This package estimates the time-varying reproduction number, rate of spread, and doubling time using a range of open-source tools (Abbott et al.), and current best practices (Gostic et al.). It aims to help users avoid some of the limitations of naive implementations in a framework that is informed by community feedback and is under active development.

It estimates the time-varying reproduction number on cases by date of infection (using a similar approach to that implemented in {EpiEstim}). Imputed infections are then mapped to observed data (for example cases by date of report) via a series of uncertain delay distributions (in the examples in the package documentation these are an incubation period and a reporting delay) and a reporting model that can include weekly periodicity.

Uncertainty is propagated from all inputs into the final parameter estimates, helping to mitigate spurious findings. This is handled internally. The time-varying reproduction estimates and the uncertain generation time also give time-varying estimates of the rate of growth.

The default model uses a non-stationary Gaussian process to estimate the time-varying reproduction number and then infer infections. Other options include:

• A stationary Gaussian process (faster to estimate but currently gives reduced performance for real time estimates).
• User specified breakpoints.
• A fixed reproduction number.
• As piecewise constant by combining a fixed reproduction number with breakpoints.
• As a random walk (by combining a fixed reproduction number with regularly spaced breakpoints (i.e weekly)).
• Inferring infections using back-calculation and then calculating the time-varying reproduction number.

The documentation for estimate_infections provides examples of the different options available.

Forecasting is also supported for the time-varying reproduction number, infections and reported cases. The time-varying reproduction number can be forecast forwards in time using an integration with the {EpiSoon} package, and converted to a case forecast using the renewal equation. Alternatively, the time-varying reproduction number and cases can be forecast using a Gaussian process.

A simple example of using the package to estimate a national Rt for Covid-19 can be found here.

## Installation

Install the stable version of the package:

install.packages("EpiNow2")

Install the stable development version of the package using {drat}:

install.packages("drat")
install.packages("EpiNow2")

Install the unstable development version of the package with:

remotes::install_github("epiforecasts/EpiNow2")

Windows users will need a working installation of Rtools in order to build the package from source. See here for a guide to installing Rtools for use with Stan (which is the statistical modelling platform used for the underlying model). For simple deployment/development a prebuilt docker image is also available (see documentation here).

## Quick start

EpiNow2 is designed to be used with a single function call or to be used in an ad-hoc fashion via individual function calls. The core functions of EpiNow2 are the two single-call functions epinow, regional_epinow, plus functions estimate_infections, and forecast_infections. In the following section we give an overview of the simple use case for epinow and regional_epinow. estimate_infections can be use on its own to infer the underlying infection case curve from reported cases and estimate Rt. Estimating the underlying infection case curve via back-calculation (and then calculating Rt) is substantially less computationally demanding than generating using default settings but may result in less reliable estimates of Rt. For more details on using each function see the function documentation.

The first step to using the package is to load it as follows.

library(EpiNow2)

### Reporting delays, incubation period and generation time

Distributions can either be fitted using package functionality or determined elsewhere and then defined with uncertainty for use in EpiNow2. When data is supplied a subsampled bootstrapped lognormal will be fit (to account for uncertainty in the observed data without being biased by changes in incidence). An arbitrary number of delay distributions are supported with the most common use case likely to be a incubation period followed by a reporting delay.

reporting_delay <- estimate_delay(rlnorm(1000,  log(3), 1),
max_value = 15, bootstraps = 1)

Here we define the incubation period and generation time based on literature estimates for Covid-19 (see here for the code that generates these estimates).

generation_time <- get_generation_time(disease = "SARS-CoV-2", source = "ganyani")
incubation_period <- get_incubation_period(disease = "SARS-CoV-2", source = "lauer")

### epinow

This function represents the core functionality of the package and includes results reporting, plotting and optional saving. It requires a data frame of cases by date of report and the distributions defined above. An additional forecasting module is supported via EpiSoon and companion packages (see documentation for an example).

