Ecological bias: use of maximum-entropy approximations

The focus of geographical studies in epidemiology has recently moved towards looking for effects of exposures based on data taken at local levels of aggregation (i.e. small areas). This paper investigates how regression coefficients measuring covariate effects at the point level are modified under aggregation. Changing the level of aggregation can lead to completely different conclusions about exposure-effect relationships, a phenomenon often referred to as ecological bias. With partial knowledge of the within-area distribution of the exposure variable, the notion of maximum entropy can be used to approximate that part of the distribution that is unknown. From the approximation, an expression for the ecological bias is obtained; simulations and an example show that the maximum-entropy approximation is often better than other commonly used approximations