A critique of statistical aspects of ecological studies in spatial epidemiology

In this article, the mathematical assumptions of a number of commonly used ecological regression models are made explicit, critically assessed, and related to ecological bias. In particular, the role and interpretation of random effects models are examined. The modeling of spatial variability is considered and related to an underlying continuous spatial field. The examination of such a field with respect to the modeling of risk in relation to a point source highlights an inconsistency in commonly used approaches. A theme of the paper is to examine how plausible individual-level models relate to those used in practice at the aggregate level. The individual-level models acknowledge confounding, within-area variability in exposures and confounders, measurement error and data anomalies and so we can examine how the area-level versions consider these aspects. We briefly discuss designs that efficiently sample individual data and would appear to be useful in environmental settings.