IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v83y2021i4p720-751.html
   My bibliography  Save this article

Covariate powered cross‐weighted multiple testing

Author

Listed:
  • Nikolaos Ignatiadis
  • Wolfgang Huber

Abstract

A fundamental task in the analysis of data sets with many variables is screening for associations. This can be cast as a multiple testing task, where the objective is achieving high detection power while controlling type I error. We consider m hypothesis tests represented by pairs ((Pi,Xi))1≤i≤m of p‐values Pi and covariates Xi, such that Pi⊥Xi if Hi is null. Here, we show how to use information potentially available in the covariates about heterogeneities among hypotheses to increase power compared to conventional procedures that only use the Pi. To this end, we upgrade existing weighted multiple testing procedures through the independent hypothesis weighting (IHW) framework to use data‐driven weights that are calculated as a function of the covariates. Finite sample guarantees, for example false discovery rate control, are derived from cross‐weighting, a data‐splitting approach that enables learning the weight‐covariate function without overfitting as long as the hypotheses can be partitioned into independent folds, with arbitrary within‐fold dependence. IHW has increased power compared to methods that do not use covariate information. A key implication of IHW is that hypothesis rejection in common multiple testing setups should not proceed according to the ranking of the p‐values, but by an alternative ranking implied by the covariate‐weighted p‐values.

