Risk estimation and boundary detection in Bayesian disease mapping

Bayesian hierarchical models with a spatially smooth conditional autoregressive prior distribution are commonly used to estimate the spatio-temporal pattern in disease risk from areal unit data. However, most of the modeling approaches do not take possible boundaries of step changes in disease risk between geographically neighbouring areas into consideration, which may lead to oversmoothing of the risk surfaces, prevent the detection of high-risk areas and yield biased estimation of disease risk. In this paper, we propose a two-stage method to jointly estimate the disease risk in small areas over time and detect the locations of boundaries that separate pairs of neighbouring areas exhibiting vastly different risks. In the first stage, we use a graph-based optimisation algorithm to construct a set of candidate neighbourhood matrices that represent a range of possible boundary structures for the disease data. In the second stage, a Bayesian hierarchical spatio-temporal model that takes the boundaries into account is fitted to the data. The performance of the methodology is evidenced by simulation, before being applied to a study of respiratory disease risk in Greater Glasgow, Scotland.