Load example case data from EpiNow2.

reported_cases <- example_confirmed[1:90]
#>          date confirm
#> 1: 2020-02-22      14
#> 2: 2020-02-23      62
#> 3: 2020-02-24      53
#> 4: 2020-02-25      97
#> 5: 2020-02-26      93
#> 6: 2020-02-27      78

Estimate cases by date of infection, the time-varying reproduction number, the rate of growth and forecast these estimates into the future by 7 days. Summarise the posterior and return a summary table and plots for reporting purposes. If a target_folder is supplied results can be internally saved (with the option to also turn off explicit returning of results). Note: For real use cases more samples and a longer warm up may be needed. See fitting progress by setting verbose = TRUE.

estimates <- epinow(reported_cases = reported_cases,
generation_time = generation_time,
delays = delay_opts(incubation_period, reporting_delay),
rt = rt_opts(prior = list(mean = 2, sd = 0.2)),
stan = stan_opts(cores = 4))
names(estimates)
#> [1] "estimates"                "estimated_reported_cases"
#> [3] "summary"                  "plots"
#> [5] "timing"

Both summary measures and posterior samples are returned for all parameters in an easily explored format which can be accessed using summary. The default is to return a summary table of estimates for key parameters at the latest date partially supported by data.

knitr::kable(summary(estimates))
measure estimate
New confirmed cases by infection date 515 (289 – 1038)
Expected change in daily cases Unsure
Effective reproduction no. 0.9 (0.7 – 1.2)
Rate of growth -0.04 (-0.1 – 0.05)
Doubling/halving time (days) -18.2 (13.5 – -7)

Summarised parameter estimates can also easily be returned, either filtered for a single parameter or for all parameters.

head(summary(estimates, type = "parameters", params = "R"))
#>          date variable strat     type   median     mean         sd lower_90
#> 1: 2020-02-22        R  <NA> estimate 2.111871 2.119982 0.13864546 1.899283
#> 2: 2020-02-23        R  <NA> estimate 2.086460 2.094418 0.11619947 1.908121
#> 3: 2020-02-24        R  <NA> estimate 2.061035 2.067174 0.09690610 1.912490
#> 4: 2020-02-25        R  <NA> estimate 2.032317 2.038242 0.08093213 1.904885
#> 5: 2020-02-26        R  <NA> estimate 2.004828 2.007648 0.06841627 1.897507
#> 6: 2020-02-27        R  <NA> estimate 1.974385 1.975444 0.05932968 1.880276
#>    lower_50 lower_20 upper_20 upper_50 upper_90
#> 1: 2.021864 2.077693 2.143147 2.210176 2.361724
#> 2: 2.013526 2.057374 2.115925 2.172291 2.296242
#> 3: 2.000372 2.035607 2.086856 2.133616 2.233151
#> 4: 1.983199 2.013435 2.056292 2.093377 2.174351
#> 5: 1.961205 1.989248 2.022717 2.052258 2.123259
#> 6: 1.936145 1.959619 1.989932 2.012621 2.076784

Reported cases are returned in a separate data frame in order to streamline the reporting of forecasts and for model evaluation.

head(summary(estimates, output = "estimated_reported_cases"))
#>          date  type median    mean       sd lower_90 lower_50 lower_20 upper_20
#> 1: 2020-02-22 gp_rt   48.0  49.051 12.75936    30.00       40       45       51
#> 2: 2020-02-23 gp_rt   65.0  66.375 16.15052    41.00       55       61       70
#> 3: 2020-02-24 gp_rt   72.5  73.982 17.47768    46.95       62       69       77
#> 4: 2020-02-25 gp_rt   75.0  76.623 18.41798    48.95       64       70       80
#> 5: 2020-02-26 gp_rt   96.0  98.136 22.77899    63.95       82       91      101
#> 6: 2020-02-27 gp_rt  129.0 130.737 29.66405    84.00      109      123      136
#>    upper_50 upper_90
#> 1:       57       72
#> 2:       77       95
#> 3:       85      104
#> 4:       88      109
#> 5:      112      138
#> 6:      149      184

A range of plots are returned (with the single summary plot shown below). These plots can also be generated using the following plot method.

plot(estimates)

### regional_epinow

The regional_epinow function runs the epinow function across multiple regions in an efficient manner.

