EpiLPS: A fast and flexible Bayesian tool for estimation of the time-varying reproduction number.
Oswaldo Gressani, Jacco Wallinga, Christian L Althaus, Niel Hens, Christel Faes
Author Information
Oswaldo Gressani: Interuniversity Institute for Biostatistics and statistical Bioinformatics (I-BioStat), Data Science Institute, Hasselt University, Hasselt, Belgium. ORCID
Jacco Wallinga: Centre for Infectious Disease Control, National Institute for Public Health and the Environment, Bilthoven, The Netherlands. ORCID
Christian L Althaus: Institute of Social and Preventive Medicine, University of Bern, Bern, Switzerland. ORCID
Niel Hens: Interuniversity Institute for Biostatistics and statistical Bioinformatics (I-BioStat), Data Science Institute, Hasselt University, Hasselt, Belgium. ORCID
Christel Faes: Interuniversity Institute for Biostatistics and statistical Bioinformatics (I-BioStat), Data Science Institute, Hasselt University, Hasselt, Belgium. ORCID
In infectious disease epidemiology, the instantaneous reproduction number [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] 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.
References
Proc Biol Sci. 2007 Feb 22;274(1609):599-604
[PMID: 17476782]
