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New testing procedures with k-FWER control for discrete data

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  • Wang, Li

Abstract

Discrete p-values are often encountered in clinical studies and genomic studies, where Fisher’s exact test or binomial test is used. Since the distributions of the p-values for discrete data are discrete, and can be heterogeneous and stochastically larger than Uniform distribution U[0,1] under the null hypotheses, the multiple testing procedure constructed for continuous p-values will be conservative when applied to discrete data. This paper will propose new procedures with k-FWER control, the probability of making no less than k false discoveries, by using the cumulative distribution function of the p-values and improving generalized Bonferroni and generalized Holm procedure for arbitrarily dependent p-values. Extensive simulations and real data analysis will demonstrate the power improvement of the newly proposed procedures.

Suggested Citation

  • Wang, Li, 2022. "New testing procedures with k-FWER control for discrete data," Statistics & Probability Letters, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:stapro:v:180:y:2022:i:c:s016771522100198x
    DOI: 10.1016/j.spl.2021.109236
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    References listed on IDEAS

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    1. Peter B. Gilbert, 2005. "A modified false discovery rate multiple‐comparisons procedure for discrete data, applied to human immunodeficiency virus genetics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 143-158, January.
    2. van der Laan Mark J. & Dudoit Sandrine & Pollard Katherine S., 2004. "Augmentation Procedures for Control of the Generalized Family-Wise Error Rate and Tail Probabilities for the Proportion of False Positives," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-27, June.
    3. Mark van der Laan & Sandrine Dudoit & Katherine Pollard, 2004. "Multiple Testing. Part III. Procedures for Control of the Generalized Family-Wise Error Rate and Proportion of False Positives," U.C. Berkeley Division of Biostatistics Working Paper Series 1140, Berkeley Electronic Press.
    4. L. Finos & A. Farcomeni, 2011. "k-FWER Control without p -value Adjustment, with Application to Detection of Genetic Determinants of Multiple Sclerosis in Italian Twins," Biometrics, The International Biometric Society, vol. 67(1), pages 174-181, March.
    5. Kun Liang, 2016. "False discovery rate estimation for large-scale homogeneous discrete p-values," Biometrics, The International Biometric Society, vol. 72(2), pages 639-648, June.
    6. Elena Kulinskaya & Alex Lewin, 2009. "On fuzzy familywise error rate and false discovery rate procedures for discrete distributions," Biometrika, Biometrika Trust, vol. 96(1), pages 201-211.
    7. Ristl, Robin & Xi, Dong & Glimm, Ekkehard & Posch, Martin, 2018. "Optimal exact tests for multiple binary endpoints," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 1-17.
    8. Guo Wenge & Romano Joseph, 2007. "A Generalized Sidak-Holm Procedure and Control of Generalized Error Rates under Independence," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 6(1), pages 1-35, January.
    9. Li Wang & Xingzhong Xu, 2015. "Bonferroni-type Plug-in Procedure Controlling Generalized Familywise Error Rate," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(14), pages 3042-3055, July.
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