd = 0.01) + +# Assume we only have the first 90 days of this data +reported_cases <- cases %>% + dplyr::slice(1:90) + +# Estimate and forecast +estimates <- EpiNow2::epinow( + data = reported_cases, + generation_time = EpiNow2::generation_time_opts(generation_time_fixed), + delays = EpiNow2::delay_opts(incubation_period_fixed + reporting_delay_fixed), + rt = rt_prior, + # Add observation model + obs = EpiNow2::obs_opts(scale = obs_scale) +) +``` + +``` output +WARN [2024-09-24 03:23:02] epinow: There were 1 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 [2024-09-24 03:23:02] epinow: Examine the pairs() plot to diagnose sampling problems + - +WARN [2024-09-24 03:23:04] 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::summary(estimates) +``` + +``` output + measure estimate + +1: New infections per day 17183 (9490 -- 30145) +2: Expected change in daily reports Likely decreasing +3: Effective reproduction no. 0.88 (0.6 -- 1.2) +4: Rate of growth -0.042 (-0.18 -- 0.091) +5: Doubling/halving time (days) -16 (7.6 -- -3.9) +``` + + +The estimates of transmission measures such as the effective reproduction number and rate of growth are similar (or the same in value) compared to when we didn't account for incomplete observations (see [quantifying transmission episode](../episodes/quantify-transmissibility.md) in the "Finding estimates" section). However the number of new confirmed cases by infection date has changed substantially in magnitude to reflect the assumption that only 40% of cases are in the data set. + +We can also change the default distribution from Negative Binomial to Poisson, remove the default week effect and more. See `?EpiNow2::obs_opts` for more details. + +::::::::::::::::::::::::::: discussion + +### What are the implications of this change? + +- Compare different percents of observations % +- How are they different in the number of infections estimated? +- What are the public health implications of this change? + +::::::::::::::::::::::::::: + +## Forecasting secondary observations + +`EpiNow2` also has the ability to estimate and forecast secondary observations, e.g., deaths and hospitalisations, from a primary observation, e.g., cases. Here we will illustrate how to forecast the number of deaths arising from observed cases of COVID-19 in the early stages of the UK outbreak. + +First, we must format our data to have the following columns: + ++ `date`: the date (as a date object see `?is.Date()`), ++ `primary`: number of primary observations on that date, in this example **cases**, ++ `secondary`: number of secondary observations date, in this example **deaths**. + + +``` r +reported_cases_deaths <- incidence2::covidregionaldataUK %>% + # use {tidyr} to preprocess missing values + tidyr::replace_na(base::list(cases_new = 0, deaths_new = 0)) %>% + # use {incidence2} to compute the daily incidence + incidence2::incidence( + date_index = "date", + counts = c(primary = "cases_new", secondary = "deaths_new"), + date_names_to = "date", + complete_dates = TRUE + ) %>% + # rearrange to wide format for {EpiNow2} + pivot_wider(names_from = count_variable, values_from = count) +``` + +
+Distribution of secondary cases (deaths). We will drop the first 30 days with no observed deaths. We will use the deaths between day 31 and day 60 to estimate the secondary observations. We will forecast deaths from day 61 to day 90. +

Distribution of secondary cases (deaths). We will drop the first 30 days with no observed deaths. We will use the deaths between day 31 and day 60 to estimate the secondary observations. We will forecast deaths from day 61 to day 90.

+
+ +Using the data on cases and deaths between day 31 and day 60, we will estimate the relationship between the primary and secondary observations using `estimate_secondary()`, then forecast future deaths using `forecast_secondary()`. For more details on the model see the [model documentation](https://epiforecasts.io/EpiNow2/dev/articles/estimate_secondary.html). + +We must specify the type of observation using `type` in `secondary_opts()`, options include: + ++ "incidence": secondary observations arise from previous primary observations, i.e., deaths arising from recorded cases. ++ "prevalence": secondary observations arise from a combination current primary observations and past secondary observations, i.e., hospital bed usage arising from current hospital admissions and past hospital bed usage. + +In this example we specify `secondary_opts(type = "incidence")`. See `?EpiNow2::secondary_opts` for more detail. + +The final key input is the delay distribution between the primary and secondary observations. Here this is the delay between case report and death, we assume this follows a gamma distribution with mean of 14 days and standard deviation of 5 days (Alternatively, we can use `{epiparameter}` to [access epidemiological delays](https://epiverse-trace.github.io/tutorials-early/delays-reuse.html)). Using `Gamma()` we specify a fixed gamma distribution. + +There are further function inputs to `estimate_secondary()` which can be specified, including adding an observation process, see `?EpiNow2::estimate_secondary` for detail on these options. + +To find the model fit between cases and deaths: + +``` r +# Estimate from day 31 to day 60 of this data +cases_to_estimate <- reported_cases_deaths %>% + slice(31:60) + +# Delay distribution between case report and deaths +delay_report_to_death <- EpiNow2::Gamma( + mean = EpiNow2::Normal(mean = 14, sd = 0.5), + sd = EpiNow2::Normal(mean = 5, sd = 0.5), + max = 30 +) + +# Estimate secondary cases +estimate_cases_to_deaths <- EpiNow2::estimate_secondary( + data = cases_to_estimate, + secondary = EpiNow2::secondary_opts(type = "incidence"), + delays = EpiNow2::delay_opts(delay_report_to_death) +) +``` + +``` output +WARN [2024-09-24 03:23:10] estimate_secondary (chain: 1): 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 - +``` + + +::::::::::::::::::::::::::::::::::::: callout + +### Be cautious of time-scale + +In the early stages of an outbreak there can be substantial changes in testing and reporting. If there are testing changes from one month to another, then there will be a bias in the model fit. Therefore, you should be cautious of the time-scale of data used in the model fit and forecast. + +:::::::::::::::::::::::::::::::::::::::::::::::: + +We plot the model fit (shaded ribbons) with the secondary observations (bar plot) and primary observations (dotted line) as follows: + + +``` r +plot(estimate_cases_to_deaths, primary = TRUE) +``` + + + +To use this model fit to forecast deaths, we pass a data frame consisting of the primary observation (cases) for dates not used in the model fit. + +*Note : in this episode we are using data where we know the deaths and cases, so we create a data frame by extracting the cases. But in practice, this would be a different data set consisting of cases only.* + +``` r +# Forecast from day 61 to day 90 +cases_to_forecast <- reported_cases_deaths %>% + dplyr::slice(61:90) %>% + dplyr::mutate(value = primary) +``` + +To forecast, we use the model fit `estimate_cases_to_deaths`: + + +``` r +# Forecast secondary cases +deaths_forecast <- EpiNow2::forecast_secondary( + estimate = estimate_cases_to_deaths, + primary = cases_to_forecast +) + +plot(deaths_forecast) +``` + + + +:::::::::::::::: spoiler + +### make a forecast plot + + +``` r +deaths_forecast %>% + purrr::pluck("predictions") %>% + ggplot(aes(x = date, y = secondary)) + + geom_col( + fill = "grey", col = "white", + show.legend = FALSE, na.rm = TRUE + ) + + geom_ribbon(aes(ymin = lower_90, ymax = upper_90), + alpha = 0.2, linewidth = 1) + + geom_ribbon(aes(ymin = lower_50, ymax = upper_50), + alpha = 0.4, linewidth = 1) + + geom_ribbon(aes(ymin = lower_20, ymax = upper_20), + alpha = 0.6, linewidth = 1) + + theme_bw() + + labs(y = "Reports per day", x = "Date") + + scale_x_date(date_breaks = "week", date_labels = "%b %d") + + scale_y_continuous(labels = scales::comma) + + theme(axis.text.x = ggplot2::element_text(angle = 90)) +``` + + + + +:::::::::::::::: + +The plot shows the forecast secondary observations (deaths) over the dates which we have recorded cases for. +It is also possible to forecast deaths using forecast cases, here you would specify `primary` as the `estimates` output from `estimate_infections()`. + + +:::::::::::::::::::::::::: callout + +### Credible intervals + +In all `{EpiNow2}` output figures, shaded regions reflect 90%, 50%, and 20% credible intervals in order from lightest to darkest. + +:::::::::::::::::::::::::: + +## Challenge: Ebola outbreak