Abstract
Conditional autoregressive models are typically used to capture the spatial autocorrelation present in areal unit disease count data when estimating the spatial pattern in disease risk. This correlation is represented by a binary neighbourhood matrix based on a border sharing specification, which enforces spatial correlation between geographically neighbouring areas. However, enforcing such correlation will mask any discontinuities in the disease risk surface, thus impeding the detection of clusters of areas that exhibit higher or lower risks compared to their neighbours. Here we propose novel methodology to account for these clusters and discontinuities in disease risk via a two-stage modelling approach, which either forces the clusters/discontinuities to be the same for all time periods or allows them to evolve dynamically over time. Stage one constructs a set of candidate neighbourhood matrices to represent a range of possible cluster/discontinuity structures in the data, and stage two estimates an appropriate structure(s) by treating the neighbourhood matrix as an additional parameter to estimate within a Bayesian spatio-temporal disease mapping model. The effectiveness of our novel methodology is evidenced by simulation, before being applied to a new study of respiratory disease risk in Greater Glasgow, Scotland from 2011 to 2017.