Risk estimation and discontinuity identification in Bayesian disease mapping

Disease mapping is the field of epidemiology that estimates the spatial or spatio-temporal pattern in disease risk. Approaches in this field are generally based on data collected on a set of non-overlapping areal units that comprise the study region, and typically utilise counts of the numbers of disease cases within each areal unit. Conditional autoregressive (CAR) models are commonly used to capture the spatial autocorrelation present in areal unit disease count data. The spatial correlation structure that is induced by these models is typically determined by a neighbourhood matrix based on geographical adjacency, which enforces spatial correlation between geographically neighbouring areas and assumes a spatially smooth risk surface. However this may not be realistic in practice, because some pairs of neighbouring areas are likely to exhibit vastly different disease risks. Therefore the aim of this thesis is to develop methodology that allows for discontinuities in the spatial risk pattern when estimating disease risk. The first two models proposed are in a purely spatial setting and account for discontinuities by identifying spatial clusters of areas that have higher or lower risks than their geographical neighbours, while the third proposed model extends this to the spatio-temporal domain to identify clusters/discontinuities and estimate the spatial pattern of disease risk over time. The final piece of work of this thesis allows for discontinuities by using a boundary analysis approach. This approach identifies the boundaries in the spatial risk surface that separate pairs of geographically adjacent areas that exhibit large differences between their risks. Each model is applied to hospital admissions data for respiratory disease from the Greater Glasgow and Clyde Health Board region. Overall, it has been found that the respiratory disease risk surface in Greater Glasgow is not globally spatially smooth. There are numerous pairs of neighbouring areas where a discontinuity in disease risk appears to exist. In addition, the respiratory disease risk in Glasgow appears to increase over time and people living in more deprived areas are at higher risk of respiratory hospital admissions than those living in more affluent areas