A Bayesian space-time model for clustering areal units based on their disease trends

Population-level disease risk across a set of non-overlapping areal units varies in space and time, and a large research literature has developed methodology for identifying clusters of areal units exhibiting elevated risks. However, almost no research has extended the clustering paradigm to identify groups of areal units exhibiting similar temporal disease trends. We present a novel Bayesian hierarchical mixture model for achieving this goal, with inference based on a Metropolis coupled Markov chain Monte Carlo ((MC)3) algorithm. The effectiveness of the (MC)3 algorithm compared to a standard MCMC implementation is demonstrated in a simulation study, and the methodology is motivated by two important case studies in Scotland. The first concerns the impact on measles susceptibility of the discredited paper linking the Measles, Mumps and Rubella vaccination to an increased risk of Autism, and investigates whether all areas in Scotland were equally affected. The second concerns respiratory hospitalisations, and investigates over a 10 year period which parts of Glasgow have shown increased, decreased, and no change in risk.