Bayesian inference in time‐varying additive hazards models with applications to disease mapping

Environmental health and disease mapping studies are often concerned with the evaluation of the combined effect of various sociodemographic and behavioral factors, and environmental exposures, on time‐to‐event outcomes of interest, such as death of individuals, organisms, or plants. In such studies, estimation of the hazard function is often of interest. In addition to the known explanatory variables, the hazard function may be subject to spatial/geographical variations, such that proximally located regions may experience hazards similar to those of regions that are distantly located. A popular approach for handling this type of spatially correlated time‐to‐event data is the Cox proportional hazards regression model with spatial frailties. However, the proportional hazards assumption poses a major practical challenge, as it entails that the effects of the various explanatory variables remain constant over time. This assumption is often unrealistic, for instance, in studies with long follow‐ups where the effects of some exposures on the hazard may vary drastically over time. Our goal in this paper is to offer a flexible semiparametric additive hazards model with spatial frailties. Our proposed model allows both the frailties and the regression coefficients to be time varying, thus relaxing the proportionality assumption. Our estimation framework is Bayesian, powered by carefully tailored posterior sampling strategies via Markov chain Monte Carlo techniques. We apply the model to a data set on prostate cancer survival from the U.S. state of Louisiana to illustrate its advantages.