Sources of bias in ecological studies of non-rare events

Ecological studies investigate relationships at the level of the group, rather than at the level of the individual. Although such studies are a common design in epidemiology, it is well-known that estimates may be subject to ecological bias. Most discussion of ecological bias has focused on rare disease events, where the tractability of the loglinear model allows some characterization of the nature of different biases. This paper concentrates on non-rare events, where the Poisson approximation to the binomial distribution is not appropriate. We limit the discussion to bias that arises from within-area variability in exposures and confounders. Our aims are to investigate the likely sizes and directions of bias and, where possible, to suggest methods for controlling the bias or for addressing the sensitivity of inference to assumptions on the nature of the bias. We illustrate that for non-rare events it is much more difficult to characterize the direction of bias than in the rare case. A series of simple numerical examples based on a chronic study of respiratory health illustrate the ideas of the paper.