A group sequential type design for three-arm non-inferiority trials with binary endpoints.

The three-arm design with a test treatment, an active control and a placebo group is the gold standard design for non-inferiority trials if it is ethically justifiable to expose patients to placebo. In this paper, we first use the closed testing principle to establish the hierarchical testing procedure for the multiple comparisons involved in the three-arm design. For the effect preservation test we derive the explicit formula for the optimal allocation ratios. We propose a group sequential type design, which naturally accommodates the hierarchical testing procedure. Under this proposed design, Monte Carlo simulations are conducted to evaluate the performance of the sequential effect preservation test when the variance of the test statistic is estimated based on the restricted maximum likelihood estimators of the response rates under the null hypothesis. When there are uncertainties for the placebo response rate, the proposed design demonstrates better operating characteristics than the fixed sample design.