Internal External Examiner

ii Hierarchical spatial modelling is useful for modelling complex spatially correlated data in a variety of settings. Due to the complexity of spatial analyses, hierarchical spatial models for disease mapping studies have not generally found application at Vital Statistics agencies. Chapter 2 compares penalized quasi-likelihood relative risk estimates to target values based on Bayesian Markov Chain Monte Carlo methods. Results show penalized quasi-likelihood to be a simple, reasonably accurate method of inference for exploratory studies of small-area relative risks and ranks of risks. Often the identification of extreme risk areas is of interest. Isolated ‘hot spots’/‘low spots ’ which are distinct from those of neighbouring sites are not accommodated by stan-dard hierarchical spatial models. In Chapter 3, spatial methods are developed which allow extreme risk areas to arise in proximity to one another in a smooth spatial surface, or in isolated ‘hot spots’/‘low spots’. The former is modelled by a spatially smooth surface using a conditional autoregressive model; the latter is addressed with the addition of a discret