analysis + +::::::::::::::::::::::::::::::::::::: challenge + +Download the file [ebola_cases.csv](data/ebola_cases.csv) and read it into R. The simulated data consists of the date of symptom onset and number of confirmed cases of the early stages of the Ebola outbreak in Sierra Leone in 2014. + +Using the first 3 months (120 days) of data: + +1. Estimate whether cases are increasing or decreasing on day 120 of the outbreak +2. Account for a capacity to observe 80% of cases. +2. Create a two week forecast of number of cases. + +You can use the following parameter values for the delay distribution(s) and generation time distribution. + ++ Incubation period: Log normal$(2.487,0.330)$ ([Eichner et al. 2011](https://doi.org/10.1016/j.phrp.2011.04.001) via `{epiparameter}`) ++ Generation time: Gamma$(15.3, 10.1)$ ([WHO Ebola Response Team 2014](https://www.nejm.org/doi/full/10.1056/NEJMoa1411100)) + +You may include some uncertainty around the mean and standard deviation of these distributions. + +::::::::::::::::: hint + +We use the effective reproduction number and growth rate to estimate whether cases are increasing or decreasing. + +We can use the `horizon` argument within the `epinow()` function to extend the time period of the forecast. The default value is of seven days. + +Ensure the data is in the correct format : + ++ `date`: the date (as a date object see `?is.Date()`), ++ `confirm`: number of confirmed cases on that date. + +:::::::::::::::::::::: + + +::::::::::::::::: solution + +### SOLUTION + +To estimate the effective reproduction number and growth rate, we will use the function `epinow()`. + +As the data consists of date of symptom onset, we only need to specify a delay distribution for the incubation period and the generation time. + +We specify the distributions with some uncertainty around the mean and standard deviation of the log normal distribution for the incubation period and the Gamma distribution for the generation time. + + +``` r +epiparameter::epidist_db(disease = "ebola", epi_dist = "incubation") %>% + epiparameter::parameter_tbl() +``` + +``` output +# Parameter table: +# A data frame: 5 × 7 + disease pathogen epi_distribution prob_distribution author year sample_size + +1 Ebola Vi… Ebola V… incubation peri… lnorm Eichn… 2011 196 +2 Ebola Vi… Ebola V… incubation peri… gamma WHO E… 2015 1798 +3 Ebola Vi… Ebola V… incubation peri… gamma WHO E… 2015 49 +4 Ebola Vi… Ebola V… incubation peri… gamma WHO E… 2015 957 +5 Ebola Vi… Ebola V… incubation peri… gamma WHO E… 2015 792 +``` + +``` r +ebola_eichner <- epiparameter::epidist_db( + disease = "ebola", + epi_dist = "incubation", + author = "Eichner" +) + +ebola_eichner_parameters <- epiparameter::get_parameters(ebola_eichner) + +ebola_incubation_period <- EpiNow2::LogNormal( + meanlog = EpiNow2::Normal( + mean = ebola_eichner_parameters["meanlog"], + sd = 0.5 + ), + sdlog = EpiNow2::Normal( + mean = ebola_eichner_parameters["sdlog"], + sd = 0.5 + ), + max = 20 +) + +ebola_generation_time <- EpiNow2::Gamma( + mean = EpiNow2::Normal(mean = 15.3, sd = 0.5), + sd = EpiNow2::Normal(mean = 10.1, sd = 0.5), + max = 30 +) +``` + +We read the data input using `readr::read_csv()`. This function recognize that the column `date` is a `` class vector. + + + + +``` r +# read data +# e.g.: if path to file is data/raw-data/ebola_cases.csv then: +ebola_cases_raw <- readr::read_csv( + here::here("data", "raw-data", "ebola_cases.csv") +) +``` + +Preprocess and adapt the raw data for `{EpiNow2}`: + + +``` r +ebola_cases <- ebola_cases_raw %>% + # use {tidyr} to preprocess missing values + tidyr::replace_na(base::list(confirm = 0)) %>% + # use {incidence2} to compute the daily incidence + incidence2::incidence( + date_index = "date", + counts = "confirm", + count_values_to = "confirm", + date_names_to = "date", + complete_dates = TRUE + ) %>% + dplyr::select(-count_variable) + +dplyr::as_tibble(ebola_cases) +``` + +``` output +# A tibble: 123 × 2 + date confirm + + 1 2014-05-18 1 + 2 2014-05-19 0 + 3 2014-05-20 2 + 4 2014-05-21 4 + 5 2014-05-22 6 + 6 2014-05-23 1 + 7 2014-05-24 2 + 8 2014-05-25 0 + 9 2014-05-26 10 +10 2014-05-27 8 +# ℹ 113 more rows +``` + + +We define an observation model to scale the estimated and forecast number of new infections: + + +``` r +# Define observation model +# mean of 80% and standard deviation of 1% +ebola_obs_scale <- base::list(mean = 0.8, sd = 0.01) +``` + +As we want to also create a two week forecast, we specify `horizon = 14` to forecast 14 days instead of the default 7 days. + + +``` r +ebola_estimates <- EpiNow2::epinow( + data = ebola_cases %>% dplyr::slice(1:120), # first 3 months of data only + generation_time = EpiNow2::generation_time_opts(ebola_generation_time), + delays = EpiNow2::delay_opts(ebola_incubation_period), + # Add observation model + obs = EpiNow2::obs_opts(scale = ebola_obs_scale), + # horizon needs to be 14 days to create two week forecast (default is 7 days) + horizon = 14 +) +``` + +``` output +WARN [2024-09-24 03:25:19] epinow: There were 3 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 [2024-09-24 03:25:19] epinow: Examine the pairs() plot to diagnose sampling problems + - +``` + +``` r +summary(ebola_estimates) +``` + +``` output + measure estimate + +1: New infections per day 83 (34 -- 206) +2: Expected change in daily reports Likely increasing +3: Effective reproduction no. 1.5 (0.82 -- 2.6) +4: Rate of growth 0.033 (-0.033 -- 0.1) +5: Doubling/halving time (days) 21 (6.7 -- -21) +``` + +The effective reproduction number $R_t$ estimate (on the last date of the data) is 1.5 (0.82 -- 2.6). The exponential growth rate of case numbers is 0.033 (-0.033 -- 0.1). + +Visualize the estimates: + + +``` r +plot(ebola_estimates) +``` + +::::::::::::::::::::::::::: + + +:::::::::::::::::::::::::::::::::::::::::::::::: + + +::::::::::::::::::::::::::::::::::::: callout + +### Forecasting with estimates of $R_t$ + +By default, the short-term forecasts are created using the latest estimate of the reproduction number $R_t$. As this estimate is based on partial data, it has considerable uncertainty. + +The reproduction number that is projected into the future can be changed to a less recent estimate based on more data using `rt_opts()`: + + +``` r +EpiNow2::rt_opts(future = "estimate") +``` + +The result will be less uncertain forecasts (as they are based on $R_t$ with a narrower uncertainty interval) but the forecasts will be based on less recent estimates of $R_t$ and assume no change since then. + +Additionally, there is the option to [project](../learners/reference.md#projection) the value of $R_t$ into the future using a generic model by setting `future = "project"`. As this option uses a model to forecast the value of $R_t$, the result will be forecasts that are more uncertain than `estimate`, for an example [see here](https://epiforecasts.io/EpiNow2/dev/articles/estimate_infections_options.html#projecting-the-reproduction-number-with-the-gaussian-process). + +:::::::::::::::::::::::::::::::::::::::::::::::: + +## Summary + +`EpiNow2` can be used to create short term forecasts and to estimate the relationship between different outcomes. There are a range of model options that can be implemented for different analysis, including adding an observational process to account for incomplete reporting. See the [vignette](https://epiforecasts.io/EpiNow2/dev/articles/estimate_infections_options.html) for more details on different model options in `EpiNow2` that aren't covered in these tutorials. + + +::::::::::::::::::::::::::::::::::::: keypoints + +- We can create short-term forecasts by making assumptions about the future behaviour of the reproduction number +- Incomplete case reporting can be accounted for in estimates + + +:::::::::::::::::::::::::::::::::::::::::::::::: diff --git a/data-severity-static.R b/data-severity-static.R new file mode 100644 index 00000000..cb2025bd --- /dev/null +++ b/data-severity-static.R @@ -0,0 +1,55 @@ +library(cfr) +library(epiparameter) +library(incidence2) +library(outbreaks) +library(tidyverse) + +sarscov2_incidence <- sarscov2_who_2019 %>% + incidence( + date_index = "date", + counts = c( + "cases_jpn", + "deaths_jpn" + ) + ) %>% + complete_dates() + +sarscov2_incidence + +sarscov2_incidence %>% + prepare_data( + cases_variable = "cases_jpn", 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z>aP3#dygv0*&IY9IYztWc|-Q$f}Ypz?SXujqJwE{g*?hBq2_2VJXo{1y@MbHZ`yck48LHanGC#~s{ugQ@-=qBFA zJ9rlxcn|O61AK^&@G&;=2|mSV_#9v0OMHc|@eRJkaeRmG@dJLu2~=h9L6h_(Jw;E^ z)ATewL(kB&^ejC`&(ZVrJiS0K(2MjUy+kk3%k(n6La)%P^eVkZuhHxDI^CjM@%WcFlJ92(~0PS zG23xW9nk?