Spatiotemporal multivariate mixture models for Bayesian model selection in disease mapping

It is often the case that researchers wish to simultaneously explore the behavior of, and estimate the overall risk for, multiple related diseases with varying rarity while accounting for potential spatial and/or temporal correlation. In this paper, we propose a flexible class of multivariate spatiotemporal mixture models to fill this role. Further, these models offer flexibility with the potential for model selection as well as the ability to accommodate lifestyle, socioeconomic, and physical environmental variables with spatial, temporal, or both structures. Here, we explore the capability of this approach via a large‐scale simulation study and examine a motivating data example involving three cancers in South Carolina. The results, which are focused on four model variants, suggest that all models possess the ability to recover the simulation ground truth and display an improved model fit over two baseline Knorr‐Held spatiotemporal interaction model variants in a real data application.