TY - JOUR

T1 - Adaptive linear step-up procedures that control the false discovery rate

AU - Benjamini, Yoav

AU - Krieger, Abba M.

AU - Yekutieli, Daniel

N1 - Funding Information:
This research was partly supported by the Focal Initiatives in Research Science and Technology foundation of the Israeli Academy of Sciences and Humanities, and by a grant from the U.S. National Institutes of Health. We would like to thank the referees for their helpful suggestions.

PY - 2006/9

Y1 - 2006/9

N2 - The linear step-up multiple testing procedure controls the false discovery rate at the desired level q for independent and positively dependent test statistics. When all null hypotheses are true, and the test statistics are independent and continuous, the bound is sharp. When some of the null hypotheses are not true, the procedure is conservative by a factor which is the proportion m0/m of the true null hypotheses among the hypotheses. We provide a new two-stage procedure in which the linear step-up procedure is used in stage one to estimate m0, providing a new level q′ which is used in the linear step-up procedure in the second stage. We prove that a general form of the two-stage procedure controls the false discovery rate at the desired level q. This framework enables us to study analytically the properties of other procedures that exist in the literature. A simulation study is presented that shows that two-stage adaptive procedures improve in power over the original procedure, mainly because they provide tighter control of the false discovery rate. We further study the performance of the current suggestions, some variations of the procedures, and previous suggestions, in the case where the test statistics are positively dependent, a case for which the original procedure controls the false discovery rate. In the setting studied here the newly proposed two-stage procedure is the only one that controls the false discovery rate. The procedures are illustrated with two examples of biological importance.

AB - The linear step-up multiple testing procedure controls the false discovery rate at the desired level q for independent and positively dependent test statistics. When all null hypotheses are true, and the test statistics are independent and continuous, the bound is sharp. When some of the null hypotheses are not true, the procedure is conservative by a factor which is the proportion m0/m of the true null hypotheses among the hypotheses. We provide a new two-stage procedure in which the linear step-up procedure is used in stage one to estimate m0, providing a new level q′ which is used in the linear step-up procedure in the second stage. We prove that a general form of the two-stage procedure controls the false discovery rate at the desired level q. This framework enables us to study analytically the properties of other procedures that exist in the literature. A simulation study is presented that shows that two-stage adaptive procedures improve in power over the original procedure, mainly because they provide tighter control of the false discovery rate. We further study the performance of the current suggestions, some variations of the procedures, and previous suggestions, in the case where the test statistics are positively dependent, a case for which the original procedure controls the false discovery rate. In the setting studied here the newly proposed two-stage procedure is the only one that controls the false discovery rate. The procedures are illustrated with two examples of biological importance.

KW - False discovery rate

KW - Multiple testing

KW - Two-stage procedure

UR - http://www.scopus.com/inward/record.url?scp=33746197428&partnerID=8YFLogxK

U2 - 10.1093/biomet/93.3.491

DO - 10.1093/biomet/93.3.491

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AN - SCOPUS:33746197428

SN - 0006-3444

VL - 93

SP - 491

EP - 507

JO - Biometrika

JF - Biometrika

IS - 3

ER -