}w(FR>4O-a6fR`BYceZp)WrG%WG2kUe*Q{QoVaVz>njHRKe*1EshX22t z>S6J + +To exemplify how to use the `{epiparameter}` R package in your analysis pipeline, our goal in this episode will be to access one specific set of epidemiological parameters from the literature, instead of copying-and-pasting them by hand, to plug them into an `{EpiNow2}` analysis workflow. + + + +Let's start loading the `{epiparameter}` package. We'll use the pipe `%>%` to connect some of their functions, some `{tibble}` and `{dplyr}` functions, so let's also call to the `{tidyverse}` package: + + +``` r +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. + +::::::::::::::::::: + + +## The problem + +If we want to estimate the transmissibility of an infection, it's common to use a package such as `{EpiEstim}` or `{EpiNow2}`. However, both require some epidemiological information as an input. For example, in `{EpiNow2}` we use `EpiNow2::Gamma()` to specify a [generation time](../learners/reference.md#generationtime) as a probability distribution adding its `mean`, standard deviation (`sd`), and maximum value (`max`). + +To specify a `generation_time` that follows a _Gamma_ distribution with mean $\mu = 4$, standard deviation $\sigma = 2$, and a maximum value of 20, we write: + +```r +generation_time <- + EpiNow2::Gamma( + mean = 4, + sd = 2, + max = 20 + ) +``` + +It is a common practice for analysts to manually search the available literature and copy and paste the **summary statistics** or the **distribution parameters** from scientific publications. A challenge that is often faced is that the reporting of different statistical distributions is not consistent across the literature. `{epiparameter}`’s objective is to facilitate the access to reliable estimates of distribution parameters for a range of infectious diseases, so that they can easily be implemented in outbreak analytic pipelines. + +In this episode, we will *access* the summary statistics of generation time for COVID-19 from the library of epidemiological parameters provided by `{epiparameter}`. These metrics can be used to estimate the transmissibility of this disease using `{EpiNow2}` in subsequent episodes. + +Let's start by looking at how many entries are available in the **epidemiological distributions database** in `{epiparameter}` using `epidist_db()` for the epidemiological distribution `epi_dist` called generation time with the string `"generation"`: + + +``` r +epiparameter::epidist_db( + epi_dist = "generation" +) +``` + +``` output +Returning 1 results that match the criteria (1 are parameterised). +Use subset to filter by entry variables or single_epidist to return a single entry. +To retrieve the citation for each use the 'get_citation' function +``` + +``` 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 +``` + +Currently, in the library of epidemiological parameters, we have one `"generation"` time entry for Influenza. Instead, we can look at the `serial` intervals for `COVID`-19. Let find what we need to consider for this! + +## Generation time vs serial interval + +The generation time, jointly with the reproduction number ($R$), provide valuable insights on the strength of transmission and inform the implementation of control measures. Given a $R>1$, the shorter the generation time, the earlier the incidence of disease cases will grow. + +![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 for diseases with pre-symptomatic transmission ([Nishiura et al., 2020](https://www.ijidonline.com/article/S1201-9712(20)30119-3/fulltext#gr2)). + + + +::::::::::::::::: callout + +### From time periods to probability distributions. + +When we calculate the *serial interval*, we see that not all case pairs have the same time length. We will observe this variability for any case pair and individual time period, including the [incubation period](../learners/reference.md#incubation) and [infectious period](../learners/reference.md#infectiousness). + +![Serial intervals of possible case pairs in (a) COVID-19 and (b) MERS-CoV. Pairs represent a presumed infector and their presumed infectee plotted by date of symptom onset ([Althobaity et al., 2022](https://www.sciencedirect.com/science/article/pii/S2468042722000537#fig6)).](fig/serial-interval-pairs.jpg) + +To summarise these data from individual and pair time periods, we can find the **statistical distributions** that best fit the data ([McFarland et al., 2023](https://www.eurosurveillance.org/content/10.2807/1560-7917.ES.2023.28.27.2200806)). + + + +![Fitted serial interval distribution for (a) COVID-19 and (b) MERS-CoV based on reported transmission pairs in Saudi Arabia. We fitted three commonly used distributions, Log normal, Gamma, and Weibull distributions, respectively ([Althobaity et al., 2022](https://www.sciencedirect.com/science/article/pii/S2468042722000537#fig5)).](fig/seria-interval-fitted-distributions.jpg) + +Statistical distributions are summarised in terms of their **summary statistics** like the *location* (mean and percentiles) and *spread* (variance or standard deviation) of the distribution, or with their **distribution parameters** that inform about the *form* (shape and rate/scale) of the distribution. These estimated values can be reported with their **uncertainty** (95% confidence intervals). + +| Gamma | mean | shape | rate/scale | +|:--------------|:--------------|:--------------|:--------------| +| MERS-CoV | 14.13(13.9–14.7) | 6.31(4.88–8.52) | 0.43(0.33–0.60) | +| COVID-19 | 5.1(5.0–5.5) | 2.77(2.09–3.88) | 0.53(0.38–0.76) | + +| Weibull | mean | shape | rate/scale | +|:--------------|:--------------|:--------------|:--------------| +| MERS-CoV | 14.2(13.3–15.2) | 3.07(2.64–3.63) | 16.1(15.0–17.1) | +| COVID-19 | 5.2(4.6–5.9) | 1.74(1.46–2.11) | 5.83(5.08–6.67) | + +| Log normal | mean | mean-log | sd-log | +|:--------------|:--------------|:--------------|:--------------| +| MERS-CoV | 14.08(13.1–15.2) | 2.58(2.50–2.68) | 0.44(0.39–0.5) | +| COVID-19 | 5.2(4.2–6.5) | 1.45(1.31–1.61) | 0.63(0.54–0.74) | + +Table: Serial interval estimates using Gamma, Weibull, and Log Normal distributions. 95% confidence intervals for the shape and scale (logmean and sd for Log Normal) parameters are shown in brackets ([Althobaity et al., 2022](https://www.sciencedirect.com/science/article/pii/S2468042722000537#tbl3)). + +::::::::::::::::::::::::: + +::::::::::::::::::::::::::::::::: challenge + +### Serial interval + +Assume that COVID-19 and SARS have similar reproduction number values and that the serial interval approximates the generation time. + +Given the serial interval of both infections in the figure below: + +- Which one would be harder to control? +- Why do you conclude that? + +![Serial interval of novel coronavirus (COVID-19) infections overlaid with a published distribution of SARS. ([Nishiura et al., 2020](https://www.ijidonline.com/article/S1201-9712(20)30119-3/fulltext))](fig/serial-interval-covid-sars.jpg) + +::::::::::::::::: hint + +The peak of each curve can inform you about the location of the mean of each distribution. The larger the mean, the larger the serial interval. + +:::::::::::::::::::::: + +::::::::::::::::: solution + +**Which one would be harder to control?** + +COVID-19 + +**Why do you conclude that?** + +COVID-19 has the lowest mean serial interval. The approximate mean value for the serial interval of COVID-19 is around four days, and SARS is about seven days. Thus, COVID-19 will likely have newer generations in less time than SARS, assuming similar reproduction numbers. + +:::::::::::::::::::::::::: + +::::::::::::::::::::::::::::::::::::::::::: + +:::::::::::::::::::::: instructor + +The objective of the assessment above is to assess the interpretation of a larger or shorter generation time. + +:::::::::::::::::::::: + +## Choosing epidemiological parameters + +In this section, we will use `{epiparameter}` to obtain the serial interval for COVID-19, as an alternative to the generation time. + +Let's ask now how many parameters we have in the epidemiological distributions database (`epidist_db()`) with the `disease` named `covid`-19. Run this locally! + + +``` r +epiparameter::epidist_db( + disease = "covid" +) +``` + +From the `{epiparameter}` package, we can use the `epidist_db()` function to ask for any `disease` and also for a specific epidemiological distribution (`epi_dist`). Run this in your console: + + +``` r +epiparameter::epidist_db( + disease = "COVID", + epi_dist = "serial" +) +``` + +With this query combination, we get more than one delay distribution. This output is an `` class object. + +::::::::::::::::: callout + +### CASE-INSENSITIVE + +`epidist_db` is [case-insensitive](https://dillionmegida.com/p/case-sensitivity-vs-case-insensitivity/#case-insensitivity). This means that you can use strings with letters in upper or lower case indistinctly. Strings like `"serial"`, `"serial interval"` or `"serial_interval"` are also valid. + +::::::::::::::::::::::::: + +As suggested in the outputs, to summarise an `` object and get the column names from the underlying parameter database, we can add the `epiparameter::parameter_tbl()` function to the previous code using the pipe `%>%`: + + +``` r +epiparameter::epidist_db( + disease = "covid", + epi_dist = "serial" +) %>% + epiparameter::parameter_tbl() +``` + +``` output +Returning 4 results that match the criteria (3 are parameterised). +Use subset to filter by entry variables or single_epidist to return a single entry. +To retrieve the citation for each use the 'get_citation' function +``` + +``` output +# Parameter table: +# A data frame: 4 × 7 + disease pathogen epi_distribution prob_distribution author year sample_size + +1 COVID-19 SARS-CoV… serial interval Alene… 2021 3924 +2 COVID-19 SARS-CoV… serial interval lnorm Nishi… 2020 28 +3 COVID-19 SARS-CoV… serial interval weibull Nishi… 2020 18 +4 COVID-19 SARS-CoV… serial interval norm Yang … 2020 131 +``` + +In the `epiparameter::parameter_tbl()` output, we can also find different types of probability distributions (e.g., Log-normal, Weibull, Normal). + +`{epiparameter}` uses the `base` R naming convention for distributions. This is why **Log normal** is called `lnorm`. + +::::::::::::::::: spoiler + +### Why do we have an 'NA' 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: + + +``` r +# get an object +distribution <- + epiparameter::epidist_db( + disease = "covid", + epi_dist = "serial" + ) + +distribution %>% + # pluck the first entry in the object class + pluck(1) %>% + # check if object have distribution parameters + is_parameterised() + +# check if the second object +# have distribution parameters +distribution %>% + pluck(2) %>% + is_parameterised() +``` + +### Parameterised entries have an Inference method + +As detailed in `?is_parameterised`, a parameterised distribution is the entry that has a probability distribution associated with it provided by an `inference_method` as shown in `metadata`: + + +``` r +distribution[[1]]$metadata$inference_method +distribution[[2]]$metadata$inference_method +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.). + +Find: + +- How many delay distributions are for that disease? + +- How many types of probability distribution (e.g., gamma, log normal) are for a given delay in that disease? + +Ask: + +- Do you recognise the papers? + +- Should `{epiparameter}` literature review consider any other paper? + +::::::::::::::::: hint + +The `epidist_db()` function with `disease` alone counts 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: + +- the complete citation, +- the **type** of a probability distribution, and +- distribution parameter values. + +The combo of `epidist_db()` plus `parameter_tbl()` gets a data frame of all entries with columns like: + +- 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 +epiparameter::epidist_db( + disease = "ebola" +) +``` + +``` output +Returning 17 results that match the criteria (17 are parameterised). +Use subset to filter by entry variables or single_epidist to return a single entry. +To retrieve the citation for each use the 'get_citation' function +``` + +``` output +# List of 17 objects +Number of diseases: 1 +❯ Ebola Virus Disease +Number of epi distributions: 9 +❯ hospitalisation to death ❯ hospitalisation to discharge ❯ incubation period ❯ notification to death ❯ notification to discharge ❯ offspring distribution ❯ onset to death ❯ onset to discharge ❯ serial interval +[[1]] +Disease: Ebola Virus Disease +Pathogen: Ebola Virus +Epi Distribution: offspring distribution +Study: Lloyd-Smith J, Schreiber S, Kopp P, Getz W (2005). "Superspreading and +the effect of individual variation on disease emergence." _Nature_. +doi:10.1038/nature04153 . +Distribution: nbinom +Parameters: + mean: 1.500 + dispersion: 5.100 + +[[2]] +Disease: Ebola Virus Disease +Pathogen: Ebola Virus-Zaire Subtype +Epi Distribution: incubation period +Study: Eichner M, Dowell S, Firese N (2011). "Incubation period of ebola +hemorrhagic virus subtype zaire." _Osong Public Health and Research +Perspectives_. doi:10.1016/j.phrp.2011.04.001 +. +Distribution: lnorm +Parameters: + meanlog: 2.487 + sdlog: 0.330 + +[[3]] +Disease: Ebola Virus Disease +Pathogen: Ebola Virus-Zaire Subtype +Epi Distribution: onset to death +Study: The Ebola Outbreak Epidemiology Team, Barry A, Ahuka-Mundeke S, Ali +Ahmed Y, Allarangar Y, Anoko J, Archer B, Abedi A, Bagaria J, Belizaire +M, Bhatia S, Bokenge T, Bruni E, Cori A, Dabire E, Diallo A, Diallo B, +Donnelly C, Dorigatti I, Dorji T, Waeber A, Fall I, Ferguson N, +FitzJohn R, Tengomo G, Formenty P, Forna A, Fortin A, Garske T, +Gaythorpe K, Gurry C, Hamblion E, Djingarey M, Haskew C, Hugonnet S, +Imai N, Impouma B, Kabongo G, Kalenga O, Kibangou E, Lee T, Lukoya C, +Ly O, Makiala-Mandanda S, Mamba A, Mbala-Kingebeni P, Mboussou F, +Mlanda T, Makuma V, Morgan O, Mulumba A, Kakoni P, Mukadi-Bamuleka D, +Muyembe J, Bathé N, Ndumbi Ngamala P, Ngom R, Ngoy G, Nouvellet P, Nsio +J, Ousman K, Peron E, Polonsky J, Ryan M, Touré A, Towner R, Tshapenda +G, Van De Weerdt R, Van Kerkhove M, Wendland A, Yao N, Yoti Z, Yuma E, +Kalambayi Kabamba G, Mwati J, Mbuy G, Lubula L, Mutombo A, Mavila O, +Lay Y, Kitenge E (2018). "Outbreak of Ebola virus disease in the +Democratic Republic of the Congo, April–May, 2018: an epidemiological +study." _The Lancet_. doi:10.1016/S0140-6736(18)31387-4 +. +Distribution: gamma +Parameters: + shape: 2.400 + scale: 3.333 + +# ℹ 14 more elements +# ℹ Use `print(n = ...)` to see more elements. +# ℹ Use `parameter_tbl()` to see a summary table of the parameters. +# ℹ Explore database online at: https://epiverse-trace.github.io/epiparameter/dev/articles/database.html +``` + +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 `parameter_tbl()` to get a summary display of all: + + +``` r +# we expect 2 different types of delay distributions +# for ebola incubation period +epiparameter::epidist_db( + disease = "ebola", + epi_dist = "incubation" +) %>% + parameter_tbl() +``` + +``` output +Returning 5 results that match the criteria (5 are parameterised). +Use subset to filter by entry variables or single_epidist to return a single entry. +To retrieve the citation for each use the 'get_citation' function +``` + +``` output +# Parameter table: +# A data frame: 5 × 7 + disease pathogen epi_distribution prob_distribution author year sample_size + +1 Ebola Vi… Ebola V… incubation peri… lnorm Eichn… 2011 196 +2 Ebola Vi… Ebola V… incubation peri… gamma WHO E… 2015 1798 +3 Ebola Vi… Ebola V… incubation peri… gamma WHO E… 2015 49 +4 Ebola Vi… Ebola V… incubation peri… gamma WHO E… 2015 957 +5 Ebola Vi… Ebola V… incubation peri… gamma WHO E… 2015 792 +``` + +We find two types of probability distributions for this query: _log normal_ and _gamma_. + +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)! + +:::::::::::::::::::::::::: + +::::::::::::::::::::::::::::::::::::::::::: + + +## Select a single distribution + +The `epiparameter::epidist_db()` function works as a filtering or subset function. Let's use the `author` argument to filter `Hiroshi Nishiura` parameters: + + +``` r +epiparameter::epidist_db( + disease = "covid", + epi_dist = "serial", + author = "Hiroshi" +) %>% + epiparameter::parameter_tbl() +``` + +``` output +Returning 2 results that match the criteria (2 are parameterised). +Use subset to filter by entry variables or single_epidist to return a single entry. +To retrieve the citation for each use the 'get_citation' function +``` + +``` output +# Parameter table: +# A data frame: 2 × 7 + disease pathogen epi_distribution prob_distribution author year sample_size + +1 COVID-19 SARS-CoV… serial interval lnorm Nishi… 2020 28 +2 COVID-19 SARS-CoV… serial interval weibull Nishi… 2020 18 +``` + +We still get more than one epidemiological parameter. We can set the `single_epidist` argument to `TRUE` to only one: + + +``` r +epiparameter::epidist_db( + disease = "covid", + epi_dist = "serial", + author = "Hiroshi", + 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 citation use the 'get_citation' function +``` + +``` 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 +``` + +::::::::::::::::: callout + +### How does 'single_epidist' works? + +Looking