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False discovery rate‐controlled multiple testing for union null hypotheses: a knockoff‐based approach

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  • Ran Dai
  • Cheng Zheng

Abstract

False discovery rate (FDR) controlling procedures provide important statistical guarantees for replicability in signal identification based on multiple hypotheses testing. In many fields of study, FDR controling procedures are used in high‐dimensional (HD) analyses to discover features that are truly associated with the outcome. In some recent applications, data on the same set of candidate features are independently collected in multiple different studies. For example, gene expression data are collected at different facilities and with different cohorts, to identify the genetic biomarkers of multiple types of cancers. These studies provide us with opportunities to identify signals by considering information from different sources (with potential heterogeneity) jointly. This paper is about how to provide FDR control guarantees for the tests of union null hypotheses of conditional independence. We present a knockoff‐based variable selection method (Simultaneous knockoffs) to identify mutual signals from multiple independent datasets, providing exact FDR control guarantees under finite sample settings. This method can work with very general model settings and test statistics. We demonstrate the performance of this method with extensive numerical studies and two real‐data examples.

Suggested Citation

  • Ran Dai & Cheng Zheng, 2023. "False discovery rate‐controlled multiple testing for union null hypotheses: a knockoff‐based approach," Biometrics, The International Biometric Society, vol. 79(4), pages 3497-3509, December.
    • Handle: RePEc:bla:biomet:v:79:y:2023:i:4:p:3497-3509
    DOI: 10.1111/biom.13848
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    References listed on IDEAS

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    1. Marina Bogomolov & Ruth Heller, 2018. "Assessing replicability of findings across two studies of multiple features," Biometrika, Biometrika Trust, vol. 105(3), pages 505-516.
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    3. Stephen Bates & Emmanuel Candès & Lucas Janson & Wenshuo Wang, 2021. "Metropolized Knockoff Sampling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(535), pages 1413-1427, July.
    4. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    5. Dongdong Xiang & Sihai Dave Zhao & T. Tony Cai, 2019. "Signal classification for the integrative analysis of multiple sequences of large‐scale multiple tests," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(4), pages 707-734, September.
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