# Estimate a Secondary Observation from a Primary Observation

Source:`R/estimate_secondary.R`

`estimate_secondary.Rd`

Estimates the relationship between a primary and secondary observation, for
example hospital admissions and deaths or hospital admissions and bed
occupancy. See `secondary_opts()`

for model structure options. See parameter
documentation for model defaults and options. See the examples for case
studies using synthetic data and
here
for an example of forecasting Covid-19 deaths from Covid-19 cases. See
here for
a prototype function that may be used to estimate and forecast a secondary
observation from a primary across multiple regions and
here # nolint
for an application forecasting Covid-19 deaths in Germany and Poland.

## Usage

```
estimate_secondary(
reports,
secondary = secondary_opts(),
delays = delay_opts(dist_spec(mean = 2.5, mean_sd = 0.5, sd = 0.47, sd_sd = 0.25, max =
30)),
truncation = trunc_opts(),
obs = obs_opts(),
burn_in = 14,
CrIs = c(0.2, 0.5, 0.9),
priors = NULL,
model = NULL,
weigh_delay_priors = FALSE,
verbose = interactive(),
...
)
```

## Arguments

- reports
A data frame containing the

`date`

of report and both`primary`

and`secondary`

reports.- secondary
A call to

`secondary_opts()`

or a list containing the following binary variables: cumulative, historic, primary_hist_additive, current, primary_current_additive. These parameters control the structure of the secondary model, see`secondary_opts()`

for details.- delays
A call to

`delay_opts()`

defining delay distributions between primary and secondary observations See the documentation of`delay_opts()`

for details. By default a diffuse prior is assumed with a mean of 14 days and standard deviation of 7 days (with a standard deviation of 0.5 and 0.25 respectively on the log scale).- truncation
A call to

`trunc_opts()`

defining the truncation of observed data. Defaults to`trunc_opts()`

. See`estimate_truncation()`

for an approach to estimating truncation from data.- obs
A list of options as generated by

`obs_opts()`

defining the observation model. Defaults to`obs_opts()`

.- burn_in
Integer, defaults to 14 days. The number of data points to use for estimation but not to fit to at the beginning of the time series. This must be less than the number of observations.

- CrIs
Numeric vector of credible intervals to calculate.

- priors
A

`data.frame`

of named priors to be used in model fitting rather than the defaults supplied from other arguments. This is typically useful if wanting to inform an estimate from the posterior of another model fit.- model
A compiled stan model to override the default model. May be useful for package developers or those developing extensions.

- weigh_delay_priors
Logical. If TRUE, all delay distribution priors will be weighted by the number of observation data points, in doing so approximately placing an independent prior at each time step and usually preventing the posteriors from shifting. If FALSE (default), no weight will be applied, i.e. delay distributions will be treated as a single parameters.

- verbose
Logical, should model fitting progress be returned. Defaults to

`interactive()`

.- ...
Additional parameters to pass to

`rstan::sampling`

.

## Value

A list containing: `predictions`

(a data frame ordered by date with
the primary, and secondary observations, and a summary of the model
estimated secondary observations), `posterior`

which contains a summary of
the entire model posterior, `data`

(a list of data used to fit the
model), and `fit`

(the `stanfit`

object).

