A generalized false discovery rate in microarray studies

The problem of identifying differentially expressed genes is considered in a microarray experiment. This motivates us to involve an appropriate multiple testing setup to high dimensional and low sample size testing problems in highly nonstandard setups. Family-wise error rate (FWER) is too conservative to control the type I error, whereas a less conservative false discovery rate has received considerable attention in a wide variety of research areas such as genomics and large biological systems. Recently, a less conservative method than FDR, the kk-FDR, which generalizes the FDR has been proposed by Sarkar (2007). Most of the current FDR procedures assume restrictive dependence structures, resulting in being less reliable. The purpose of this paper is to address these very large multiplicity problems by adopting a proposed kk-FDR controlling procedure under suitable dependence structures and based on a Poisson distributional approximation in a unified framework. We compare the performance of the proposed kk-FDR procedure with that of other FDR controlling procedures, with an illustration of the leukemia microarray study of Golub et al. (1999) and simulated data. For power consideration, different FDR procedures are assessed using false negative rate (FNR). An unbiased property is appraised by FDR≤α and a higher value of 1−(FDR+FNR). The proposed kk-FDR procedure is characterized by greater power without much elevation of kk-FDR.