Bayesian Average FDR and FNR in Single-step Procedure with Application to Microarray Experiments

• Activity Number: 274
• Type: Contributed
• Date/Time: Tuesday, August 10, 2004 : 2:00 PM to 3:50 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Jie Chen*+ and Sanat K. Sarkar
• Companies: Merck & Co., Inc. and Temple University
• Keywords: average FDR ; average FNR ; average Bayes error rate ; hierarchical mixture priors ; microarray experiments ; gene expression

Abstract

The original definition of the FDR can be understood as the frequentist risk of false rejections conditional on the unknown parameter, while the Bayesian posterior FDR is conditioned on the data, a particular realization of an experiment. From a Bayesian point of view, it seems natural to take into account the uncertainty in both the parameter and the data. We propose the average FDR (AFDR) and average FNR (AFNR) approaches in which the frequentist risks of false rejections and false nonrejections are averaged out with respect to some prior distribution of parameter. 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 minimizing the ABER is illustrated using a gene expression data and a simulation study.