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Accumulation Tests for FDR Control in Ordered Hypothesis Testing

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  • Ang Li
  • Rina Foygel Barber

Abstract

Multiple testing problems arising in modern scientific applications can involve simultaneously testing thousands or even millions of hypotheses, with relatively few true signals. In this article, we consider the multiple testing problem where prior information is available (for instance, from an earlier study under different experimental conditions), that can allow us to test the hypotheses as a ranked list to increase the number of discoveries. Given an ordered list of n hypotheses, the aim is to select a data-dependent cutoff k and declare the first k hypotheses to be statistically significant while bounding the false discovery rate (FDR). Generalizing several existing methods, we develop a family of “accumulation tests” to choose a cutoff k that adapts to the amount of signal at the top of the ranked list. We introduce a new method in this family, the HingeExp method, which offers higher power to detect true signals compared to existing techniques. Our theoretical results prove that these methods control a modified FDR on finite samples, and characterize the power of the methods in the family. We apply the tests to simulated data, including a high-dimensional model selection problem for linear regression. We also compare accumulation tests to existing methods for multiple testing on a real data problem of identifying differential gene expression over a dosage gradient. Supplementary materials for this article are available online.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:518:p:837-849
    DOI: 10.1080/01621459.2016.1180989
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    References listed on IDEAS

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    1. 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.
    2. John D. Storey, 2002. "A direct approach to false discovery rates," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 479-498, August.
    3. 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.
    4. 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.
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    Cited by:

    1. Damian Kozbur, 2020. "Analysis of Testing‐Based Forward Model Selection," Econometrica, Econometric Society, vol. 88(5), pages 2147-2173, September.
    2. Wesley Tansey & Yixin Wang & Raul Rabadan & David Blei, 2020. "Double Empirical Bayes Testing," International Statistical Review, International Statistical Institute, vol. 88(S1), pages 91-113, December.
    3. Wang, Jiangzhou & Cui, Tingting & Zhu, Wensheng & Wang, Pengfei, 2023. "Covariate-modulated large-scale multiple testing under dependence," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    4. Pengfei Wang & Wensheng Zhu, 2022. "Large‐scale covariate‐assisted two‐sample inference under dependence," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1421-1447, December.
    5. 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.

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