Refining reproduction number estimates to account for unobserved generations of infection in emerging epidemics

Background Estimating the transmissibility of infectious diseases is key to inform situational awareness and for response planning. Several methods tend to overestimate the basic (R 0 ) and effective (R t ) reproduction numbers during the initial phases of an epidemic. The reasons driving the observed bias are unknown. In this work we explore the impact of incomplete observations and underreporting of the first generations of infections during the initial epidemic phase. Methods We propose a debiasing procedure which utilises a linear exponential growth model to infer unobserved initial generations of infections and apply it to EpiEstim. We assess the performance of our adjustment using simulated data, considering different levels of transmissibility and reporting rates. We also apply the proposed correction to SARS-CoV-2 incidence data reported in Italy, Sweden, the United Kingdom and the United States of America. Results In all simulation scenarios, our adjustment outperforms the original EpiEstim method. The proposed correction reduces the systematic bias and the quantification of uncertainty is more precise, as better coverage of the true R 0 values is achieved with tighter credible intervals. When applied to real world data, the proposed adjustment produces basic reproduction number estimates which closely match the estimates obtained in other studies while making use of a minimal amount of data. Conclusions The proposed adjustment refines the reproduction number estimates obtained with the current EpiEstim implementation by producing improved, more precise estimates earlier than with the original method. This has relevant public health implications. Summary We propose a back-imputation procedure tackling the issue of unobserved initial generations of infections to reduce the bias observed in the early R 0 and R t estimates and apply it to EpiEstim using simulated and reported COVID-19 data to evaluate it.