Bayesian spatio-temporal survival analysis for all types of censoring with application to a wildlife disease study

In this article, we consider modeling arbitrarily censored survival data with spatio-temporal covariates. We demonstrate that under the piecewise constant hazard function, the likelihood for uncensored or right-censored subjects is proportional to the likelihood of multiple conditionally independent Poisson random variables. To address left- or interval-censored subjects, we propose to impute the exact event times and convert them into uncensored subjects, enabling the application of the integrated nested Laplace approximation to update model parameters using the imputed data. We introduce an iterative algorithm that alternates between imputing event times for left- and interval-censored subjects and re-estimating model parameters. The proposed method is assessed through a simulation study and applied to analyze a spatio-temporal survival dataset in a wildlife disease study investigating bovine tuberculosis in white-tailed deer in Michigan.