EpiLPS: A fast and flexible Bayesian tool for estimation of the time-varying reproduction number

• Published in: PLoS computational biology Vol. 18; no. 10; p. e1010618
• Main Authors: Gressani, Oswaldo, Wallinga, Jacco, Althaus, Christian L, Hens, Niel, Faes, Christel
• Format: Journal Article
• Language: English
• Published: San Francisco Public Library of Science 10.10.2022; Public Library of Science (PLoS)
• Subjects: Analysis; Approximation; Bayesian analysis; Bayesian statistical decision theory; Binomial distribution; Chain dynamics; Epidemics; Epidemiology; Estimates; Fines & penalties; Infectious diseases; Influenza A; Markov chains; Markov processes; Mathematical models; Medicine and Health Sciences; Methods; Monte Carlo method; Pandemics; Parameters; Physical Sciences; Public health; Reproduction; Research and Analysis Methods; Severe acute respiratory syndrome coronavirus 2; Smoothing; Spline functions; Time series; Viral diseases
• ISSN: 1553-7358; 1553-734X; 1553-7358
• DOI: 10.1371/journal.pcbi.1010618

In infectious disease epidemiology, the instantaneous reproduction number R t is a time-varying parameter defined as the average number of secondary infections generated by an infected individual at time t . It is therefore a crucial epidemiological statistic that assists public health decision makers in the management of an epidemic. We present a new Bayesian tool (EpiLPS) for robust estimation of the time-varying reproduction number. The proposed methodology smooths the epidemic curve and allows to obtain (approximate) point estimates and credible intervals of R t by employing the renewal equation, using Bayesian P-splines coupled with Laplace approximations of the conditional posterior of the spline vector. Two alternative approaches for inference are presented: (1) an approach based on a maximum a posteriori argument for the model hyperparameters, delivering estimates of R t in only a few seconds; and (2) an approach based on a Markov chain Monte Carlo (MCMC) scheme with underlying Langevin dynamics for efficient sampling of the posterior target distribution. Case counts per unit of time are assumed to follow a negative binomial distribution to account for potential overdispersion in the data that would not be captured by a classic Poisson model. Furthermore, after smoothing the epidemic curve, a “plug-in’’ estimate of the reproduction number can be obtained from the renewal equation yielding a closed form expression of R t as a function of the spline parameters. The approach is extremely fast and free of arbitrary smoothing assumptions. EpiLPS is applied on data of SARS-CoV-1 in Hong-Kong (2003), influenza A H1N1 (2009) in the USA and on the SARS-CoV-2 pandemic (2020-2021) for Belgium, Portugal, Denmark and France.