Skip to contents

Estimate Rt via a random walk

Source: R/model_infections.R
R_estimate_rw.Rd

This option estimates the effective reproduction number over time using a random walk.

Usage

R_estimate_rw(
  R_start_prior_mu = 1,
  R_start_prior_sigma = 0.8,
  sd_base_prior_mu = 0,
  sd_base_prior_sd = 0.025,
  sd_change_prior_shape = 0.5,
  sd_change_prior_scale = 1e-04,
  sd_change_distance = 7 * 26,
  link = "inv_softplus",
  R_max = 6,
  differenced = FALSE,
  noncentered = TRUE,
  modeldata = modeldata_init()
)

Arguments

R_start_prior_mu

Prior (mean) on the initial value of Rt.

R_start_prior_sigma

Prior (standard deviation) on the initial value of Rt.

sd_base_prior_mu

Prior (mean) on the baseline standard deviation of the innovations. Please note that for consistency, the overall standard deviation of innovations will always be the baseline plus an additive component from sd_change_prior even if no changepoints are modeled (see below).

sd_base_prior_sd

Prior (standard deviation) on the baseline standard deviation of the innovations. See sd_base_prior_mu for details.

sd_change_prior_shape

Exponential-Gamma prior (shape) on standard deviation additional to baseline. This prior describes the distribution of the standard deviation of Rt over time. EpiSewer will estimate a baseline standard deviation (see sd_base_prior_sd), and model additional variation on top of the baseline using a changepoint model. Please see the details for more explanation.

sd_change_prior_scale

Exponential-Gamma prior (scale) on standard deviation additional to baseline. See sd_change_prior_shape and the details for more explanation.

sd_change_distance

Distance between changepoints used to model additional variation in Rt. The default change point distance is 4 weeks. Very short changepoint distances must be chosen with care, as they can make the Rt time series too flexible. If set to zero, no change points are modeled.

Link function. Currently supported are inv_softplus (default) and scaled_logit. Both of these links are configured to behave approximately like the identity function around R=1, but become increasingly non-linear below (and in the case of scaled_logit also above) R=1.

R_max

If link=scaled_logit is used, a maximum reproduction number must be assumed. This should be higher than any realistic R value for the modeled pathogen. Default is 6.

differenced

If FALSE (default), the random walk is applied to the absolute Rt time series. If TRUE, it is instead applied to the differenced time series, i.e. now the trend is modeled as a random walk.

noncentered

If TRUE (default), a non-centered parameterization is used to model the innovations of the random walk (for better sampling efficiency).

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 smoothness of Rt estimates is influenced by the prior on the standard deviation of the random walk. It also influences the uncertainty of Rt estimates towards the present / date of estimation, when limited data signal is available. The prior on the intercept of the random walk should reflect your expectation of Rt at the beginning of the time series. If estimating from the start of an epidemic, you might want to use a prior with mean > 1 for the intercept.

The variability of Rt can change over time. For example, during the height of an epidemic wave, countermeasures may lead to much faster changes in Rt than observable at other times (baseline). This potential additional variability is accounted for using change points placed at regular intervals. The additional standard deviation of the state space model innovations on top of the baseline then evolves linearly between the change points. The additional variation defined at the changepoints is modeled as independently distributed and following a Lomax distribution, also known as Exponential-Gamma (EG) distribution. This is an exponential distribution where the rate is Gamma distributed. The prior sd_change_prior defines the shape and scale of this Gamma distribution. The distribution has a strong peak towards zero and a long tail. This regularizes the estimated deviations from the baseline standard deviation - most deviations are small, but during special time periods, the deviation might also be larger.

The priors of this component have the following functional form:

  • intercept of the random walk: Normal

  • baseline standard deviation of the random walk: Half-normal

  • additional standard deviation at changepoints: Exponential-Gamma

See also

Other Rt models: R_estimate_approx(), R_estimate_changepoint_splines(), R_estimate_ets(), R_estimate_gp(), R_estimate_piecewise(), R_estimate_smooth_derivative(), R_estimate_splines()