Explicit Modeling of Correlation Structure For Bayesian Analysis of Spatial Survival Data: Estimating the Relative Risk of Prostate Cancer Patients

Models with spatial stochastic effects are commonly used to model the relationship between response variables and spatially dependent observations and explanatory variables. In many applications, some models' explanatory variables are dependent. Depending on the type of dependence, the statistical inference of the models with random effects and their applications are complicated; because the explanatory variables, random effects, and model error expression compete with each other in explaining the variability of the response variable.In this paper, a method for modeling and analyzing spatial survival data is proposed to solve this problem. Instead of using spatial stochastic effects in the model, the spatial dependence of observations is explicitly included in density, survival, and hazard functions. Then, in a simulation study, the effects of explanatory variables in the model are calculated and evaluated using the comparative Metropolis-Hastings algorithm. The proposed method is then used to analyze patients' data with prostate cancer, and the Bayesian approach is used to estimate the relative death risk of patients. Finally, a discussion and conclusion will be presented.