Rt.GLM: 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 (Rt), 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 Rt based on Generalized Linear and Additive Models (GLM/GAM). By integrating the renewal equation model within GLM/GAM, the proposed framework, “Rt.glm”, allows smooth estimation of Rt variations over time and space without relying on arbitrary scaling parameters. The performance of Rt.glm 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 Rt estimation relied on a smoothing term, Rt.glm was marginally overconfident in its estimates. The method offers substantial improvement for the real-time estimation of spatio-temporal trends in Rt, 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. Highlights A novel framework is introduced to estimate Rt using GLM and GAM approaches. This allows smooth spatio-temporal estimation of Rt without predefined scales. Overall, it outperforms EpiEstim, with lower Mean Square Error and CRPS scores. An open-source, user-friendly R package is provided for real-time Rt estimation. This proof-of-concept provides a strong foundation for future developments. Competing Interest Statement The authors have declared no competing interest. Funding Statement OneBat through EU Horizon program (Grant agreement ID: 101095712) and Zoonotic influenza preparedness: a transdisciplinary One Health approach (ZIP) through UKRI. Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes Data Availability All data produced in the present study are available upon reasonable request to the authors