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 socio-demographic and behavioral factors, and environmental exposures on time-to-events 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 known explanatory variables, the hazard function maybe subject to spatial/geographical variations, such that proximally located regions may experience similar hazards than regions that are distantly located. A popular approach for handling this type of spatially-correlated time-to-event data is the Cox's Proportional Hazards (PH) regression model with spatial frailties. However, the PH 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 (AH) with spatial frailties. Our proposed model allows both the frailties as well as 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 dataset on prostate cancer survival from the US state of Louisiana to illustrate its advantages.