Abstract
The incubation period is of paramount importance in infectious disease epidemiology as it informs about the transmission potential of a pathogenic organism and helps the planning of 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. We developed a new Bayesian methodology using Laplacian-P-splines that provides a semiparametric 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. Algorithms underlying our method find a natural nest within the EpiLPS package, which has been extended to cover estimation of incubation times. Various simulation scenarios accounting for different levels of data coarseness are considered with encouraging results. Applications to real data on coronavirus disease 2019, Middle East respiratory syndrome, and Mpox reveal results that are in alignment with what has been obtained in recent studies. The proposed flexible approach is an interesting alternative to classic Bayesian parametric methods for estimation of the incubation distribution.