TY - JOUR

T1 - Optimal control of false discovery criteria in the two-group model

AU - Heller, Ruth

AU - Rosset, Saharon

N1 - Publisher Copyright:
© 2020 Royal Statistical Society

PY - 2021/2

Y1 - 2021/2

N2 - 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.

AB - 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.

KW - false discovery rate

KW - infinite linear programming

KW - large-scale inference

KW - multiple testing

KW - positive FDR

UR - http://www.scopus.com/inward/record.url?scp=85097009377&partnerID=8YFLogxK

U2 - 10.1111/rssb.12403

DO - 10.1111/rssb.12403

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AN - SCOPUS:85097009377

SN - 1369-7412

VL - 83

SP - 133

EP - 155

JO - Journal of the Royal Statistical Society. Series B: Statistical Methodology

JF - Journal of the Royal Statistical Society. Series B: Statistical Methodology

IS - 1

ER -