estimate_R: Estimated Instantaneous Reproduction Number
`estimate_R` estimates the reproduction number of an epidemic, given the incidence time series and the serial interval distribution.

Description

Estimated Instantaneous Reproduction Number

estimate_R estimates the reproduction number of an epidemic, given the incidence time series and the serial interval distribution.

Usage

estimate_R(incid, method = c("non_parametric_si", "parametric_si",
  "uncertain_si", "si_from_data", "si_from_sample"), si_data = NULL,
  si_sample = NULL, config = make_config(incid = incid, method =
  method))

Arguments

incid

One of the following

A vector (or a dataframe with a single column) of non-negative integers containing the incidence time series
A dataframe of non-negative integers with either i) incid$I containing the total incidence, or ii) two columns, so that incid$local contains the incidence of cases due to local transmission and incid$imported contains the incidence of imported cases (with incid$local + incid$imported the total incidence). If the dataframe contains a column incid$dates, this is used for plotting. incid$dates must contains only dates in a row.
An object of class incidence

Note that the cases from the first time step are always all assumed to be imported cases.

method

One of "non_parametric_si", "parametric_si", "uncertain_si", "si_from_data" or "si_from_sample" (see details).

si_data

For method "si_from_data" ; the data on dates of symptoms of pairs of infector/infected individuals to be used to estimate the serial interval distribution (see details).

si_sample

For method "si_from_sample" ; a matrix where each column gives one distribution of the serial interval to be explored (see details).

config

An object of class estimate_R_config, as returned by function make_config.

Value

an object of class estimate_R, with components:

R: a dataframe containing: the times of start and end of each time window considered ; the posterior mean, std, and 0.025, 0.05, 0.25, 0.5, 0.75, 0.95, 0.975 quantiles of the reproduction number for each time window.
method: the method used to estimate R, one of "non_parametric_si", "parametric_si", "uncertain_si", "si_from_data" or "si_from_sample"
si_distr: a vector or dataframe (depending on the method) containing the discrete serial interval distribution(s) used for estimation
SI.Moments: a vector or dataframe (depending on the method) containing the mean and std of the discrete serial interval distribution(s) used for estimation
I: the time series of total incidence
I_local: the time series of incidence of local cases (so that I_local + I_imported = I)
I_imported: the time series of incidence of imported cases (so that I_local + I_imported = I)
dates: a vector of dates corresponding to the incidence time series
MCMC_converged (only for method si_from_data): a boolean showing whether the Gelman-Rubin MCMC convergence diagnostic was successful (TRUE) or not (FALSE)

Details

Analytical estimates of the reproduction number for an epidemic over predefined time windows can be obtained within a Bayesian framework, for a given discrete distribution of the serial interval (see references).

Several methods are available to specify the serial interval distribution.

In short there are five methods to specify the serial interval distribution (see help for function make_config for more detail on each method). In the first two methods, a unique serial interval distribution is considered, whereas in the last three, a range of serial interval distributions are integrated over:

In method "non_parametric_si" the user specifies the discrete distribution of the serial interval
In method "parametric_si" the user specifies the mean and sd of the serial interval
In method "uncertain_si" the mean and sd of the serial interval are each drawn from truncated normal distributions, with parameters specified by the user
In method "si_from_data", the serial interval distribution is directly estimated, using MCMC, from interval censored exposure data, with data provided by the user together with a choice of parametric distribution for the serial interval
In method "si_from_sample", the user directly provides the sample of serial interval distribution to use for estimation of R. This can be a useful alternative to the previous method, where the MCMC estimation of the serial interval distribution could be run once, and the same estimated SI distribution then used in estimate_R in different contexts, e.g. with different time windows, hence avoiding to rerun the MCMC everytime estimate_R is called.

References

Cori, A. et al. A new framework and software to estimate time-varying reproduction numbers during epidemics (AJE 2013). Wallinga, J. and P. Teunis. Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures (AJE 2004). Reich, N.G. et al. Estimating incubation period distributions with coarse data (Statis. Med. 2009)

Examples

Run this code

# NOT RUN {
## load data on pandemic flu in a school in 2009
data("Flu2009")

## estimate the reproduction number (method "non_parametric_si")
## when not specifying t_start and t_end in config, they are set to estimate
## the reproduction number on sliding weekly windows                          
res <- estimate_R(incid = Flu2009$incidence, 
                  method = "non_parametric_si",
                  config = make_config(list(si_distr = Flu2009$si_distr)))
plot(res)

## the second plot produced shows, at each each day,
## the estimate of the reproduction number over the 7-day window 
## finishing on that day.

