Estimate Truncation of Observed Data

Estimates a truncation distribution from multiple snapshots of the same data source over time. This distribution can then be used passed to the truncation argument in regional_epinow(), epinow(), and estimate_infections() to adjust for truncated data and propagate the uncertainty associated with data truncation into the estimates.

See here for an example of using this approach on Covid-19 data in England. The functionality offered by this function is now available in a more principled manner in the epinowcast R package.

The model of truncation is as follows:

The truncation distribution is assumed to be discretised log normal wit a mean and standard deviation that is informed by the data.
The data set with the latest observations is adjusted for truncation using the truncation distribution.
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 with an additive noise term to deal with zero observations.

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

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(
  data,
  truncation = trunc_opts(LogNormal(meanlog = Normal(0, 1), sdlog = Normal(1, 1), max =
    10)),
  stan = stan_opts(),
  CrIs = c(0.2, 0.5, 0.9),
  filter_leading_zeros = FALSE,
  zero_threshold = Inf,
  verbose = TRUE,
  ...
)

Arguments

data: A list of <data.frame>s each containing a date variable and a confirm (numeric) variable. Each data set should be a snapshot of the reported data over time. All data sets must contain a complete vector of dates.
truncation: A call to trunc_opts() defining the truncation of the observed data. Defaults to trunc_opts(), i.e. no truncation. See the estimate_truncation() help file for an approach to estimating this from data where the dist list element returned by estimate_truncation() is used as the truncation argument here, thereby propagating the uncertainty in the estimate.
stan: A list of stan options as generated by stan_opts(). Defaults to stan_opts(). Can be used to override data, init, and verbose settings if desired.
CrIs: Numeric vector of credible intervals to calculate.
filter_leading_zeros: Logical, defaults to FALSE. Should zeros at the start of the time series be filtered out.
zero_threshold: Numeric defaults to Inf. Indicates if detected zero cases are meaningful by using a threshold number of cases based on the 7-day average. If the average is above this threshold then the zero is replaced using fill.
verbose: Logical, should model fitting progress be returned.
...: Additional parameters to pass to rstan::sampling().

Value

An <estimate_truncation> object containing:

observations: The input data (list of <data.frame>s).
args: A list of arguments used for fitting (stan data).
fit: The stan fit object.

Examples

# \donttest{
# set number of cores to use
old_opts <- options()
options(mc.cores = ifelse(interactive(), 4, 1))

# fit model to example data
# See [example_truncated] for more details
# iterations and calculation time have been reduced for this example
# for real analyses, use more
est <- estimate_truncation(example_truncated,
  verbose = interactive(),
  chains = 2, iter = 200
)

# extract the estimated truncation distribution
get_parameters(est)[["truncation"]]
#> - lognormal distribution (max: 10):
#>   meanlog:
#>     - normal distribution:
#>       mean:
#>         0.9
#>       sd:
#>         0.005
#>   sdlog:
#>     - normal distribution:
#>       mean:
#>         0.6
#>       sd:
#>         0.007
# summarise the truncation distribution parameters
summary(est)
#> Truncation distribution: lognormal (max: 10) 
#> 
#> Parameter estimates:
#>    variable    median      mean          sd  lower_90  lower_50  lower_20
#>      <char>     <num>     <num>       <num>     <num>     <num>     <num>
#> 1:  meanlog 0.9008178 0.9007605 0.005458562 0.8920170 0.8970814 0.8994484
#> 2:    sdlog 0.5994500 0.5995709 0.006840967 0.5884631 0.5948740 0.5977749
#>     upper_20  upper_50  upper_90
#>        <num>     <num>     <num>
#> 1: 0.9022168 0.9045303 0.9098537
#> 2: 0.6010510 0.6038428 0.6109858
# validation plot of observations vs estimates
plot(est)
#> Ignoring unknown labels:
#> • fill : "Type"


# Pass the truncation distribution to `epinow()`.
# Note, we're using the last snapshot as the observed data as it contains
# all the previous snapshots. Also, we're using the default options for
# illustrative purposes only.
out <- epinow(
  generation_time = generation_time_opts(example_generation_time),
  example_truncated[[5]],
  truncation = trunc_opts(get_parameters(est)[["truncation"]])
)
#> Logging threshold set at INFO for the name logger
#> Writing EpiNow2 logs to the console and:
#> /tmp/RtmpLHqUKz/regional-epinow/2020-04-21.log.
#> Logging threshold set at INFO for the name logger
#> Writing EpiNow2.epinow logs to the console and:
#> /tmp/RtmpLHqUKz/epinow/2020-04-21.log.
#> WARN [2026-02-10 19:27:37] 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 [2026-02-10 19:27:37] epinow: Examine the pairs() plot to diagnose sampling problems
#>  - 
plot(out)

options(old_opts)
# }

Usage

Arguments

Value

See also

Examples