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Levin's measure of attributable risk is extended to account for confounding. Maximum likelihood estimates and confidence intervals for this extended measure are presented. The estimates and confidence intervals apply both to matched and to stratified case-control studies. The statistical methods are illustrated by the use of data from a study of factors of womanhood as related to breast cancer, and data from a study of cigarette smoking as related to bladder cancer. The results of computer simulations are used to describe the behavior of the estimates and confidence intervals when sample size is small relative to the number of strata of the confounding factor.
Alice S. Whittemore (Sat,) studied this question.