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Optimal control of false discovery criteria in the two‐group model

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  • Ruth Heller
  • Saharon Rosset

Abstract

The highly influential two‐group model in testing a large number of statistical hypotheses assumes that the test statistics are drawn independently from a mixture of a high probability null distribution and a low probability alternative. Optimal control of the marginal false discovery rate (mFDR), in the sense that it provides maximal power (expected true discoveries) subject to mFDR control, is known to be achieved by thresholding the local false discovery rate (locFDR), the probability of the hypothesis being null given the set of test statistics, with a fixed threshold. We address the challenge of controlling optimally the popular false discovery rate (FDR) or positive FDR (pFDR) in the general two‐group model, which also allows for dependence between the test statistics. These criteria are less conservative than the mFDR criterion, so they make more rejections in expectation. We derive their optimal multiple testing (OMT) policies, which turn out to be thresholding the locFDR with a threshold that is a function of the entire set of statistics. We develop an efficient algorithm for finding these policies, and use it for problems with thousands of hypotheses. We illustrate these procedures on gene expression studies.

Suggested Citation

  • Ruth Heller & Saharon Rosset, 2021. "Optimal control of false discovery criteria in the two‐group model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(1), pages 133-155, February.
    • Handle: RePEc:bla:jorssb:v:83:y:2021:i:1:p:133-155
    DOI: 10.1111/rssb.12403
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    References listed on IDEAS

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    Cited by:

    1. Pallavi Basu & Luella Fu & Alessio Saretto & Wenguang Sun, 2021. "Empirical Bayes Control of the False Discovery Exceedance," Working Papers 2115, Federal Reserve Bank of Dallas.

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