title: Estimating attributable fraction in partially ecologic case-control studies.
abstract: 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.
authors.affiliation: Department of Occupational and Environmental Medicine, Lund University Hospital, SE-221 85 Lund, Sweden. Jonas.Bjork@ymed.lu.se
authors.forename: Jonas
authors.initials: J
authors.lastname: Björk
authors.forename: Ulf
authors.initials: U
authors.lastname: Strömberg
mesh_terms: D015982:Bias; D016022:Case-Control Studies; D004812:Epidemiologic Methods; D006801:Humans; D016014:Linear Models; D016273:Occupational Exposure; D016017:Odds Ratio; D012680:Sensitivity and Specificity