In epidemiological disease mapping one aims to estimate the spatio-temporal pattern in disease risk and identify high-risk clusters, allowing health interventions to be appropriately targeted. Bayesian spatio-temporal models are used to estimate smoothed risk surfaces, but this is contrary to the aim of identifying groups of areal units that exhibit elevated risks compared with their neighbours. Therefore, in this paper we propose a new Bayesian hierarchical modelling approach for simultaneously estimating disease risk and identifying high-risk clusters in space and time. Inference for this model is based on Markov chain Monte Carlo simulation, using the freely available R package CARBayesST that has been developed in conjunction with this paper. Our methodology is motivated by two case studies, the first of which assesses if there is a relationship between Public health Districts and colon cancer clusters in Georgia, while the second looks at the impact of the smoking ban in public places in England on cardiovascular disease clusters.
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