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α‐investing: a procedure for sequential control of expected false discoveries

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  • Dean P. Foster
  • Robert A. Stine

Abstract

Summary. α‐investing is an adaptive sequential methodology that encompasses a large family of procedures for testing multiple hypotheses. All control mFDR, which is the ratio of the expected number of false rejections to the expected number of rejections. mFDR is a weaker criterion than the false discovery rate, which is the expected value of the ratio. We compensate for this weakness by showing that α‐investing controls mFDR at every rejected hypothesis. α‐investing resembles α‐spending that is used in sequential trials, but it has a key difference. When a test rejects a null hypothesis, α‐investing earns additional probability towards subsequent tests. α‐investing hence allows us to incorporate domain knowledge into the testing procedure and to improve the power of the tests. In this way, α‐investing enables the statistician to design a testing procedure for a specific problem while guaranteeing control of mFDR.

Suggested Citation

  • Dean P. Foster & Robert A. Stine, 2008. "α‐investing: a procedure for sequential control of expected false discoveries," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(2), pages 429-444, April.
    • Handle: RePEc:bla:jorssb:v:70:y:2008:i:2:p:429-444
    DOI: 10.1111/j.1467-9868.2007.00643.x
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    Cited by:

    1. Foster, Dean P. & Stine, Robert & Young, H. Peyton, 2011. "A Markov Test for Alpha," Working Papers 11-49, University of Pennsylvania, Wharton School, Weiss Center.
    2. Heath, Davidson & Ringgenberg, Matthew C. & Samadi, Mehrdad & Werner, Ingrid M., 2019. "Reusing Natural Experiments," Working Paper Series 2019-21, Ohio State University, Charles A. Dice Center for Research in Financial Economics.
    3. Ang Li & Rina Foygel Barber, 2017. "Accumulation Tests for FDR Control in Ordered Hypothesis Testing," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 837-849, April.
    4. Shiyun Chen & Ery Arias-Castro, 2021. "On the power of some sequential multiple testing procedures," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(2), pages 311-336, April.
    5. Jean Feng & Scott Emerson & Noah Simon, 2021. "Approval policies for modifications to machine learning‐based software as a medical device: A study of bio‐creep," Biometrics, The International Biometric Society, vol. 77(1), pages 31-44, March.
    6. Hahn, Georg, 2022. "Online multivariate changepoint detection with type I error control and constant time/memory updates per series," Statistics & Probability Letters, Elsevier, vol. 181(C).
    7. Gong, Siliang & Zhang, Kai & Liu, Yufeng, 2018. "Efficient test-based variable selection for high-dimensional linear models," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 17-31.
    8. Maede S. Nouri & Daniel J. Lizotte & Kamran Sedig & Sheikh S. Abdullah, 2021. "VISEMURE: A Visual Analytics System for Making Sense of Multimorbidity Using Electronic Medical Record Data," Data, MDPI, vol. 6(8), pages 1-19, August.

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