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) over cap (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) over cap (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 is necessary (AF) over cap (T) and (AF) over cap (L) are compared with respect to precision and bias. (AF) over cap (L) is also unbiased when the exposure prevalence is zero in the group(s) assessed as unexposed. Using (AF) over cap (L) will consistently result in improved precision compared with (AF) over cap (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.