Improving ecological inference using individual-level data.

In typical small-area studies of health and environment we wish to make inference on the relationship between individual-level quantities using aggregate, or ecological, data. Such ecological inference is often subject to bias and imprecision, due to the lack of individual-level information in the data. Conversely, individual-level survey data often have insufficient power to study small-area variations in health. Such problems can be reduced by supplementing the aggregate-level data with small samples of data from individuals within the areas, which directly link exposures and outcomes. We outline a hierarchical model framework for estimating individual-level associations using a combination of aggregate and individual data. We perform a comprehensive simulation study, under a variety of realistic conditions, to determine when aggregate data are sufficient for accurate inference, and when we also require individual-level information. Finally, we illustrate the methods in a case study investigating the relationship between limiting long-term illness, ethnicity and income in London.