## Examples

```
# \donttest{
# set number of cores to use
old_opts <- options()
options(mc.cores = ifelse(interactive(), 4, 1))
# load data.table for manipulation
library(data.table)
#### Incidence data example ####
# make some example secondary incidence data
cases <- example_confirmed
cases <- as.data.table(cases)[, primary := confirm]
# Assume that only 40 percent of cases are reported
cases[, scaling := 0.4]
#> date confirm primary scaling
#> 1: 2020-02-22 14 14 0.4
#> 2: 2020-02-23 62 62 0.4
#> 3: 2020-02-24 53 53 0.4
#> 4: 2020-02-25 97 97 0.4
#> 5: 2020-02-26 93 93 0.4
#> ---
#> 126: 2020-06-26 296 296 0.4
#> 127: 2020-06-27 255 255 0.4
#> 128: 2020-06-28 175 175 0.4
#> 129: 2020-06-29 174 174 0.4
#> 130: 2020-06-30 126 126 0.4
# Parameters of the assumed log normal delay distribution
cases[, meanlog := 1.8][, sdlog := 0.5]
#> date confirm primary scaling meanlog sdlog
#> 1: 2020-02-22 14 14 0.4 1.8 0.5
#> 2: 2020-02-23 62 62 0.4 1.8 0.5
#> 3: 2020-02-24 53 53 0.4 1.8 0.5
#> 4: 2020-02-25 97 97 0.4 1.8 0.5
#> 5: 2020-02-26 93 93 0.4 1.8 0.5
#> ---
#> 126: 2020-06-26 296 296 0.4 1.8 0.5
#> 127: 2020-06-27 255 255 0.4 1.8 0.5
#> 128: 2020-06-28 175 175 0.4 1.8 0.5
#> 129: 2020-06-29 174 174 0.4 1.8 0.5
#> 130: 2020-06-30 126 126 0.4 1.8 0.5
# Simulate secondary cases
cases <- simulate_secondary(cases, type = "incidence")
#
# fit model to example data specifying a weak prior for fraction reported
# with a secondary case
inc <- estimate_secondary(cases[1:60],
obs = obs_opts(scale = list(mean = 0.2, sd = 0.2), week_effect = FALSE)
)
plot(inc, primary = TRUE)
# forecast future secondary cases from primary
inc_preds <- forecast_secondary(
inc, cases[seq(61, .N)][, value := primary]
)
plot(inc_preds, new_obs = cases, from = "2020-05-01")
#### Prevalence data example ####
# make some example prevalence data
cases <- example_confirmed
cases <- as.data.table(cases)[, primary := confirm]
# Assume that only 30 percent of cases are reported
cases[, scaling := 0.3]
#> date confirm primary scaling
#> 1: 2020-02-22 14 14 0.3
#> 2: 2020-02-23 62 62 0.3
#> 3: 2020-02-24 53 53 0.3
#> 4: 2020-02-25 97 97 0.3
#> 5: 2020-02-26 93 93 0.3
#> ---
#> 126: 2020-06-26 296 296 0.3
#> 127: 2020-06-27 255 255 0.3
#> 128: 2020-06-28 175 175 0.3
#> 129: 2020-06-29 174 174 0.3
#> 130: 2020-06-30 126 126 0.3
# Parameters of the assumed log normal delay distribution
cases[, meanlog := 1.6][, sdlog := 0.8]
#> date confirm primary scaling meanlog sdlog
#> 1: 2020-02-22 14 14 0.3 1.6 0.8
#> 2: 2020-02-23 62 62 0.3 1.6 0.8
#> 3: 2020-02-24 53 53 0.3 1.6 0.8
#> 4: 2020-02-25 97 97 0.3 1.6 0.8
#> 5: 2020-02-26 93 93 0.3 1.6 0.8
#> ---
#> 126: 2020-06-26 296 296 0.3 1.6 0.8
#> 127: 2020-06-27 255 255 0.3 1.6 0.8
#> 128: 2020-06-28 175 175 0.3 1.6 0.8
#> 129: 2020-06-29 174 174 0.3 1.6 0.8
#> 130: 2020-06-30 126 126 0.3 1.6 0.8
# Simulate secondary cases
cases <- simulate_secondary(cases, type = "prevalence")
# fit model to example prevalence data
prev <- estimate_secondary(cases[1:100],
secondary = secondary_opts(type = "prevalence"),
obs = obs_opts(
week_effect = FALSE,
scale = list(mean = 0.4, sd = 0.1)
)
)
plot(prev, primary = TRUE)
# forecast future secondary cases from primary
prev_preds <- forecast_secondary(
prev, cases[seq(101, .N)][, value := primary]
)
plot(prev_preds, new_obs = cases, from = "2020-06-01")
options(old_opts)
# }
```