Flexible Bayesian estimation of incubation times

Motivation The incubation period is of paramount importance in infectious disease epidemiology as it informs about the transmission potential of a pathogenic organism and helps to plan public health strategies to keep an epidemic outbreak under control. Estimation of the incubation period distribution from reported exposure times and symptom onset times is challenging as the underlying data is coarse. Methodology We develop a new Bayesian methodology using Laplacian-P-splines that provides a semi-parametric estimation of the incubation density based on a Langevinized Gibbs sampler. A finite mixture density smoother informs a set of parametric distributions via moment matching and an information criterion arbitrates between competing candidates. Results Our method has a natural nest within EpiLPS, a tool originally developed to estimate the time-varying reproduction number. Various simulation scenarios accounting for different levels of data coarseness are considered with encouraging results. Applications to real data on COVID-19, MERS-CoV and Mpox reveal results that are in alignment with what has been obtained in recent studies. Conclusion The proposed flexible approach is an interesting alternative to classic Bayesian parametric methods for estimation of the incubation distribution.