EpiNow2 (version 1.3.2)

estimate_truncation: Estimate Truncation of Observed Data

Description

Estimates a truncation distribution from multiple snapshots of the same data source over time. This distribution can then be used in regional_epinow, epinow, and estimate_infections to adjust for truncated data. See here for an example of using this approach on Covid-19 data in England.

The model of truncation is as follows:

1. The truncation distribution is assumed to be log normal with a mean and standard deviation that is informed by the data.

2. The data set with the latest observations is adjusted for truncation using the truncation distribution.

3. Earlier data sets are recreated by applying the truncation distribution to the adjusted latest observations in the time period of the earlier data set. These data sets are then compared to the earlier observations assuming a negative binomial observation model.

This model is then fit using stan with standard normal, or half normal, prior for the mean, standard deviation and 1 over the square root of the over dispersion.

This approach assumes that:

• Current truncation is related to past truncation.

• Truncation is a multiplicative scaling of underlying reported cases.

• Truncation is log normally distributed.

Usage

estimate_truncation(
  obs,
  max_truncation = 10,
  model = NULL,
  CrIs = c(0.2, 0.5, 0.9),
  verbose = TRUE,
  ...
)

Arguments

obs

A list of data frames each containing a date variable and a confirm (integer) variable. Each data set should be a snapshot of the reported data over time. All data sets must contain a complete vector of dates.

max_truncation

Integer, defaults to 10. Maximum number of days to include in the truncation distribution.

model

A compiled stan model to override the default model. May be useful for package developers or those developing extensions.

CrIs

Numeric vector of credible intervals to calculate.

verbose

Logical, should model fitting progress be returned.

...

Additional parameters to pass to rstan::sampling.

Value

A list containing: the summary parameters of the truncation distribution (dist), the estimated CMF of the truncation distribution (cmf, can be used to adjusted new data), a data frame containing the observed truncated data, latest observed data and the adjusted for truncation observations (obs), a data frame containing the last observed data (last_obs, useful for plotting and validation), the data used for fitting (data) and the fit object (fit).

Examples

# NOT RUN {
#set number of cores to use
options(mc.cores = ifelse(interactive(), 4, 1))
# get example case counts
reported_cases <- example_confirmed[1:60]

# define example truncation distribution (note not integer adjusted)
trunc_dist <- list(mean = convert_to_logmean(3, 2),
                   mean_sd = 0.1,
                   sd = convert_to_logsd(3, 2),
                   sd_sd = 0.1,
                   max = 10)

# apply truncation to example data
construct_truncation <- function(index, cases, dist) {
set.seed(index)
  cmf <- cumsum(
     dlnorm(1:(dist$max + 1), 
            rnorm(1, dist$mean, dist$mean_sd),
            rnorm(1, dist$sd, dist$sd_sd)))
  cmf <- cmf / cmf[dist$max + 1]
  cmf <- rev(cmf)[-1]
  trunc_cases <- data.table::copy(cases)[1:(.N - index)]
  trunc_cases[(.N - length(cmf) + 1):.N, confirm := as.integer(confirm * cmf)]
  return(trunc_cases)
 }
example_data <- purrr::map(c(20, 15, 10, 0), 
                           construct_truncation,
                           cases = reported_cases,
                           dist = trunc_dist)

# fit model to example data
est <- estimate_truncation(example_data, verbose = interactive(),
                           chains = 2, iter = 2000)
                           
# summary of the distribution
est$dist
# summary of the estimated truncation cmf (can be applied to new data)
print(est$cmf)
# observations linked to truncation adjusted estimates
print(est$obs)    
# validation plot of observations vs estimates
plot(est)
# }