A hybrid model for reducing ecological bias

A major drawback of epidemiological ecological studies, in which the association between area-level summaries of risk and exposure is used to make inference about individual risk, is the difficulty in characterizing within-area variability in exposure and confounder variables.To avoid ecological bias, samples of individual exposure/confounder data within each area are required.Unfortunately, these may be difficult or expensive to obtain, particularly if large samples are required. In this paper, we propose a new approach suitable for use with small samples.We combine a Bayesian nonparametric Dirichlet process prior with an estimating functions. approach and show that this model gives a compromise between 2 previously described methods.The method is investigated using simulated data, and a practical illustration is provided through an analysis of lung cancer mortality and residential radon exposure in counties of Minnesota.We conclude that we require good quality prior information about the exposure/confounder distributions and a large between- to within-area variability ratio for an ecological study to be feasible using only small samples of individual data.