at the help documentation for `?epiparameter::epidist_db()`: + +- If multiple entries match the arguments supplied and `single_epidist = TRUE`, then the parameterised +`` with the *largest sample size* will be returned. +- If multiple entries are equal after this sorting, the *first entry* will be returned. + +What is a *parametrised* ``? Look at `?is_parameterised`. + +::::::::::::::::::::::::: + +Let's assign this `` class object to the `covid_serialint` object. + + +``` r +covid_serialint <- + epiparameter::epidist_db( + disease = "covid", + epi_dist = "serial", + author = "Nishiura", + single_epidist = TRUE + ) +``` + + + +You can use `plot()` to `` objects to visualise: + +- the *Probability Density Function (PDF)* and +- the *Cumulative Distribution Function (CDF)*. + + +``` r +# plot object +plot(covid_serialint) +``` + + + +With the `xlim` argument, you can change the length or number of days in the `x` axis. Explore what this looks like: + + +``` r +# plot object +plot(covid_serialint, xlim = c(1, 60)) +``` + + +## Extract the summary statistics + +We can get the `mean` and standard deviation (`sd`) from this `` diving into the `summary_stats` object: + + +``` r +# get the mean +covid_serialint$summary_stats$mean +``` + +``` output +[1] 4.7 +``` + +Now, we have an epidemiological parameter we can reuse! Given that the `covid_serialint` is a `lnorm` or log normal distribution, we can replace the **summary statistics** numbers we plug into the `EpiNow2::LogNormal()` function: + +```r +generation_time <- + EpiNow2::LogNormal( + mean = covid_serialint$summary_stats$mean, # replaced! + sd = covid_serialint$summary_stats$sd, # replaced! + max = 20 + ) +``` + +In the next episode we'll learn how to use `{EpiNow2}` to correctly specify distributions, estimate transmissibility. Then, how to use **distribution functions** to get a maximum value (`max`) for `EpiNow2::LogNormal()` and use `{epiparameter}` in your analysis. + +:::::::::::::::::::::::::::::: callout + +### Log normal distributions + +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 +``` + +This gets a vector of class `` ready to use as input for any other package! + +:::::::::::::::::::::::::::::: + +## Challenges + +:::::::::::::::::::::::::::::: challenge + +### Ebola's serial interval + +Take 1 minute to: + +Get access to the Ebola serial interval with the highest sample size. + +Answer: + +- What is the `sd` of the epidemiological distribution? + +- What is the `sample_size` used in that study? + +::::::::: hint + +Use the `$` operator plus the tab or keyboard button to explore them as an expandable list: + +```r +covid_serialint$ +``` + +Use the `str()` to display the structure of the `` R object. + +:::::::::::::::::: + +:::::::::: solution + + +``` r +# ebola serial interval +ebola_serial <- + epiparameter::epidist_db( + disease = "ebola", + epi_dist = "serial", + single_epidist = TRUE + ) +``` + +``` output +Using WHO Ebola Response Team, Agua-Agum J, Ariyarajah A, Aylward B, Blake I, +Brennan R, Cori A, Donnelly C, Dorigatti I, Dye C, Eckmanns T, Ferguson +N, Formenty P, Fraser C, Garcia E, Garske T, Hinsley W, Holmes D, +Hugonnet S, Iyengar S, Jombart T, Krishnan R, Meijers S, Mills H, +Mohamed Y, Nedjati-Gilani G, Newton E, Nouvellet P, Pelletier L, +Perkins D, Riley S, Sagrado M, Schnitzler J, Schumacher D, Shah A, Van +Kerkhove M, Varsaneux O, Kannangarage N (2015). "West African Ebola +Epidemic after One Year — Slowing but Not Yet under Control." _The New +England Journal of Medicine_. doi:10.1056/NEJMc1414992 +.. +To retrieve the citation use the 'get_citation' function +``` + +``` r +ebola_serial +``` + +``` output +Disease: Ebola Virus Disease +Pathogen: Ebola Virus +Epi Distribution: serial interval +Study: WHO Ebola Response Team, Agua-Agum J, Ariyarajah A, Aylward B, Blake I, +Brennan R, Cori A, Donnelly C, Dorigatti I, Dye C, Eckmanns T, Ferguson +N, Formenty P, Fraser C, Garcia E, Garske T, Hinsley W, Holmes D, +Hugonnet S, Iyengar S, Jombart T, Krishnan R, Meijers S, Mills H, +Mohamed Y, Nedjati-Gilani G, Newton E, Nouvellet P, Pelletier L, +Perkins D, Riley S, Sagrado M, Schnitzler J, Schumacher D, Shah A, Van +Kerkhove M, Varsaneux O, Kannangarage N (2015). "West African Ebola +Epidemic after One Year — Slowing but Not Yet under Control." _The New +England Journal of Medicine_. doi:10.1056/NEJMc1414992 +. +Distribution: gamma +Parameters: + shape: 2.188 + scale: 6.490 +``` + + +``` r +# get the sd +ebola_serial$summary_stats$sd +``` + +``` output +[1] 9.6 +``` + +``` r +# get the sample_size +ebola_serial$metadata$sample_size +``` + +``` output +[1] 305 +``` + +Try to visualise this distribution using `plot()`. + +Also, explore all the other nested elements within the `` object. + +Share about: + +- What elements do you find useful for your analysis? +- What other elements would you like to see in this object? How? + +:::::::::::::::::::: + +:::::::::::::::::::::::::::::::: + +:::::::::::::::::::::::::::::: instructor + +An interesting element is the `method_assess` nested entry, which refers to the methods used by the study authors to assess for bias while estimating the serial interval distribution. + + +``` r +covid_serialint$method_assess +``` + +``` output +$censored +[1] TRUE + +$right_truncated +[1] TRUE + +$phase_bias_adjusted +[1] FALSE +``` + +We will explore these concepts following episodes! + +:::::::::::::::::::::::::::::: + + +::::::::::::::::::::::::::::::::: challenge + +### Ebola's severity parameter + +A severity parameter like the duration of hospitalisation could add to the information needed about the bed capacity in response to an outbreak ([Cori et al., 2017](https://royalsocietypublishing.org/doi/10.1098/rstb.2016.0371)). + + + +For Ebola: + +- What is the reported *point estimate* of the mean duration of health care and case isolation? + +::::::::::::::::: hint + +An informative delay should measure the time from symptom onset to recovery or death. + +Find a way to access the whole `{epiparameter}` database and find how that delay may be stored. The `parameter_tbl()` output is a dataframe. + +:::::::::::::::::::::: + +::::::::::::::::: solution + + +``` r +# one way to get the list of all the available parameters +epidist_db(disease = "all") %>% + parameter_tbl() %>% + as_tibble() %>% + distinct(epi_distribution) +``` + +``` output +Returning 122 results that match the criteria (99 are parameterised). +Use subset to filter by entry variables or single_epidist to return a single entry. +To retrieve the citation for each use the 'get_citation' function +``` + +``` output +# A tibble: 12 × 1 + epi_distribution + + 1 incubation period + 2 serial interval + 3 generation time + 4 onset to death + 5 offspring distribution + 6 hospitalisation to death + 7 hospitalisation to discharge + 8 notification to death + 9 notification to discharge +10 onset to discharge +11 onset to hospitalisation +12 onset to ventilation +``` + +``` r +ebola_severity <- epidist_db( + disease = "ebola", + epi_dist = "onset to discharge" +) +``` + +``` output +Returning 1 results that match the criteria (1 are parameterised). +Use subset to filter by entry variables or single_epidist to return a single entry. +To retrieve the citation for each use the 'get_citation' function +``` + +``` r +# point estimate +ebola_severity$summary_stats$mean +``` + +``` output +[1] 15.1 +``` + +Check that for some `{epiparameter}` entries you will also have the *uncertainty* around the *point estimate* of each summary statistic: + + +``` r +# 95% confidence intervals +ebola_severity$summary_stats$mean_ci +``` + +``` output +[1] 95 +``` + +``` r +# limits of the confidence intervals +ebola_severity$summary_stats$mean_ci_limits +``` + +``` output +[1] 14.6 15.6 +``` + +:::::::::::::::::::::::::: + +::::::::::::::::::::::::::::::::::::::::::: + +::::::::::::::::: discussion + +### The distribution zoo + +Explore this shinyapp called **The Distribution Zoo**! + +Follow these steps to reproduce the form of the COVID serial interval distribution from `{epiparameter}` (`covid_serialint` object): + +1. Access the shiny app website, +2. Go to the left panel, +3. Keep the *Category of distribution*: `Continuous Univariate`, +4. Select a new *Type of distribution*: `Log-Normal`, +5. Move the **sliders**, i.e. the graphical control element that allows you to adjust a value by moving a handle along a horizontal track or bar to the `covid_serialint` parameters. + +Replicate these with the `distribution` object and all its list elements: `[[2]]`, `[[3]]`, and `[[4]]`. Explore how the shape of a distribution changes when