## to specify t_start and t_end in config, e.g. to have biweekly sliding
## windows      
t_start <- seq(2, nrow(Flu2009$incidence)-13)   
t_end <- t_start + 13                 
res <- estimate_R(incid = Flu2009$incidence, 
                  method = "non_parametric_si",
                  config = make_config(list(
                      si_distr = Flu2009$si_distr, 
                      t_start = t_start, 
                      t_end = t_end)))
plot(res)

## the second plot produced shows, at each each day,
## the estimate of the reproduction number over the 14-day window 
## finishing on that day.

## example with an incidence object

## create fake data
library(incidence)
data <- c(0,1,1,2,1,3,4,5,5,5,5,4,4,26,6,7,9)
location <- sample(c("local","imported"), length(data), replace=TRUE)
location[1] <- "imported" # forcing the first case to be imported

## get incidence per group (location)
incid <- incidence(data, groups = location)

## Estimate R with assumptions on serial interval
res <- estimate_R(incid, method = "parametric_si",
                  config = make_config(list(
                  mean_si = 2.6, std_si = 1.5)))
plot(res)
## the second plot produced shows, at each each day,
## the estimate of the reproduction number over the 7-day window
## finishing on that day.

## estimate the reproduction number (method "parametric_si")
res <- estimate_R(Flu2009$incidence, method = "parametric_si",
                  config = make_config(list(mean_si = 2.6, std_si = 1.5)))
plot(res)
## the second plot produced shows, at each each day,
## the estimate of the reproduction number over the 7-day window
## finishing on that day.

## estimate the reproduction number (method "uncertain_si")
res <- estimate_R(Flu2009$incidence, method = "uncertain_si",
                  config = make_config(list(
                  mean_si = 2.6, std_mean_si = 1,
                  min_mean_si = 1, max_mean_si = 4.2,
                  std_si = 1.5, std_std_si = 0.5,
                  min_std_si = 0.5, max_std_si = 2.5,
                  n1 = 100, n2 = 100)))
plot(res)
## the bottom left plot produced shows, at each each day,
## the estimate of the reproduction number over the 7-day window
## finishing on that day.

# }
# NOT RUN {
## Note the following examples use an MCMC routine
## to estimate the serial interval distribution from data,
## so they may take a few minutes to run

## load data on rotavirus
data("MockRotavirus")

## estimate the reproduction number (method "si_from_data")
MCMC_seed <- 1
overall_seed <- 2
R_si_from_data <- estimate_R(MockRotavirus$incidence,
                            method = "si_from_data",
                            si_data = MockRotavirus$si_data,
                            config = make_config(list(si_parametric_distr = "G",
                                        mcmc_control = make_mcmc_control(list(burnin = 1000,
                                        thin = 10, seed = MCMC_seed),
                                        n1 = 500, n2 = 50,
                                        seed = overall_seed))))

## compare with version with no uncertainty
R_Parametric <- estimate_R(MockRotavirus$incidence,
                          method = "parametric_si",
                          config = make_config(list(
                          mean_si = mean(R_si_from_data$SI.Moments$Mean),
                             std_si = mean(R_si_from_data$SI.Moments$Std))))
## generate plots
p_uncertainty <- plot(R_si_from_data, "R", options_R=list(ylim=c(0, 1.5)))
p_no_uncertainty <- plot(R_Parametric, "R", options_R=list(ylim=c(0, 1.5)))
gridExtra::grid.arrange(p_uncertainty, p_no_uncertainty,ncol=2)

## the left hand side graph is with uncertainty in the SI distribution, the
## right hand side without.
## The credible intervals are wider when accounting for uncertainty in the SI
## distribution.

## estimate the reproduction number (method "si_from_sample")
MCMC_seed <- 1
overall_seed <- 2
SI.fit <- coarseDataTools::dic.fit.mcmc(dat = MockRotavirus$si_data,
                 dist = "G",
                 init.pars = init_mcmc_params(MockRotavirus$si_data, "G"),
                 burnin = 1000,
                 n.samples = 5000,
                 seed = MCMC_seed)
si_sample <- coarse2estim(SI.fit, thin = 10)$si_sample
R_si_from_sample <- estimate_R(MockRotavirus$incidence,
                               method = "si_from_sample",
                               si_sample = si_sample,
                               config = make_config(list(n2 = 50, 
                               seed = overall_seed)))
plot(R_si_from_sample)

## check that R_si_from_sample is the same as R_si_from_data
## since they were generated using the same MCMC algorithm to generate the SI
## sample (either internally to EpiEstim or externally)
all(R_si_from_sample$R$`Mean(R)` == R_si_from_data$R$`Mean(R)`)
# }
# NOT RUN {
# }

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