Group sequential designs for three-arm 'gold standard' non-inferiority trials with fixed margin

In the recent years there have been numerous publications on the design and the analysis of three-arm 'gold standard' noninferiority trials. Whenever feasible, regulatory authorities recommend the use of such three-arm designs including a test treatment, an active control, and a placebo. Nevertheless, it is desirable in many respects, for example, ethical reasons, to keep the placebo group size as small as possible. We first give a short overview on the fixed sample size design of a three-arm noninferiority trial with normally distributed outcomes and a fixed noninferiority margin. An optimal single stage design is derived that should serve as a benchmark for the group sequential designs proposed in the main part of this work. It turns out, that the number of patients allocated to placebo is substantially low for the optimal design. Subsequently, approaches for group sequential designs aiming to further reduce the expected sample sizes are presented. By means of choosing different rejection boundaries for the respective null hypotheses, we obtain designs with quite different operating characteristics. We illustrate the approaches via numerical calculations and a comparison with the optimal single stage design. Furthermore, we derive approximately optimal boundaries for different goals, for example, to reduce the overall average sample size. The results show that the implementation of a group sequential design further improves the optimal single stage design. Besides cost and time savings, the possible early termination of the placebo arm is a key advantage that could help to overcome ethical concerns.