its parameters change. + +Share about: + +- What other features of the website do you find helpful? + +::::::::::::::::::::::::: + +::::::::::::::::::::::::: instructor + +In the context of user interfaces and graphical user interfaces (GUIs), like the [Distribution Zoo](https://ben18785.shinyapps.io/distribution-zoo/) shiny app, a **slider** is a graphical control element that allows users to adjust a value by moving a handle along a track or bar. Conceptually, it provides a way to select a numeric value within a specified range by visually sliding or dragging a pointer (the handle) along a continuous axis. + +::::::::::::::::::::::::: + + + +::::::::::::::::::::::::::::::::::::: keypoints + +- Use `{epiparameter}` to access the literature catalogue of epidemiological delay distributions. +- Use `epidist_db()` to select single delay distributions. +- Use `parameter_tbl()` for an overview of multiple delay distributions. +- Reuse known estimates for unknown disease in the early stage of an outbreak when no contact tracing data is available. + +:::::::::::::::::::::::::::::::::::::::::::::::: + diff --git a/delays-functions.md b/delays-functions.md new file mode 100644 index 00000000..4806ed41 --- /dev/null +++ b/delays-functions.md @@ -0,0 +1,957 @@ +--- +title: 'Use delay distributions in analysis' +teaching: 20 +exercises: 10 +editor_options: + chunk_output_type: inline +--- + +:::::::::::::::::::::::::::::::::::::: questions + +- How to reuse delays stored in the `{epiparameter}` library with my existing analysis pipeline? + +:::::::::::::::::::::::::::::::::::::::::::::::: + +::::::::::::::::::::::::::::::::::::: objectives + +- Use distribution functions to continuous and discrete distributions stored as `` objects. +- Convert a continuous to a discrete distribution with `{epiparameter}`. +- Connect `{epiparameter}` outputs with `{EpiNow2}` inputs. + +:::::::::::::::::::::::::::::::::::::::::::::::: + +::::::::::::::::::::::::::::::::::::: prereq + +## Prerequisites + +- Complete tutorial [Quantifying transmission](https://epiverse-trace.github.io/tutorials-middle/quantify-transmissibility.html) + +This episode requires you to be familiar with: + +**Data science** : Basic programming with R. + +**Statistics** : Probability distributions. + +**Epidemic theory** : Epidemiological parameters, time periods, Effective reproductive number. + +::::::::::::::::::::::::::::::::: + +## Introduction + + + +`{epiparameter}` help us to *choose* one specific set of epidemiological parameters from the literature, instead of copy/pasting them *by hand*: + + +``` r +covid_serialint <- + epiparameter::epidist_db( + disease = "covid", + epi_dist = "serial", + author = "Nishiura", + single_epidist = TRUE + ) +``` + +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::LogNormal()` + +```r +generation_time <- + EpiNow2::LogNormal( + mean = covid_serialint$summary_stats$mean, # replaced! + sd = covid_serialint$summary_stats$sd, # replaced! + max = 20 + ) +``` + +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! + +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: + + +``` r +library(epiparameter) +library(EpiNow2) +library(tidyverse) + +withr::local_options(list(mc.cores = 4)) +``` + +::::::::::::::::::: 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. + +::::::::::::::::::: + +## Distribution functions + +In R, all the statistical distributions have functions to access the following: + +- `density()`: Probability **Density** function (PDF), +- `cdf()`: Cumulative Distribution function (**CDF**), +- `quantile()`: **Quantile** function, and +- `generate()`: **Random** values from the given distribution. + +:::::::::::: checklist + +### Functions for the Normal distribution + +If you need it, read in detail about 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), each of its definitions and identify in which part of a distribution they are located! + +![The four probability functions for the normal distribution ([Jack Weiss, 2012](https://sakai.unc.edu/access/content/group/3d1eb92e-7848-4f55-90c3-7c72a54e7e43/public/docs/lectures/lecture13.htm#probfunc))](fig/fig5a-normaldistribution.png) + +:::::::::::::::::::: + +If you look at `?stats::Distributions`, each type of distribution has a unique set of functions. However, `{epiparameter}` gives you the same four functions to access each of the values above for any `` object you want! + + +``` r +# plot this to have a visual reference +plot(covid_serialint, day_range = 0:20) +``` + + +``` r +# the density value at quantile value of 10 (days) +density(covid_serialint, at = 10) +``` + +``` output +[1] 0.01911607 +``` + +``` r +# the cumulative probability at quantile value of 10 (days) +cdf(covid_serialint, q = 10) +``` + +``` output +[1] 0.9466605 +``` + +``` r +# the quantile value (day) at a cumulative probability of 60% +quantile(covid_serialint, p = 0.6) +``` + +``` output +[1] 4.618906 +``` + +``` r +# generate 10 random values (days) given +# the distribution family and its parameters +generate(covid_serialint, times = 10) +``` + +``` output + [1] 7.663488 6.717673 2.782662 2.731463 3.450016 9.705230 3.705973 1.589038 + [9] 4.884075 3.595120 +``` + +::::::::: instructor + +Access to the reference documentation (Help files) for these functions is accessible with the three double-colon notation: `epiparameter:::` + +- `?epiparameter:::density.epidist()` +- `?epiparameter:::cdf.epidist()` +- `?epiparameter:::quantile.epidist()` +- `?epiparameter:::generate.epidist()` + +:::::::::::::::::: + +::::::::::::::::::::::::::::::::: challenge + +### Window for contact tracing and the serial interval + +The **serial interval** is important in the optimisation of contact tracing since it provides a time window for the containment of a disease spread ([Fine, 2003](https://academic.oup.com/aje/article/158/11/1039/162725)). Depending on the serial interval, we can evaluate the need to expand the number of days pre-onset to consider in the contact tracing to include more backwards contacts ([Davis et al., 2020](https://assets.publishing.service.gov.uk/media/61e9ab3f8fa8f50597fb3078/S0523_Oxford_-_Backwards_contact_tracing.pdf)). + +With the COVID-19 serial interval (`covid_serialint`) calculate: + +- How much more of the backward cases could be captured if the contact tracing method considered contacts up to 6 days pre-onset compared to 2 days pre-onset? + +::::::::::::::::: hint + +In Figure 5 from 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), the shadowed section represents a cumulative probability of `0.997` for the quantile value at `x = 2`. + +:::::::::::::::::::::: + +::::::::::::::::: solution + + +``` r +plot(covid_serialint) +``` + + +``` r +cdf(covid_serialint, q = 2) +``` + +``` output +[1] 0.1111729 +``` + +``` r +cdf(covid_serialint, q = 6) +``` + +``` output +[1] 0.7623645 +``` + +Given the COVID-19 serial interval: + +- A contact tracing method considering contacts up to 2 days pre-onset will capture around 11.1% of backward cases. + +- If this period is extended to 6 days pre-onset, this could include 76.2% of backward contacts. + +:::::::::::::::::::::::::: + +::::::::::::::::: solution + +### What if + +If we exchange the question between days and cumulative probability to: + +- When considering secondary cases, how many days following the symptom onset of primary cases can we expect 55% of symptom onset to occur? + + +``` r +quantile(covid_serialint, p = 0.55) +``` + +An interpretation could be: + +- The 55% percent of the symptom onset of secondary cases will happen after 4.2 days after the symptom onset of primary cases. + +:::::::::::::::::::::::::: + + +::::::::::::::::::::::::::::::::::::::::::: + + +## Discretise a continuous distribution + +We are getting closer to the end! `EpiNow2::LogNormal()` still needs a maximum value (`max`). + +One way to do this is to get the quantile value for the distribution's 99th percentile or `0.99` cumulative probability. For this, we need access to the set of distribution functions for our `` object. + +We can use the set of distribution functions for a _continuous_ distribution (as above). However, these values will be _continuous_ numbers. We can **discretise** the continuous distribution stored in our `` object to get discrete values from a continuous distribution. + +When we `epiparameter::discretise()` the continuous distribution we get a **discrete**(-ized) distribution: + + +``` r +covid_serialint_discrete <- + epiparameter::discretise(covid_serialint) + +covid_serialint_discrete +``` + +``` 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: discrete