Rtglm: Unifying estimation of the time-varying reproduction number, Rt, under the Generalised Linear and Additive Models

Abstract

Most current methods to estimate the time-varying reproduction number (R_t), such as EpiEstim, rely on branching processes and the renewal equation. They also require subjective choices to set the level of temporal and spatial heterogeneity assumed. We propose a novel framework to estimate R_t based on Generalized Linear and Additive Models (GLM/GAM). By integrating the renewal equation model within GLM/GAM, the proposed framework, “Rtglm”, allows smooth estimation of R_t variations over time and space without relying on arbitrary scaling parameters. The performance of Rtglm was evaluated using historical datasets and simulated outbreaks. It demonstrated improved overall performance and accuracy compared to EpiEstim, as measured by the CRPS scores and Mean Square Errors respectively. However, when case incidence was low and R_t estimation relied on a smoothing term, Rtglm was marginally overconfident in its estimates. The method offers substantial improvement for the real-time estimation of spatio-temporal trends in R_t, with improved performance and lower reliance on arbitrarily set parameters. The open-source and user-friendly R package developed will also simplify user experience. Finally, the framework bridges gaps between epidemic monitoring methodologies and sets the stage for future extensions to enhance statistical inference and integrate additional epidemiological complexities, including the evaluation of intervention strategies.