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The optimal discovery procedure in multiple significance testing: an empirical Bayes approach
Author(s) -
Noma Hisashi,
Matsui Shigeyuki
Publication year - 2011
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.4375
Subject(s) - bayes' theorem , computer science , false discovery rate , false positive paradox , statistical hypothesis testing , null hypothesis , multiple comparisons problem , prior probability , bayesian probability , null distribution , statistics , data mining , machine learning , mathematics , artificial intelligence , test statistic , biology , biochemistry , gene
Multiple testing has been widely adopted for genome‐wide studies such as microarray experiments. To improve the power of multiple testing, Storey ( J. Royal Statist. Soc. B 2007; 69: 347–368) recently developed the optimal discovery procedure (ODP) which maximizes the number of expected true positives for each fixed number of expected false positives. However, in applying the ODP, we must estimate the true status of each significance test (null or alternative) and the true probability distribution corresponding to each test. In this article, we derive the ODP under hierarchical, random effects models and develop an empirical Bayes estimation method for the derived ODP. Our methods can effectively circumvent the estimation problems in applying the ODP presented by Storey. Simulations and applications to clinical studies of leukemia and breast cancer demonstrated that our empirical Bayes method achieved theoretical optimality and performed well in comparison with existing multiple testing procedures. Copyright © 2011 John Wiley & Sons, Ltd.