Estimating the epidemic reproduction number from temporally aggregated incidence data: a statistical modelling approach and software tool

Background The time-varying reproduction number (Rt) is an important measure of epidemic transmissibility; it can directly inform policy decisions and the optimisation of control measures. EpiEstim is a widely used software tool that uses case incidence and the serial interval (SI, time between symptoms in a case and their infector) to estimate Rt in real-time. The incidence and the SI distribution must be provided at the same temporal resolution, which limits the applicability of EpiEstim and other similar methods, e.g. for pathogens with a mean SI shorter than the frequency of incidence reporting. Methods We use an expectation-maximisation algorithm to reconstruct daily incidence from temporally aggregated data, from which Rt can then be estimated using EpiEstim. We assess the validity of our method using an extensive simulation study and apply it to COVID-19 and influenza data. The method is implemented in the opensource R package EpiEstim. Findings For all datasets, the influence of intra-weekly variability in reported data was mitigated by using aggregated weekly data. Rt estimated on weekly sliding windows using incidence reconstructed from weekly data was strongly correlated with estimates from the original daily data. The simulation study revealed that Rt was well estimated in all scenarios and regardless of the temporal aggregation of the data. In the presence of weekend effects, Rt estimates from reconstructed data were more successful at recovering the true value of Rt than those obtained from reported daily data. Interpretation Rt can be successfully recovered from aggregated data, and estimation accuracy can even be improved by smoothing out administrative noise in the reported data. Funding MRC doctoral training partnership, MRC centre for global infectious disease analysis, the NIHR HPRU in Modelling and Health Economics, and the Academy of Medical Sciences Springboard, funded by the AMS, Wellcome Trust, BEIS, the British Heart Foundation and Diabetes UK.