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Adaptive designs with arbitrary dependence structure based on Fisher’s combination test

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  • René Schmidt
  • Andreas Faldum
  • Joachim Gerß

Abstract

Adaptive designs were originally developed for independent and uniformly distributed $$p$$ p -values. However, in general the type I error rate of a given adaptive design depends on the true dependence structure between the stage-wise $$p$$ p -values. Since there are settings, where the $$p$$ p -values of the stages might be dependent with even unknown dependence structure, it is of interest to consider the most adverse dependence structure maximizing the type I error rate of a given adaptive design (worst case). In this paper, we explicitly study the type I error rate in the worst case for adaptive designs without futility stop based on Fisher’s combination test. Potential inflation of the type I error rate is studied if the dependence structure between the $$p$$ p -values of the stages is not taken into account adequately. It turns out that considerable inflation of the type I error rate can occur. This emphasizes that the examination of the true dependence structure between the stage-wise $$p$$ p -values and an adequate choice of the conditional error function is crucial when adaptive designs are used. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • René Schmidt & Andreas Faldum & Joachim Gerß, 2015. "Adaptive designs with arbitrary dependence structure based on Fisher’s combination test," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(3), pages 427-447, September.
    • Handle: RePEc:spr:stmapp:v:24:y:2015:i:3:p:427-447
    DOI: 10.1007/s10260-014-0291-6
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    References listed on IDEAS

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    1. Brannath W. & Posch M. & Bauer P., 2002. "Recursive Combination Tests," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 236-244, March.
    2. Walter Lehmacher & Gernot Wassmer, 1999. "Adaptive Sample Size Calculations in Group Sequential Trials," Biometrics, The International Biometric Society, vol. 55(4), pages 1286-1290, December.
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    Cited by:

    1. Steffen Nico & Dickhaus Thorsten, 2020. "Optimizing effective numbers of tests by vine copula modeling," Dependence Modeling, De Gruyter, vol. 8(1), pages 172-185, January.
    2. André Neumann & Thorsten Dickhaus, 2020. "Nonparametric Archimedean generator estimation with implications for multiple testing," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(2), pages 309-323, June.
    3. Steffen Nico & Dickhaus Thorsten, 2020. "Optimizing effective numbers of tests by vine copula modeling," Dependence Modeling, De Gruyter, vol. 8(1), pages 172-185, January.

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