Hypothesis testing for two-stage designs with over or under enrollment.

Simon's two-stage designs are widely used in cancer phase II clinical trials for assessing the efficacy of a new treatment. However in practice, the actual sample size for the second stage is often different from the planned sample size, and the original inference procedure is no longer valid. Previous work on this problem has certain limitations in computation. In this paper, we attempt to maximize the unconditional power while controlling for the type I error for the modified second stage sample size. A normal approximation is used for computing the power, and the numerical results show that the approximation is accurate even under small sample sizes. The corresponding confidence intervals for the response rate are constructed by inverting the hypothesis test, and they have reasonable coverage while preserving the type I error.