Avoiding bias from aggregate measures of exposure

Background: Sometimes in descriptive epidemiology or in the evaluation of a health intervention policy change, proportions exposed to a risk factor or to an intervention are used as explanatory variables in log-linear regressions for disease incidence or mortality. Aim: To demonstrate how estimates from such models can be substantially inaccurate as estimates of the effect of the risk factor or intervention at individual level. To show how the individual level effect can be correctly estimated by excess relative risk models. Methods: The problem and solution are demonstrated using data on prostate-specific antigen testing and prostate cancer incidence.