Empirical Bayes estimators and non‐parametric mixture models for space and time–space disease mapping and surveillance

The analysis of the geographic variation of disease and its representation on a map is an important topic in epidemiological research and in public health in general. Identification of spatial heterogeneity of relative risk using morbidity and mortality data is required. Frequently, interest is also in the analysis of space data with respect to time, where typically data are used which are aggregated in certain time windows like 5 or 10 years. The occurrence measure of interest is usually the standardized mortality (morbidity) ratio (SMR). It is well known that disease maps in space or in space and time should not solely be based upon the crude SMR but rather some smoothed version of it. This fact has led to a tremendous amount of theoretical developments in spatial methodology, in particular in the area of hierarchical modeling in connection with fully Bayesian estimation techniques like Markov chain Monte Carlo. It seems, however, that at the same time, where these theoretical developments took place, on the practical side only very few of these developments have found their way into daily practice of epidemiological work and surveillance routines. In this article we focus on developments that avoid the pitfalls of the crude SMR and simultaneously retain a simplicity and, at least approximately, the validity of more complex models. After an illustration of the typical pitfalls of the crude SMR the article is centered around three issues: (a) the separation of spatial random variation from spatial structural variation; (b) a simple mixture model for capturing spatial heterogeneity; (c) an extension of this model for capturing temporal information. The techniques are illustrated by numerous examples. Public domain software like Dismap is mentioned that enables easy mixture modeling in the context of disease mapping. Copyright © 2003 John Wiley & Sons, Ltd.