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Exact Calculations of Average Power for the Benjamini-Hochberg Procedure

Author

Listed:
  • Glueck Deborah H

    (University of Colorado Denver)

  • Mandel Jan

    (University of Colorado Denver)

  • Karimpour-Fard Anis

    (University of Colorado Denver)

  • Hunter Lawrence

    (University of Colorado Denver)

  • Muller Keith E

    (University of Florida)

Abstract

Exact analytic expressions are developed for the average power of the Benjamini and Hochberg false discovery control procedure. The result is based on explicit computation of the joint probability distribution of the total number of rejections and the number of false rejections, and expressed in terms of the cumulative distribution functions of the p-values of the hypotheses. An example of analytic evaluation of the average power is given. The result is confirmed by numerical experiments and applied to a meta-analysis of three clinical studies in mammography.

Suggested Citation

  • Glueck Deborah H & Mandel Jan & Karimpour-Fard Anis & Hunter Lawrence & Muller Keith E, 2008. "Exact Calculations of Average Power for the Benjamini-Hochberg Procedure," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-22, June.
    • Handle: RePEc:bpj:ijbist:v:4:y:2008:i:1:n:11
    DOI: 10.2202/1557-4679.1103
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    References listed on IDEAS

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    1. David Ruppert & Dan Nettleton & J. T. Gene Hwang, 2007. "Exploring the Information in p-Values for the Analysis and Planning of Multiple-Test Experiments," Biometrics, The International Biometric Society, vol. 63(2), pages 483-495, June.
    2. Christopher Genovese & Larry Wasserman, 2002. "Operating characteristics and extensions of the false discovery rate procedure," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 499-517, August.
    3. Quinn McNemar, 1947. "Note on the sampling error of the difference between correlated proportions or percentages," Psychometrika, Springer;The Psychometric Society, vol. 12(2), pages 153-157, June.
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    1. von Schroeder, Jonathan & Dickhaus, Thorsten, 2020. "Efficient calculation of the joint distribution of order statistics," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    2. Izmirlian, Grant, 2020. "Strong consistency and asymptotic normality for quantities related to the Benjamini–Hochberg false discovery rate procedure," Statistics & Probability Letters, Elsevier, vol. 160(C).

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