Model-based estimation of the attributable risk in case-control and cohort studies

In a comprehensive review, Benichou recently discussed adjusted estimators of the attributable risk (AR). Among these are model-based estimates, where adjustment for confounding factors is based on a regression model. Different model-based approaches have been developed for case-control and cohort studies. The purpose of this article is to provide a detailed review and illustration of model-based methods for both types of sampling. For case-control studies, we show that two previously proposed approaches for the common case of a logistic regression model are in fact identical. This allows a unified approach to the estimation of the adjusted AR, which also accommodates stratified sampling. For cohort studies, a loglinear model is proposed for the case where cross-sectional sampling allows estimation of the prevalence of exposure; the approach can also be used for stratified sampling when the prevalence is known or can be estimated. For both designs, the standard error of the adjusted AR is estimated using the delta method. Estimation of the generalized AR is also discussed for both types of sampling. Examples show that for even fairly complex models, the computations are practical using standard statistical software. The bootstrap provides an easily implemented alternative to the delta method for the computation of standard errors.