Estimate Rt using an approximation of the generative renewal model

This option estimates the effective reproduction number Rt using an approximation of the generative renewal model. It can be considerably faster than the fully generative options, but is often less exact. It is recommended to check the results of this method against a fully generative version like R_estimate_splines() before using it for real-time R estimation. See the details for an explanation of the method and its limitations.

Usage

R_estimate_approx(
  inf_sd_prior_mu = 0.05,
  inf_sd_prior_sigma = 0.025,
  inf_smooth = 0.75,
  inf_trend_smooth = 0.75,
  inf_trend_dampen = 0.9,
  knot_distance = 7,
  spline_degree = 3,
  R_window = 1,
  modeldata = modeldata_init()
)

Arguments

inf_sd_prior_mu

Prior (mean) on the standard deviation of daily changes in infections. Infection numbers are modeled on the log scale, thus the standard deviation can be roughly interpreted in terms of percentage changes. A higher standard deviation will lead to more volatile infections and more uncertainty in R estimates. The default (inf_sd_prior_mu = 0.05) allows daily growth/decline rates of up +-10%. We suggest to only decrease this if you are very certain that the modeled scenario has lower maximum growth/decline rates, and to increase this if you expect a more extreme scenario. Note that the smoothness of the infection curve is also influenced by the exponential smoothing parameters (inf_smooth, inf_trend_smooth). Still, inf_sd_prior_mu is the primary hyperparameter to adjust if you think the estimated infection trajectory is too volatile / not flexible enough.

inf_sd_prior_sigma

Prior (standard deviation) on standard deviation of daily changes of infections. This reflects uncertainty around inf_sd_prior_mu. The default (inf_sd_prior_mu=0.025) allows the standard deviation to be roughly 0.5 higher or lower than inf_sd_prior_mu. For the default setting with inf_sd_prior_mu = 0.05, this means that growth/decline rates of up to +-20% are still supported by the prior.

inf_smooth

Smoothing parameter (alpha) for infections. The infection time series is smoothed based on earlier time steps, with exponentially decaying weights, as controlled by the alpha parameter. The default is 0.5, smaller values will lead to stronger smoothing, and larger values to less smoothing.

inf_trend_smooth

Trend smoothing parameter (beta) for infections. The exponential trend in infections is also smoothed based on the trend over earlier time steps, with exponentially decaying weights, as controlled by the beta parameter. Default is 0.5, smaller values will lead to stronger smoothing of the trend (useful for longer generation times), and larger values to less smoothing of the trend (useful for shorter generation times).

inf_trend_dampen

Trend dampening parameter (phi) for infections. The exponential trend in infections is dampened over time (exponential growth will not continue for ever). This mainly influences the trend towards the present. For the default value (0.9), the trend will only roughly half as strong after two weeks. Note that increasing phi to close to 1 can reduce sampling speed.

knot_distance

The infection time series is smoothed using penalized B-splines. The distance between spline breakpoints (knots) is 7 days by default. Placing knots further apart increases the smoothness of the infection time series and can speed up model fitting. Placing knots closer to each other increases the volatility of the infections. Note however that the uncertainty of R estimates produced by R_estimate_approx() is also sensitive to the smoothness of the infection time series, i.e. changing the knot distance can make the R estimates appear more or less uncertain. This effect is however rather small since the regularization of the spline coefficients adjusts for the knot distance.

spline_degree

Degree of the spline polynomials (default is 3 for cubic splines).

R_window

Smoothing window size for R estimates. Default is 1 (i.e. no smoothing). This is provided for compatibility with the EpiEstim method by Cori et al., which assumes that R stays constant over a certain time window. However, this can artificially reduce the uncertainty of the R estimates and is therefore generally not recommended. It also means that R cannot be estimated up to the present because the smoothing window must be centered.

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

This method uses an approximation of the renewal model to estimate the effective reproduction number. Instead of generating the infections through a renewal process, the infection time series is estimated using a non-parametric smoothing prior that mimics the characteristics of a renewal process. Rt is then computed from the infection time series by applying the classical renewal equation. This still gives Bayesian estimates of Rt and the infection time series, but is less exact than a fully generative model.

To smooth the infection time series, penalized B-splines similar to the ones in R_estimate_splines() are used, but they are applied to the expected number of infections on the log scale, not Rt. The spline coefficients are themselves smoothed using an exponential smoothing prior with a trend component. The trend component is important as it reflects the default assumption of constant transmission dynamics that leads to exponential growth in infections. This ensures consistent results of R_estimate_approx() also towards the present.

The method can also model infection noise as specified by infection_noise_estimate(). To account for the autocorrelation of infection noise, a correction that applies the renewal model specifically to the noise component is used. This correction is most accurate when R is close to 1 and less accurate when it is far from 1.

The main limitation of R_estimate_approx() is that its priors and hyperparameters are less interpretable and thus difficult to specify. In particular the assumed generation time distribution is only used for R estimation but does not inform the smoothness of the expected infection time series. Instead, the smoothness is determined by the spline settings and exponential smoothing parameters, which are difficult to translate into a generation time assumption. The best approach is therefore to compare estimates from R_estimate_approx() with those from another method like R_estimate_splines() for a pathogen of interest and to carefully adjust the smoothing hyperparameters if needed.

See also

Other Rt models: R_estimate_ets(), R_estimate_rw(), R_estimate_splines()