Bayesian tele-connected spatial clustering of multivariate spatial data with applications to disease-mapping.

Spatial clustering is crucial in disease mapping by identifying subregions with different patterns of disease incidence or mortality. This study proposes a novel Bayesian spatial clustering method for multivariate spatial disease data, which allows for understanding geographic variations of multivariate disease patterns while accounting for both spatial information and dependence among multiple disease measurements. We develop a new random tele-connected graph partition model with an unknown number of clusters, which is capable of encouraging locally contiguous clusters and allowing for remote subregions to be clustered together. We use this prior in a Bayesian hierarchical model to detect spatial clusters and estimate cluster-specific disease patterns and dependence across the multivariate disease variables. We develop a tailored Markov chain Monte Carlo (MCMC) algorithm for posterior inference, utilizing efficient doubly split-merge samplers taking advantage of graph algorithms. We illustrate our method with simulation studies and apply it to investigate the clustering patterns of county-level prostate cancer mortality rate decline across six southern U.S. states from 1985 to 2014.