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A Bayesian determination of threshold for identifying differentially expressed genes in microarray experiments
Author(s) -
Chen Jie,
Sarkar Sanat K.
Publication year - 2005
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.2422
Subject(s) - false discovery rate , frequentist inference , bayesian probability , prior probability , bayes' theorem , multiple comparisons problem , posterior probability , bayes factor , statistics , false positive rate , mathematics , data set , computer science , bayesian inference , biology , gene , genetics
The original definitions of false discovery rate (FDR) and false non‐discovery rate (FNR) can be understood as the frequentist risks of false rejections and false non‐rejections, respectively, conditional on the unknown parameter, while the Bayesian posterior FDR and posterior FNR are conditioned on the data. From a Bayesian point of view, it seems natural to take into account the uncertainties in both the parameter and the data. In this spirit, we propose averaging out the frequentist risks of false rejections and false non‐rejections with respect to some prior distribution of the parameters to obtain the average FDR (AFDR) and average FNR (AFNR), respectively. A linear combination of the AFDR and AFNR, called the average Bayes error rate (ABER), is considered as an overall risk. Some useful formulas for the AFDR, AFNR and ABER are developed for normal samples with hierarchical mixture priors. The idea of finding threshold values by minimizing the ABER or controlling the AFDR is illustrated using a gene expression data set. Simulation studies show that the proposed approaches are more powerful and robust than the widely used FDR method. Copyright © 2005 John Wiley & Sons, Ltd.