Define cases in multiple regions delineated by the region variable.

reported_cases <- data.table::rbindlist(list(
data.table::copy(reported_cases)[, region := "testland"],
reported_cases[, region := "realland"]))
#>          date confirm   region
#> 1: 2020-02-22      14 testland
#> 2: 2020-02-23      62 testland
#> 3: 2020-02-24      53 testland
#> 4: 2020-02-25      97 testland
#> 5: 2020-02-26      93 testland
#> 6: 2020-02-27      78 testland

Calling regional_epinow runs the epinow on each region in turn (or in parallel depending on the settings used).

estimates <- regional_epinow(reported_cases = reported_cases,
generation_time = generation_time,
delays = delay_opts(incubation_period, reporting_delay),
rt = rt_opts(prior = list(mean = 2, sd = 0.2)),
stan = stan_opts(cores = 4))
#> INFO [2020-11-12 15:49:50] Producing following optional outputs: regions, summary, samples, plots, latest
#> INFO [2020-11-12 15:49:50] Reporting estimates using data up to: 2020-05-21
#> INFO [2020-11-12 15:49:50] No target directory specified so returning output
#> INFO [2020-11-12 15:49:50] Producing estimates for: testland, realland
#> INFO [2020-11-12 15:49:50] Regions excluded: none
#> INFO [2020-11-12 15:49:50] Showing progress using progressr. Modify this behaviour using progressr::handlers.
#> INFO [2020-11-12 16:00:20] Completed estimates for: testland
#> INFO [2020-11-12 16:10:54] Completed estimates for: realland
#> INFO [2020-11-12 16:10:54] Completed regional estimates
#> INFO [2020-11-12 16:10:54] Regions with estimates: 2
#> INFO [2020-11-12 16:10:54] Regions with runtime errors: 0
#> INFO [2020-11-12 16:10:54] Producing summary
#> INFO [2020-11-12 16:10:54] No summary directory specified so returning summary output
#> INFO [2020-11-12 16:10:55] No target directory specified so returning timings

Results from each region are stored in a regional list with across region summary measures and plots stored in a summary list. All results can be set to be internally saved by setting the target_folder and summary_dir arguments. Each region can be estimated in parallel using the future package (when in most scenarios cores should be set to 1). For routine use each MCMC chain can also be run in parallel (with future = TRUE) with a time out (max_execution_time) allowing for partial results to be returned if a subset of chains is running longer than expected. See the documentation for the future package for details on nested futures.

Summary measures that are returned include a table formatted for reporting (along with raw results for further processing). Futures updated will extend the S3 methods used above to smooth access to this output.

knitr::kable(estimates$summary$summarised_results$table) Region New confirmed cases by infection date Expected change in daily cases Effective reproduction no. Rate of growth Doubling/halving time (days) realland 520 (285 – 924) Unsure 0.9 (0.6 – 1.2) -0.03 (-0.1 – 0.04) -20 (17.1 – -6.8) testland 513 (297 – 996) Unsure 0.9 (0.7 – 1.2) -0.04 (-0.1 – 0.05) -18.5 (14.1 – -6.9) A range of plots are again returned (with the single summary plot shown below). estimates$summary\$summary_plot

### Reporting templates

Rmarkdown templates are provided in the package (templates) for semi-automated reporting of estimates. These are currently undocumented but an example integration can be seen here. If using these templates to report your results please highlight our limitations as these are key to understanding the results from EpiNow2 .

## Interactive figures

EpiNow2 is integrated with the {RtD3} package which provides interactive visualisations of Rt estimates. See the package documentation for details.

## Contributing

File an issue here if you have identified an issue with the package. Please note that due to operational constraints priority will be given to users informing government policy or offering methodological insights. We welcome all contributions, in particular those that improve the approach or the robustness of the code base.