Abstract
In a one-sided hypothesis testing problem in clinical trials, the monotonic condition of a tail probability function is fundamentally important to guarantee that the actual type I and II error rates occur at the boundary of their associated parameter spaces. Otherwise, one has to search for the actual rates over the complete parameter space, which could be very computationally intensive. This important property has been extensively studied in traditional one-stage study settings (e.g., non-inferiority or superiority between two binomial proportions), but there is very limited research for this property in a two-stage design setting, e.g., Simon’s two-stage design. In this note, we theoretically prove that the tail probability is an increasing function of the parameter in Simon’s two-stage design. This proof not only provides theoretical justification that p-value occurs at the boundary of the parameter space, but also helps to reduce the computational intensity for study design search.
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Acknowledgments
The authors are very grateful to the Associate Editor and a referee for their insightful comments that help improve the manuscript. Shan’s research is partially supported by grants from the National Institute of General Medical Sciences from the National Institutes of Health: P20GM109025, P20GM103440, and 5U54GM104944. Zhang’s work was supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. LY15F020001) and the National Natural Science Foundation of China (Grant No. 61170099). We also thank Dr. Huichi Huang from Chongqing University for the discussion of this research.
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Shan, G., Zhang, H., Jiang, T. et al. Exact p-Values for Simon’s Two-Stage Designs in Clinical Trials. Stat Biosci 8, 351–357 (2016). https://doi.org/10.1007/s12561-016-9152-1
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DOI: https://doi.org/10.1007/s12561-016-9152-1