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Optimal design for p-value consistent step-up procedures for multiple comparisons with a control in direction-mixed families

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  • Kwong, Koon Shing
  • Cheung, Siu Hung

Abstract

It is common in clinical studies for several treatments to be compared to a control. Most of the related statistical techniques have been developed to accommodate inferential families in which all hypotheses are either one- or two-sided such that the familywise error rate is controlled at a specified level. Several multiple testing procedures were recently proposed to perform multiple comparisons with a control in direction-mixed families that contain a mixture of one- and two-sided inferences. Of these procedures, the p-value consistent step-up procedure is found to be superior in terms of its power and p-value consistent property. In this paper, we examine the techniques for computing the all-pairs power of this testing procedure. We also provide the means to obtain the optimal design when a desired level of all-pairs power is given. Compared to the conservative method of treating all hypotheses as two-sided, the proposed procedure requires a substantially smaller sample, as all useful information on the direction of the alternatives is utilized in an optimal way. The computation of the optimal design relies on an efficient algorithm, which is also discussed in this paper. A clinical study example is employed to illustrate the proposed procedure.

Suggested Citation

  • Kwong, Koon Shing & Cheung, Siu Hung, 2012. "Optimal design for p-value consistent step-up procedures for multiple comparisons with a control in direction-mixed families," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4157-4164.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:12:p:4157-4164
    DOI: 10.1016/j.csda.2012.05.001
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    References listed on IDEAS

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    1. Cheung, Siu Hung & Holland, Burt, 1992. "Extension of Dunnett's multiple comparison procedure with differing sample sizes to the case of several groups," Computational Statistics & Data Analysis, Elsevier, vol. 14(2), pages 165-182, August.
    2. Charles W. Dunnett, 1989. "Multivariate Normal Probability Integrals with Product Correlation Structure," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 38(3), pages 564-579, November.
    3. Kwong, Koon-Shing & Chan, Yiu-Man, 2008. "On the evaluation of the joint distribution of order statistics," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5091-5099, August.
    4. Kwong, K. S. & Liu, W., 2000. "Calculation of critical values for Dunnett and Tamhane's step-up multiple test procedure," Statistics & Probability Letters, Elsevier, vol. 49(4), pages 411-416, October.
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