Optimal inference for Simon's two-stage design with over or under enrollment at the second stage

ABSTRACT

Simon's two-stage designs are widely used in clinical trials to assess the activity of a new treatment. In practice, it is often the case that the second stage sample size is different from the planned one. For this reason, the critical value for the second stage is no longer valid for statistical inference. Existing approaches for making statistical inference are either based on asymptotic methods or not optimal. We propose an approach to maximize the power of a study while maintaining the type I error rate, where the type I error rate and power are calculated exactly from binomial distributions. The critical values of the proposed approach are numerically searched by an intelligent algorithm over the complete parameter space. It is guaranteed that the proposed approach is at least as powerful as the conditional power approach which is a valid but non-optimal approach. The power gain of the proposed approach can be substantial as compared to the conditional power approach. We apply the proposed approach to a real Phase II clinical trial.

KEYWORDS:

• Adaptive design
• Clinical trials
• Conditional power
• Sample size
• Simon's two-stage design

MATHEMATICS SUBJECT CLASSIFICATION:

• 62K05
• 62L15

Acknowledgment

We would like to thank the Associate Editor and the referee for their valuable comments and suggestions that helped to improve this article. Shan's research is supported by grants from the National Institute of General Medical Sciences 5U54GM104944, P20GM109025, and P20GM103440 from the National Institutes of Health. Chen's research is partially supported by U54MD007584, G12MD007601, P20GM103466, and U54GM104944 from the National Institutes of Health.