A two-stage sample size recalculation procedure for placebo- and active-controlled non-inferiority trials

Many non-inferiority trials of a test treatment versus an active control may also, if ethical, incorporate a placebo arm. Inclusion of a placebo arm enables a direct assessment of assay sensitivity. It also allows construction of a non-inferiority test that avoids the problematic specification of an absolute non-inferiority margin, and instead evaluates whether the test treatment preserves a pre-specified proportion of the effect of the active control over placebo. We describe a two-stage procedure for sample size recalculation in such a setting that maintains the desired power more closely than a fixed sample approach when the magnitude of the effect of the active control differs from that anticipated. We derive an allocation rule for randomization under which the procedure preserves the type I error rate, and show that this coincides with that previously presented for optimal allocation of the sample size among the three treatment arms.