Suggested Citation

  • Nikolaos Ignatiadis & Wolfgang Huber, 2021. "Covariate powered cross‐weighted multiple testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(4), pages 720-751, September.
    • Handle: RePEc:bla:jorssb:v:83:y:2021:i:4:p:720-751
    DOI: 10.1111/rssb.12411
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/rssb.12411
    Download Restriction: no
    File URL: https://libkey.io/10.1111/rssb.12411?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Edgar Dobriban & Kristen Fortney & Stuart K. Kim & Art B. Owen, 2015. "Optimal multiple testing under a Gaussian prior on the effect sizes," Biometrika, Biometrika Trust, vol. 102(4), pages 753-766.
    2. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    3. Allison, David B. & Gadbury, Gary L. & Heo, Moonseong & Fernandez, Jose R. & Lee, Cheol-Koo & Prolla, Tomas A. & Weindruch, Richard, 2002. "A mixture model approach for the analysis of microarray gene expression data," Computational Statistics & Data Analysis, Elsevier, vol. 39(1), pages 1-20, March.
    4. Sun, Wenguang & Cai, T. Tony, 2007. "Oracle and Adaptive Compound Decision Rules for False Discovery Rate Control," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 901-912, September.
    5. M Sesia & C Sabatti & E J Candès, 2019. "Gene hunting with hidden Markov model knockoffs," Biometrika, Biometrika Trust, vol. 106(1), pages 1-18.
    6. Kun Liang & Dan Nettleton, 2012. "Adaptive and dynamic adaptive procedures for false discovery rate control and estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(1), pages 163-182, January.
    7. Stefan Wager & Susan Athey, 2018. "Estimation and Inference of Heterogeneous Treatment Effects using Random Forests," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1228-1242, July.
    8. Xinkun Nie & Stefan Wager, 2017. "Quasi-Oracle Estimation of Heterogeneous Treatment Effects," Papers 1712.04912, arXiv.org, revised Aug 2020.
    9. John D. Storey & Jonathan E. Taylor & David Siegmund, 2004. "Strong control, conservative point estimation and simultaneous conservative consistency of false discovery rates: a unified approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 187-205, February.
    10. Christopher R. Genovese & Kathryn Roeder & Larry Wasserman, 2006. "False discovery control with p-value weighting," Biometrika, Biometrika Trust, vol. 93(3), pages 509-524, September.
    11. Rubin Daniel & Dudoit Sandrine & van der Laan Mark, 2006. "A Method to Increase the Power of Multiple Testing Procedures Through Sample Splitting," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 5(1), pages 1-20, August.
    12. Ang Li & Rina Foygel Barber, 2019. "Multiple testing with the structure‐adaptive Benjamini–Hochberg algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(1), pages 45-74, February.
    13. Lihua Lei & William Fithian, 2018. "AdaPT: an interactive procedure for multiple testing with side information," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(4), pages 649-679, September.
    14. Martin J. Zhang & Fei Xia & James Zou, 2019. "Fast and covariate-adaptive method amplifies detection power in large-scale multiple hypothesis testing," Nature Communications, Nature, vol. 10(1), pages 1-11, December.
    15. Sankaran, Kris & Holmes, Susan, 2014. "structSSI: Simultaneous and Selective Inference for Grouped or Hierarchically Structured Data," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 59(i13).
    16. Hu, James X. & Zhao, Hongyu & Zhou, Harrison H., 2010. "False Discovery Rate Control With Groups," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1215-1227.
    17. M Sesia & C Sabatti & E J Candès, 2019. "Rejoinder: ‘Gene hunting with hidden Markov model knockoffs’," Biometrika, Biometrika Trust, vol. 106(1), pages 35-45.
    18. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey, 2017. "Double/Debiased/Neyman Machine Learning of Treatment Effects," American Economic Review, American Economic Association, vol. 107(5), pages 261-265, May.
    19. Cai, T. Tony & Sun, Wenguang, 2009. "Simultaneous Testing of Grouped Hypotheses: Finding Needles in Multiple Haystacks," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1467-1481.
    20. Habiger, Joshua D. & Peña, Edsel A., 2014. "Compound p-value statistics for multiple testing procedures," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 153-166.
    21. Alejandro Ochoa & John D Storey & Manuel Llinás & Mona Singh, 2015. "Beyond the E-Value: Stratified Statistics for Protein Domain Prediction," PLOS Computational Biology, Public Library of Science, vol. 11(11), pages 1-21, November.
    22. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2016. "Double/Debiased Machine Learning for Treatment and Causal Parameters," Papers 1608.00060, arXiv.org, revised Nov 2024.
    23. Efron B. & Tibshirani R. & Storey J.D. & Tusher V., 2001. "Empirical Bayes Analysis of a Microarray Experiment," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1151-1160, December.
    24. Oliver Stegle & Leopold Parts & Richard Durbin & John Winn, 2010. "A Bayesian Framework to Account for Complex Non-Genetic Factors in Gene Expression Levels Greatly Increases Power in eQTL Studies," PLOS Computational Biology, Public Library of Science, vol. 6(5), pages 1-11, May.
    25. Wenguang Sun & T. Tony Cai, 2009. "Large‐scale multiple testing under dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 393-424, April.
    26. James G. Scott & Ryan C. Kelly & Matthew A. Smith & Pengcheng Zhou & Robert E. Kass, 2015. "False Discovery Rate Regression: An Application to Neural Synchrony Detection in Primary Visual Cortex," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 459-471, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. T. Tony Cai & Wenguang Sun & Weinan Wang, 2019. "Covariate‐assisted ranking and screening for large‐scale two‐sample inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(2), pages 187-234, April.
    2. Zhaoyang Tian & Kun Liang & Pengfei Li, 2021. "A powerful procedure that controls the false discovery rate with directional information," Biometrics, The International Biometric Society, vol. 77(1), pages 212-222, March.
    3. Habiger, Joshua D. & Peña, Edsel A., 2014. "Compound p-value statistics for multiple testing procedures," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 153-166.
    4. Ghosh Debashis, 2012. "Incorporating the Empirical Null Hypothesis into the Benjamini-Hochberg Procedure," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(4), pages 1-21, July.
    5. Miruna Oprescu & Vasilis Syrgkanis & Zhiwei Steven Wu, 2018. "Orthogonal Random Forest for Causal Inference," Papers 1806.03467, arXiv.org, revised Sep 2019.
    6. Alejandro Ochoa & John D Storey & Manuel Llinás & Mona Singh, 2015. "Beyond the E-Value: Stratified Statistics for Protein Domain Prediction," PLOS Computational Biology, Public Library of Science, vol. 11(11), pages 1-21, November.
    7. Dennis Leung & Wenguang Sun, 2022. "ZAP: Z$$ Z $$‐value adaptive procedures for false discovery rate control with side information," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 1886-1946, November.
    8. Zhao, Haibing & Fung, Wing Kam, 2016. "A powerful FDR control procedure for multiple hypotheses," Computational Statistics & Data Analysis, Elsevier, vol. 98(C), pages 60-70.
    9. Otília Menyhart & Boglárka Weltz & Balázs Győrffy, 2021. "MultipleTesting.com: A tool for life science researchers for multiple hypothesis testing correction," PLOS ONE, Public Library of Science, vol. 16(6), pages 1-12, June.
    10. Ruoxuan Xiong & Allison Koenecke & Michael Powell & Zhu Shen & Joshua T. Vogelstein & Susan Athey, 2021. "Federated Causal Inference in Heterogeneous Observational Data," Papers 2107.11732, arXiv.org, revised Apr 2023.
    11. Mark Kattenberg & Bas Scheer & Jurre Thiel, 2023. "Causal forests with fixed effects for treatment effect heterogeneity in difference-in-differences," CPB Discussion Paper 452, CPB Netherlands Bureau for Economic Policy Analysis.
    12. Yuya Sasaki & Takuya Ura & Yichong Zhang, 2022. "Unconditional quantile regression with high‐dimensional data," Quantitative Economics, Econometric Society, vol. 13(3), pages 955-978, July.
    13. Joshua Habiger & David Watts & Michael Anderson, 2017. "Multiple testing with heterogeneous multinomial distributions," Biometrics, The International Biometric Society, vol. 73(2), pages 562-570, June.
    14. Guido W. Imbens, 2020. "Potential Outcome and Directed Acyclic Graph Approaches to Causality: Relevance for Empirical Practice in Economics," Journal of Economic Literature, American Economic Association, vol. 58(4), pages 1129-1179, December.
    15. Jushan Bai & Sung Hoon Choi & Yuan Liao, 2021. "Feasible generalized least squares for panel data with cross-sectional and serial correlations," Empirical Economics, Springer, vol. 60(1), pages 309-326, January.
    16. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2023. "Machine learning advances for time series forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 76-111, February.
    17. Valente, Marica, 2023. "Policy evaluation of waste pricing programs using heterogeneous causal effect estimation," Journal of Environmental Economics and Management, Elsevier, vol. 117(C).
    18. Falco J. Bargagli Stoffi & Kenneth De Beckker & Joana E. Maldonado & Kristof De Witte, 2021. "Assessing Sensitivity of Machine Learning Predictions.A Novel Toolbox with an Application to Financial Literacy," Papers 2102.04382, arXiv.org.
    19. Anna Baiardi & Andrea A. Naghi, 2021. "The Value Added of Machine Learning to Causal Inference: Evidence from Revisited Studies," Papers 2101.00878, arXiv.org.
    20. Ganesh Karapakula, 2023. "Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap," Papers 2301.05703, arXiv.org, revised Jan 2023.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jorssb:v:83:y:2021:i:4:p:720-751. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.