Estimating attributable fraction in partially ecologic case-control studies.

Partially ecologic case-control studies combine group-level exposure data with individual-level data on disease status, group membership, and covariates. If the exposure measure is the exposure prevalence of various groups, the attributable fraction (AF; the estimated proportion of cases that are attributable to exposure) can be estimated by classifying all subjects in groups with exposure prevalence above zero as exposed. Such a threshold AF estimator ([AF]T) is unbiased in confounding-free situations if the threshold is 100% sensitive, but it might be imprecise. We propose an alternative AF estimator, [AF]L, for partially ecologic case-control studies under a linear model for the association between the exposure prevalence and the odds ratio. The proposed estimator can also be applied to situations in which covariate adjustment is necessary. [AF]T and [AF]L are compared with respect to precision and bias. [AF]L is also unbiased when the exposure prevalence is zero in the group(s) assessed as unexposed. Using [AF]L will consistently result in improved precision compared with [AF]T, although the results may not differ substantially. The 95% confidence intervals for both AF estimators show satisfactory coverage in bias-free exposure scenarios. Pronounced negative bias and decreased coverage result for both AF estimators even when small fractions (3-9%) of exposed subjects are included in the group assessed as unexposed.