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. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement This work was supported by the ESCAPE project (101095619) and the VERDI project (101045989), funded by the European Union. Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the Health and Digital Executive Agency (HADEA). Neither the European Union nor the granting authority can be held responsible for them. ### 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I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the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