Mapping Disease and Mortality Rates Using Empirical Bayes Estimators

Methods for estimating regional mortality and disease rates, with a view to mapping disease, are discussed. A new empirical Bayes estimator, with parameters simply estimated by moments, is proposed and compared with iterative alternatives suggested by Clayton and Kaldor. These methods are shrinkage estimators, in which the crude disease rate is shrunk towards an overall regional rate, and are in this sense ‘global’ and invariant to spatial configuration. However, it seems unjustifiable, in effect, to ignore the spatial aspect of the problem. A ‘local’ shrinkage estimator is therefore also suggested in which the crude rate is shrunk towards a local, neighbourhood, rate. Comparison of the estimators is done by some simulation experiments and an example showing infant mortality in Auckland, New Zealand, is presented. When disease is relatively rare a global estimator gives the lowest total mean‐square error, but for diseases that are more common and where the underlying spatial pattern is not uniform the local estimator performs best.