Article first published online: 4 OCT 2011
Copyright © 2011 John Wiley & Sons, Ltd.
Statistics in Medicine
Volume 31, Issue 2, pages 165–176, 30 January 2012
How to Cite
Noma, H. and Matsui, S. (2012), The optimal discovery procedure in multiple significance testing: an empirical Bayes approach. Statist. Med., 31: 165–176. doi: 10.1002/sim.4375
- Issue published online: 28 DEC 2011
- Article first published online: 4 OCT 2011
- Manuscript Accepted: 1 AUG 2011
- Manuscript Received: 23 DEC 2010
- Japan Society for the Promotion of Science
- empirical Bayes;
- false discovery rate;
- multiple significance testing;
- optimal discovery procedure
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.