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Exact p-Values for Simon’s Two-Stage Designs in Clinical Trials

Author

Listed:
  • Guogen Shan

    (School of Community Health Sciences, University of Nevada Las Vegas)

  • Hua Zhang

    (Zhejiang Gongshang University)

  • Tao Jiang

    (Zhejiang Gongshang University)

  • Hanna Peterson

    (School of Community Health Sciences, University of Nevada Las Vegas)

  • Daniel Young

    (School of Community Health Sciences, University of Nevada Las Vegas)

  • Changxing Ma

    (University at Buffalo)

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.

Suggested Citation

  • Guogen Shan & Hua Zhang & Tao Jiang & Hanna Peterson & Daniel Young & Changxing Ma, 2016. "Exact p-Values for Simon’s Two-Stage Designs in Clinical Trials," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 8(2), pages 351-357, October.
    • Handle: RePEc:spr:stabio:v:8:y:2016:i:2:d:10.1007_s12561-016-9152-1
    DOI: 10.1007/s12561-016-9152-1
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    References listed on IDEAS

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    1. Kang, Le & Tian, Lili, 2013. "Estimation of the volume under the ROC surface with three ordinal diagnostic categories," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 39-51.
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