lnorm +Parameters: + meanlog: 1.386 + sdlog: 0.568 +``` + +We identify this change in the `Distribution:` output line of the `` object. Double check this line: + +``` +Distribution: discrete lnorm +``` + +While for a **continuous** distribution, we plot the *Probability Density Function (PDF)*, for a **discrete** distribution, we plot the *Probability Mass Function (PMF)*: + + +``` r +# continuous +plot(covid_serialint) + +# discrete +plot(covid_serialint_discrete) +``` + +To finally get a `max` value, let's access the quantile value of the 99th percentile or `0.99` probability of the distribution with the `prob_dist$q` notation, similarly to how we access the `summary_stats` values. + + +``` r +covid_serialint_discrete_max <- + quantile(covid_serialint_discrete, p = 0.99) +``` + +::::::::::::::::::::::::::::::::: challenge + +### Length of quarantine and incubation period + +The **incubation period** distribution is a useful delay to assess the length of active monitoring or quarantine ([Lauer et al., 2020](https://www.acpjournals.org/doi/10.7326/M20-0504)). Similarly, delays from symptom onset to recovery (or death) will determine the required duration of health care and case isolation ([Cori et al., 2017](https://royalsocietypublishing.org/doi/10.1098/rstb.2016.0371)). + +Calculate: + +- Within what exact time frame do 99% of individuals exhibiting COVID-19 symptoms exhibit them after infection? + +::::::::::::::::: hint + +What delay distribution measures the time between infection and the onset of symptoms? + +The probability functions for `` **discrete** distributions are the same that we used for the *continuous* ones! + + +``` r +# plot to have a visual reference +plot(covid_serialint_discrete, day_range = 0:20) + +# density value at quantile value 10 (day) +density(covid_serialint_discrete, at = 10) + +# cumulative probability at quantile value 10 (day) +cdf(covid_serialint_discrete, q = 10) + +# In what quantile value (days) do we have the 60% cumulative probability? +quantile(covid_serialint_discrete, p = 0.6) + +# generate random values +generate(covid_serialint_discrete, times = 10) +``` + +:::::::::::::::::::::: + +::::::::::::::::: solution + + +``` r +covid_incubation <- + epiparameter::epidist_db( + disease = "covid", + epi_dist = "incubation", + 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 citation use the 'get_citation' function +``` + +``` r +covid_incubation_discrete <- epiparameter::discretise(covid_incubation) + +quantile(covid_incubation_discrete, p = 0.99) +``` + +``` output +[1] 19 +``` + +99% of those who develop COVID-19 symptoms will do so within 16 days of infection. + +Now, _Is this result expected in epidemiological terms?_ + +:::::::::::::::::::::::::: + +::::::::::::::::: solution + +### How to create a distribution plot? + +From a maximum value with `quantile()`, we can create a sequence of quantile values as a numeric vector and calculate `density()` values for each: + + +``` r +# create a discrete distribution visualisation +# from a maximum value from the distribution +quantile(covid_serialint_discrete, p = 0.99) %>% + # generate quantile values + # as a sequence for each natural number + seq(1L, to = ., by = 1L) %>% + # coerce numeric vector to data frame + as_tibble_col(column_name = "quantile_values") %>% + mutate( + # calculate density values + # for each quantile in the density function + density_values = + density( + x = covid_serialint_discrete, + at = quantile_values + ) + ) %>% + # create plot + ggplot( + aes( + x = quantile_values, + y = density_values + ) + ) + + geom_col() +``` + + + +**Remember:** In infections with pre-symptomatic transmission, serial intervals can have negative values ([Nishiura et al., 2020](https://www.ijidonline.com/article/S1201-9712(20)30119-3/fulltext)). When we use the _serial interval_ to approximate the _generation time_ we need to make this distribution with positive values only! + +:::::::::::::::::::::::::: + +::::::::::::::::::::::::::::::::::::::::::: + + +## Plug-in `{epiparameter}` to `{EpiNow2}` + +Now we can plug everything into the `EpiNow2::LogNormal()` function! + +- the **summary statistics** `mean` and `sd` of the distribution, +- a maximum value `max`, +- the `distribution` name. + +When using `EpiNow2::LogNormal()` to define a **log normal** distribution like the one in the `covid_serialint` object we can specify the mean and sd as parameters. Alternatively, to get the "natural" parameters for a log normal distribution we can convert its summary statistics to distribution parameters named `meanlog` and `sdlog`. With `{epiparameter}` we can directly get the *distribution parameters* using `epiparameter::get_parameters()`: + + +``` r +covid_serialint_parameters <- + epiparameter::get_parameters(covid_serialint) +``` + +Then, we have: + + +``` r +serial_interval_covid <- + EpiNow2::LogNormal( + meanlog = covid_serialint_parameters["meanlog"], + sdlog = covid_serialint_parameters["sdlog"], + max = covid_serialint_discrete_max + ) + +serial_interval_covid +``` + +``` output +- lognormal distribution (max: 14): + meanlog: + 1.4 + sdlog: + 0.57 +``` + +Assuming a COVID-19 scenario, let's use the first 60 days of the `example_confirmed` data set from the `{EpiNow2}` package as `reported_cases` and the recently created `serial_interval_covid` object as inputs to estimate the time-varying reproduction number using `EpiNow2::epinow()`. + + +``` r +epinow_estimates_cg <- epinow( + # cases + data = example_confirmed[1:60], + # delays + generation_time = generation_time_opts(serial_interval_covid) +) +``` + +``` output +WARN [2024-09-24 02:59:27] epinow: There were 1 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 [2024-09-24 02:59:27] epinow: Examine the pairs() plot to diagnose sampling problems + - +``` + +``` r +base::plot(epinow_estimates_cg) +``` + + + +The `plot()` output includes the estimated cases by date of infection, which are reconstructed from the reported cases and delays. + +:::::::::: callout + +### Warning + +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 + +Estimating $R_t$ requires data on the daily number of new infections. Due to lags in the development of detectable viral loads, symptom onset, seeking care, and reporting, these numbers are not readily available. All observations reflect transmission events from some time in the past. In other words, if $d$ is the delay from infection to observation, then observations at time $t$ inform $R_{t−d}$, not $R_t$. [(Gostic et al., 2020)](https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1008409#sec007) + +![**Timeline for chain of disease reporting, the Netherlands.** Lab, laboratory; PHA, public health authority. From [Marinović et al., 2015](https://wwwnc.cdc.gov/eid/article/21/2/13-0504_article)](fig/disease-reporting.jpg) + +The **delay distribution** could be inferred jointly with the underlying times of infection or estimated as the sum of the [incubation period](../learners/reference.md#incubation) distribution and the distribution of delays from symptom onset to observation from line list data ([reporting delay](../learners/reference.md#reportingdelay)). For `{EpiNow2}`, we can specify these two complementary delay distributions in the `delays` argument. + +![**$R_{t}$ is a measure of transmission at time $t$.** Observations after time $t$ must be adjusted. ICU, intensive care unit. From [Gostic et al., 2020](https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1008409#sec007)](fig/rt-adjusting-delays.png) + +::::::::::::::::::::::::::::::::: challenge + +### Use an incubation period for COVID-19 to estimate Rt + +Estimate the time-varying reproduction number for the first 60 days of the `example_confirmed` data set from `{EpiNow2}`. Access to an incubation period for COVID-19 from `{epiparameter}` to use it as a reporting delay. + +::::::::::::::::: hint + +Use the last `epinow()` calculation using the `delays` argument and the `delay_opts()` helper function. + +The `delays` argument and the `delay_opts()` helper function are analogous to the `generation_time` argument and the `generation_time_opts()` helper function. + +```r +epinow_estimates <- epinow( + # cases + reported_cases = example_confirmed[1:60], + # delays + generation_time = generation_time_opts(covid_serial_interval), + delays = delay_opts(covid_incubation_time) +) +``` + +:::::::::::::::::::::: + +::::::::::::::::: solution + + +``` r +# generation time --------------------------------------------------------- + +# get covid serial interval +covid_serialint <- + epiparameter::epidist_db( + disease = "covid", + epi_dist = "serial", + author = "Nishiura", + single_epidist = TRUE + ) + +# adapt epidist to epinow2 +covid_serialint_discrete_max <- covid_serialint %>% + epiparameter::discretise() %>% + quantile(p = 0.99) + +covid_serialint_parameters <- + epiparameter::get_parameters(covid_serialint) + +covid_serial_interval <- + EpiNow2::LogNormal( + meanlog = covid_serialint_parameters["meanlog"], + sdlog = covid_serialint_parameters["sdlog"], + max = covid_serialint_discrete_max + ) + +# incubation time --------------------------------------------------------- + +# get covid incubation period +covid_incubation <- epiparameter::epidist_db( + disease = "covid", + epi_dist = "incubation", + author = "Natalie", + single_epidist = TRUE +) + +# adapt epiparameter to epinow2 +covid_incubation_discrete_max <- covid_incubation %>% + epiparameter::discretise() %>% + quantile(p = 0.99) + +covid_incubation_parameters <- + epiparameter::get_parameters(covid_incubation) + +covid_incubation_time <- + EpiNow2::LogNormal( + meanlog = covid_incubation_parameters["meanlog"], + sdlog = covid_incubation_parameters["sdlog"], + max = covid_incubation_discrete_max + ) + +# epinow ------------------------------------------------------------------ + +# run epinow +epinow_estimates_cgi <- epinow( + # cases + data = example_confirmed[1:60], + # delays + generation_time = generation_time_opts(covid_serial_interval), + delays = delay_opts(covid_incubation_time) +) +``` + +``` output +WARN [2024-09-24 03:01:12] epinow: There were 4 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 [2024-09-24 03:01:12] epinow: Examine the pairs() plot to diagnose sampling problems + - +``` + +``` r +base::plot(epinow_estimates_cgi) +``` + + + +Try to complement the `delays` argument with a reporting delay like the `reporting_delay_fixed` object of the previous episode. + +:::::::::::::::::::::::::: + +::::::::::::::::::::::::::::::::::::::::::: + +:::::::::::::::::::::::::::::::::::::::::::::::::::::::: discussion + +### How much has it changed? + +After adding the incubation period, discuss: + +- Does the trend of the model fit in the "Estimate" section change? +- Has the uncertainty changed? +- How would you explain or interpret any of these changes? + +Compare all the `{EpiNow2}` figures generated previously. + +:::::::::::::::::::::::::::::::::::::::::::::::::::::::: + +## Challenges + +:::::::::::::::::::::::::::::: 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) + +This gives 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! + +:::::::::::::::::::::::::::::: + +::::::::::::::::::::::::::::::::: challenge + +### Ebola's effective reproduction number adjusted by reporting delays + +Download and read the [Ebola dataset](data/ebola_cases.csv): + +- Estimate the effective reproduction number using `{EpiNow2}` +- Adjust the estimate by the available reporting delays in `{epiparameter}` +- 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). + +To get delay distribution using `{epiparameter}` we can use functions like: + +- `epiparameter::epidist_db()` +- `epiparameter::parameter_tbl()` +- `discretise()` +- `quantile()` + +:::::::::::::::::::::: + +::::::::::::::::: 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 +epiparameter::epidist_db(disease = "ebola") %>% + epiparameter::parameter_tbl() +``` + + +``` r +# generation time --------------------------------------------------------- + +# subset one distribution for the generation time +ebola_serial <- epiparameter::epidist_db( + disease = "ebola", + epi_dist = "serial", + single_epidist = TRUE +) + +# adapt epiparameter to epinow2 +ebola_serial_discrete <- epiparameter::discretise(ebola_serial) + +serial_interval_ebola <- + EpiNow2::Gamma( + mean = ebola_serial$summary_stats$mean, + sd = ebola_serial$summary_stats$sd, + max = quantile(ebola_serial_discrete, p = 0.99) + ) + +# incubation time --------------------------------------------------------- + +# subset one distribution for delay of the incubation period +ebola_incubation <- epiparameter::epidist_db( + disease = "ebola", + epi_dist = "incubation", + single_epidist = TRUE +) + +# adapt epiparameter to epinow2 +ebola_incubation_discrete <- epiparameter::discretise(ebola_incubation) + +incubation_period_ebola <- + EpiNow2::Gamma( + mean = ebola_incubation$summary_stats$mean, + sd = ebola_incubation$summary_stats$sd, + max = quantile(ebola_serial_discrete, p = 0.99) + ) + +# epinow ------------------------------------------------------------------ + +# run epinow +epinow_estimates_egi <- epinow( + # cases + data = ebola_confirmed, + # delays + generation_time = generation_time_opts(serial_interval_ebola), + delays = delay_opts(incubation_period_ebola) +) +``` + +``` output +WARN [2024-09-24 03:03:22] 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 [2024-09-24 03:03:22] 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::NonParametric()` accepts Probability Mass Functions (PMF) from any distribution family. Read the reference guide on [Probability distributions](https://epiforecasts.io/EpiNow2/reference/Distributions.html). + +:::::::::::::::::::::: + +::::::::::::::::: solution + + +``` r +# What parameters are available for Influenza? +epiparameter::epidist_db(disease = "influenza") %>% + epiparameter::parameter_tbl() %>% + count(epi_distribution) +``` + +``` output +# Parameter table: +# A data frame: 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 <- + epiparameter::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 = 0.99) + +influenza_generation_pmf <- + density( + influenza_generation_discrete, + at = 1:influenza_generation_max + ) + +influenza_generation_pmf +``` + +``` output +[1] 0.06312336 0.22134988 0.29721220 0.23896828 0.12485164 0.04309454 +``` + +``` r +# EpiNow2::NonParametric() can also accept the PMF values +generation_time_influenza <- + EpiNow2::NonParametric( + pmf = influenza_generation_pmf + ) + +# incubation period ------------------------------------------------------- + +# Read the incubation period +influenza_incubation <- + epiparameter::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 = 0.99) + +influenza_incubation_pmf <- + density( + influenza_incubation_discrete, + at = 1:influenza_incubation_max + ) + +influenza_incubation_pmf +``` + +``` output +[1] 0.05749151 0.16687705 0.22443092 0.21507632 0.16104546 0.09746609 0.04841928 +``` + +``` r +# EpiNow2::NonParametric() can also accept the PMF values +incubation_time_influenza <- + EpiNow2::NonParametric( + 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 + data = influenza_cleaned, + # delays + generation_time = generation_time_opts(generation_time_influenza), + delays = delay_opts(incubation_time_influenza) +) + +plot(epinow_estimates_igi) +``` + + + +:::::::::::::::::::::::::: + +::::::::::::::::::::::::::::::::::::::::::: + +## Next steps + +::::::::::::::::: testimonial + +### How to get distribution parameters from statistical distributions? + +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::Gamma()` or `EpiNow2::LogNormal()`? + +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)! + +::::::::::::::::::::::::::::: + +::::::::::::::::: testimonial + +### How to estimate delay distributions for Disease X? + +Refer to this excellent tutorial on estimating the serial interval and incubation period of Disease X accounting for *censoring* using Bayesian inference with packages like `{rstan}` and `{coarseDataTools}`. + +- Tutorial in English: +- Tutorial en Español: + +**Then,** after you get your estimated values, you can manually create your own` ` class objects with `epiparameter::epidist()`! Take a look at its [reference guide on "Create an `` object"](https://epiverse-trace.github.io/epiparameter/reference/epidist.html#ref-examples)! + +Lastly, take a look at the latest [`{epidist}` R package](https://epidist.epinowcast.org/) which provide methods to address key challenges in estimating distributions, including truncation, interval censoring, and dynamical biases. + +::::::::::::::::::::::::::::: + + + + +::::::::::::::::::::::::::::::::::::: keypoints + +- Use distribution functions with `` objects to get summary statistics and informative parameters for public health interventions like the Window for contact tracing and Length of quarantine. +- Use `discretise()` to convert continuous to discrete delay distributions. +- Use `{epiparameter}` to get reporting delays required in transmissibility estimates. + +:::::::::::::::::::::::::::::::::::::::::::::::: + diff --git a/fig/SEE-dist.png b/fig/SEE-dist.png new file mode 100644 index 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