A comparison of the hierarchical likelihood and Bayesian approaches to spatial epidemiological modelling

Recently Bayesian methods have been widely used in disease mapping. Hierarchical (h-) likelihood methods allow reliable likelihood inference in random-effect models and it is therefore interesting to compare h-likelihood and Bayesian methods. For comparison we consider three examples: low birth weight and cancer mortality data in South Carolina and lip cancer data in Scotland. Mean estimates from both h-likelihood and Bayesian approaches are almost identical, while variance-component estimates can be somewhat different, depending upon choice of priors.