Title: Identifying Boundaries in Spatial Modelling for Disease Mapping
Abstract: The aim of disease mapping is to estimate the spatial pattern in disease risk across a set of areal units, in order to identify units which have elevated disease risk. Existing methods use Bayesian hierarchical models with spatially smooth conditional autoregressive priors to estimate disease risk, but these methods cannot identify the geographical extent of spatially contiguous high-risk clusters of areal units. We propose a two stage approach, which first produces a set of potential cluster structures for the data and then chooses the optimal structure by fitting an extension of the Bayesian hierarchical model. The first stage uses a hierarchical agglomerative clustering algorithm, spatially adjusted to account for the neighbourhood structure of the data. This algorithm is applied to data prior to the study period, and produces a set of n potential cluster structures. The second stage fits a Poisson log-linear model to the data, in which the optimal cluster structure and the spatial pattern in disease risk is estimated via a Markov Chain Monte Carlo (MCMC) algorithm. After assessing the methodology with a simulation study, it was applied to a study of respiratory disease risk in Glasgow, Scotland, where a number of high risk clusters were identified.