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Approximate Power and Sample Size Calculations with the Benjamini-Hochberg Method

Author

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  • Ferreira José António

    (AMC - University of Amsterdam)

  • Zwinderman Aeilko H

    (University of Amsterdam)

Abstract

We provide a method for calculating the sample size required to attain a given average power (the ratio of rejected hypotheses to the number of false hypotheses) and a given false discovery rate (the number of incorrect rejections divided by the number of rejections) in adaptive versions of the Benjamini-Hochberg method of multiple testing. The method works in an asymptotic sense as the number of hypotheses grows to infinity and under quite general conditions, and it requires data from a pilot study. The consistency of the method follows from several results in classical areas of nonparametric statistics developed in a new context of "weak" dependence.

Suggested Citation

  • Ferreira José António & Zwinderman Aeilko H, 2006. "Approximate Power and Sample Size Calculations with the Benjamini-Hochberg Method," The International Journal of Biostatistics, De Gruyter, vol. 2(1), pages 1-38, September.
    • Handle: RePEc:bpj:ijbist:v:2:y:2006:i:1:n:8
    DOI: 10.2202/1557-4679.1018
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    Cited by:

    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. Ferreira José A. & Berkhof Johannes & Souverein Olga & Zwinderman Koos, 2009. "A Multiple Testing Approach to High-Dimensional Association Studies with an Application to the Detection of Associations between Risk Factors of Heart Disease and Genetic Polymorphisms," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-56, January.
    3. Song Li & Mervyn J. Silvapulle & Param Silvapulle & Xibin Zhang, 2015. "Bayesian Approaches to Nonparametric Estimation of Densities on the Unit Interval," Econometric Reviews, Taylor & Francis Journals, vol. 34(3), pages 394-412, March.
    4. Farcomeni, Alessio & Pacillo, Simona, 2011. "A conservative estimator for the proportion of false nulls based on Dvoretzky, Kiefer and Wolfowitz inequality," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1867-1870.
    5. Ferreira, J.A. & Nyangoma, S.O., 2008. "A multivariate version of the Benjamini-Hochberg method," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2108-2124, October.
    6. Dean Palejev & Mladen Savov, 2021. "On the Convergence of the Benjamini–Hochberg Procedure," Mathematics, MDPI, vol. 9(17), pages 1-19, September.

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