Estimate seeding infections using a random walk model — seeding_estimate

This option estimates initial infections at the start of the modeled time period, when the renewal model cannot be applied yet. It uses a geometric random walk to model these seeding infections.

Usage

seeding_estimate_rw(
  intercept_prior_q5 = NULL,
  intercept_prior_q95 = NULL,
  rel_change_prior_mu = 0.05,
  rel_change_prior_sigma = 0.025,
  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).
rel_change_prior_mu: Prior (mean) on the relative change rate of the geometric random walk during the seeding phase. The default value (0.05) assumes that daily changes are +-5% on expectation and likely less than +-10% per day.
rel_change_prior_sigma: Prior (standard deviation) on the relative change rate of the geometric random walk during the seeding phase. This expresses your uncertainty about the change rate. The default value (0.025) assumes that the daily change rate could be 5% points higher or lower than your prior mean. For example, if rel_change_prior_mu = 0.05 and rel_change_prior_sigma = 0.025, this means you expect the daily change rate to be between 0 (0%) and 0.1 (10%).
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). The reproduction number will only be modeled from that date onward. This option often makes sense, as infection numbers are typically very low during a period with many non-detects, which can lead to sampling problems when estimating Rt. If you nevertheless want Rt estimates also for this period, you can use extend = FALSE. Note though 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). Traditionally, seeding refers to the first few (potentially imported) infections of an epidemic, but depending on what time period the model is fitted to, this may also cover a different phase with stronger growth dynamics.

If 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:

intercept of the random walk (log scale): Normal
standard deviation of the random walk (log scale): 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.