Oracle and Adaptive Compound Decision Rules for False Discovery Rate Control

• Published in: Journal of the American Statistical Association Vol. 102; no. 479; pp. 901 - 912
• Main Authors: Sun, Wenguang, Cai, T. Tony
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.09.2007; American Statistical Association; Taylor & Francis Ltd
• Subjects: Adaptive procedure; Applications; Applied statistics; Compound decision rule; Decision making; Decision theory; Density estimation; Exact sciences and technology; False discovery rate; False positive errors; General topics; Hypothesis testing; Local false discovery rate; Mathematical procedures; Mathematics; Monotone likelihood ratio; Multivariate analysis; Null hypothesis; Oracles; P values; Probability and statistics; Proportions; Sciences and techniques of general use; Significance tests; Statistical methods; Statistical models; Statistics; Theory and Methods; Weighted classification; Non parametric estimation; Multivariate analysis; Microarray; Multiple decision; Hypothesis test; Statistical test; Law of large numbers; P value; Oracle; Compound decision rule; Human; Adaptive procedure; Data analysis; Retroviridae; Statistical estimation; Statistical decision; Monotone likelihood ratio; Lentivirus; Decision rule; Weighted classification; Virus; Statistical method; Decision theory; Local false discovery rate; False discovery rate; Human immunodeficiency virus; Application
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/016214507000000545

We develop a compound decision theory framework for multiple-testing problems and derive an oracle rule based on the z values that minimizes the false nondiscovery rate (FNR) subject to a constraint on the false discovery rate (FDR). We show that many commonly used multiple-testing procedures, which are p value-based, are inefficient, and propose an adaptive procedure based on the z values. The z value-based adaptive procedure asymptotically attains the performance of the z value oracle procedure and is more efficient than the conventional p value-based methods. We investigate the numerical performance of the adaptive procedure using both simulated and real data. In particular, we demonstrate our method in an analysis of the microarray data from a human immunodeficiency virus study that involves testing a large number of hypotheses simultaneously.