Adaptive sample size re-estimation designs for a two-stage randomized trial with binary outcome

A parallel randomized trial is frequently used to investigate the treatment effectiveness as compared to the gold standard. In early phase trials, a group sequential design has the potential to reduce the expected sample size as compared to the traditional one-stage design, and protect participants when a new treatment is not as effective as expected. When the outcome is binary, a group sequential design based on exact binomial distribution is preferable as compared to the asymptotic limiting distribution. To improve the design efficiency, we propose to develop new parallel two-stage adaptive design and promising zone design allowing sample size adjustment in the second stage based on the outcome from the first stage. The conditional probability is guaranteed in the proposed designs when a trial proceeds to the second stage. All these designs control the type I error rate, but only the proposed two designs guarantee the conditional probability constraint. We used a real example from a completed cancer trial to illustrate the application of the proposed designs. The adaptive design substantially increases unconditional power but requires a large sample size as compared to the group sequential design. The promising zone design achieves a good balance between statistical power and the expected sample size.