Estimate seeding infections with a time-varying growth rate — seeding_estimate

This option estimates an exponential growth of infections at the start of the modeled time period, with the growth rate varying over time.

Usage

seeding_estimate_growth(
  intercept_prior_q5 = NULL,
  intercept_prior_q95 = NULL,
  growth_change_prior_mu = 0,
  growth_change_prior_sigma = 0.01,
  extend = TRUE,
  modeldata = modeldata_init()
)

Arguments

intercept_prior_q5: Prior (5% quantile) on the initial number of infections. Can be interpreted as an approximate lower bound. If NULL (default), this is computed from a crude empirical estimate of the number of cases (see details).
intercept_prior_q95: Prior (95% quantile) on the initial number of infections. Can be interpreted as an approximate upper bound. If NULL (default), this is computed from a crude empirical estimate of the number of cases (see details).
growth_change_prior_mu: Prior (mean) on the daily standard deviation of the random walk for the epidemic growth rate.
growth_change_prior_sigma: Prior (standard deviation) on the daily standard deviation of the random walk for the epidemic growth rate.
extend: Should the seeding phase be extended when concentrations are very low at the start of the measurement time series? If TRUE, then the seeding phase will be extended to the first date with three consecutive detects (i.e. non-zero measurements). Before that date, the reproduction number will be retrospectively computed based on the seeded infections. Explicit modeling of the Rt time series will only begin after the seeding phase. This option avoids sampling problems when estimating Rt from very low infection numbers during a period with many non-detects. Note that estimated reproduction numbers are not necessarily meaningful during periods with very low infection numbers, as transmission dynamics may be dominated by chance events and importations.
modeldata: A modeldata object to which the above model specifications should be added. Default is an empty model given by modeldata_init(). Can also be an already partly specified model returned by other EpiSewer modeling functions.

Value

A modeldata object containing data and specifications of the model to be fitted. Can be passed on to other EpiSewer modeling functions to add further data and model specifications.

The modeldata object also includes information about parameter initialization (.init), meta data (.metainfo), and checks to be performed before model fitting (.checks).

Details

The seeding phase has the length of the maximum generation time (during this time, the renewal model cannot be applied). It is here assumed that the expected number of new infections follows an exponential growth or decline process during this time period. The exponential growth rate of the seeding phase follows a random walk that ends with a growth rate representing the first estimated reproduction number at the start of the modeling phase. This means that the intercept of the seeding phase growth rate depends on the R_start_prior provided in the R_estimate_* component.

If the lower and upper intervals of the prior for the initial number of infections, i.e. intercept_prior_q5 or intercept_prior_q95 are not specified by the user, EpiSewer will compute a rough median empirical estimate of the number of cases using the supplied wastewater measurements and shedding assumptions, and then infer the missing quantiles based on this. If none of the quantiles are provided, they are set to be roughly 1/10 and 10 times the empirical median estimate. We note that this is a violation of Bayesian principles (data must not be used to inform priors) - but a neglectable one, since it only ensures that the seeding is modeled on the right order of magnitude and does not have relevant impacts on later Rt estimates.

The priors of this component have the following functional form:

initial number of infections (log scale): Normal
standard deviation of the random walk on the growth rate: Truncated normal

The priors for these parameters are determined based on the user-supplied arguments, using appropriate transformations and the two-sigma-rule of thumb.

Credits to Samuel Brand and the authors of the EpiAware toolkit for the idea to back-calculate the growth rate of the seeding phase from the initial reproduction number.