Practical considerations for measuring the effective reproductive number, R(t)

Gostic, Katelyn M.; McGough, Lauren; Baskerville, Edward B.; Abbott, Sam; Joshi, Keya; Tedijanto, Christine; Kahn, Rebecca; Niehus, Rene; Hay, James A.; De Salazar, Pablo M.; Hellewell, Joel; Meakin, Sophie; Munday, James D.; Bosse, Nikos I.; Sherrat, Katharine; Thompson, Robin N.; White, Laura F.; Huisman, Jana S.; Scire, Jérémie; Bonhoeffer, Sebastian; Stadler, Tanja; Wallinga, Jacco; Funk, Sebastian; Lipsitch, Marc; Cobey, Sarah

Estimation of the effective reproductive number R(t) is important for detecting changes in disease transmission over time. During the Coronavirus Disease 2019 (COVID-19) pandemic, policy makers and public health officials are using R(t) to assess the effectiveness of interventions and to inform policy. However, estimation of R(t) 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 recommendations. For near real-time estimation of R(t), we recommend the approach of Cori and colleagues, 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, are conceptually and methodologically less suited for near real-time estimation, but may be appropriate for retrospective analyses of how individuals infected at different time points contributed to the spread. We advise caution when using methods derived from the approach of Bettencourt and Ribeiro, as the resulting R(t) estimates may be biased if the underlying structural assumptions are not met. Two key challenges common to all approaches are accurate specification of the generation interval and 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 R(t) estimation.