Practical considerations for measuring the effective reproductive number,R_t

Abstract

Estimation of the effective reproductive number, Rt, is important for detecting changes in disease transmission over time. During the COVID-19 pandemic, policymakers and public health officials are using Rt to assess the effectiveness of interventions and to inform policy. However, estimation of Rt from available data presents several challenges, with critical implications for the interpretation of the course of the pandemic. The purpose of this document is to summarize these challenges, illustrate them with examples from synthetic data, and, where possible, make methodological recommendations. For near real-time estimation of Rt, we recommend the approach of Cori et al. (2013), which uses data from before time t and empirical estimates of the distribution of time between infections. Methods that require data from after time t, such as Wallinga and Teunis (2004), are conceptually and methodologically less suited for near real-time estimation, but may be appropriate for some retrospective analyses. We advise against using methods derived from Bettencourt and Ribeiro (2008), as the resulting Rt estimates may be biased if the underlying structural assumptions are not met. A challenge common to all approaches is reconstruction of the time series of new infections from observations occurring long after the moment of transmission. Naive approaches for dealing with observation delays, such as subtracting delays sampled from a distribution, can introduce bias. We provide suggestions for how to mitigate this and other technical challenges and highlight open problems in Rt estimation.

Impact of COVID-19 epidemic curtailment strategies in selected Indian states: An analysis by reproduction number and doubling time with incidence modelling

“…The estimates might be influenced by certain effect modifiers and confounders like population density, climatic variations and violation of the assumption of random mixing. Conceptually, this phenomenon is dynamic and non-linear and hence should be read with caution [ 20 , 23 ]. The estimated transmission parameters (including doubling time during early outbreak period) in some states show a wider confidence interval with higher uncertainty.…”

Improved estimation of time-varying reproduction numbers at low case incidence and between epidemic waves

“…5. More involved analyses can be performed by pre-processing the data for known delays or case ascertainment fractions as in [12], [6]. We compute smoothed and filtered reproduction number estimates,R s andR s respectively, from the COVID-19 incidence curve for New Zealand (available at [39]).…”

“…The WT method reconstructs the average number of new cases caused by infectious individuals at s and so requires incidence data beyond time s for its estimate, which is called the case reproduction number. It is better suited for retrospective analyses [12]. Alternatively, EpiEstim infers how past infections propagate to form the incidence observed at s, only requiring data prior to time s. EpiEstim is preferred for real-time investigations and its R s estimate is termed the instantaneous reproduction number [3].…”

O potencial de propagação da COVID-19 e a tomada de decisão governamental: uma análise retrospectiva em Florianópolis, Brasil

“…Mathematical and statistical models have been increasingly used to assist in decision making and planning interventions to control epidemics [9][10][11] , including the pandemic caused by SARS-CoV-2 [12][13][14] . Recently, statistical estimators of the number of time-dependent reproductions (R t ) have been proposed based on a set of assumptions regarding the dynamics of epidemics 11,15,16 . These estimators offer an important contribution to the monitoring of disease coping efforts 17 .…”