Nondifferential Treatment Misclassification Biases Toward the Null? Not a Safe Bet for Active Comparator Studies

Active comparator studies are increasingly common, particularly in pharmacoepidemiology. In such studies, the parameter of interest is a contrast (difference or ratio) in the outcome risks between the treatment of interest and the selected active comparator. While it may appear treatment is dichotomous, treatment is actually polytomous as there are at least 3 levels: no treatment, the treatment of interest, and the active comparator. Because misclassification may occur between any of these groups, independent nondifferential treatment misclassification may not be toward the null (as expected with a dichotomous treatment). In this work, we describe bias from independent nondifferential treatment misclassification in active comparator studies with a focus on misclassification that occurs between each active treatment and no treatment. We derive equations for bias in the estimated outcome risks, risk difference, and risk ratio, and we provide bias correction equations that produce unbiased estimates, in expectation. Using data obtained from US insurance claims data, we present a hypothetical comparative safety study of antibiotic treatment to illustrate factors that influence bias and provide an example probabilistic bias analysis using our derived bias correction equations.