Planning and analysis of three-arm non-inferiority trials with binary endpoints

Three-arm trials including an experimental treatment, an active control and a placebo group are frequently preferred for the assessment of non-inferiority. In contrast to two-arm non-inferiority studies, these designs allow a direct proof of efficacy of a new treatment by comparison with placebo. As a further advantage, the test problem for establishing non-inferiority can be formulated in such a way that rejection of the null hypothesis assures that a pre-defined portion of the (unknown) effect the reference shows versus placebo is preserved by the treatment under investigation. We present statistical methods for this study design and the situation of a binary outcome variable. Asymptotic test procedures are given and their actual type I error rates are calculated. Approximate sample size formulae are derived and their accuracy is discussed. Furthermore, the question of optimal allocation of the total sample size is considered. Power properties of the testing strategy including a pre-test for assay sensitivity are presented. The derived methods are illustrated by application to a clinical trial in depression.