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Empirical Bayes ranking and selection methods via semiparametric hierarchical mixture models in microarray studies


Correspondence to: Hisashi Noma, Department of Data Science, The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan.



The main purpose of microarray studies is screening of differentially expressed genes as candidates for further investigation. Because of limited resources in this stage, prioritizing genes are relevant statistical tasks in microarray studies. For effective gene selections, parametric empirical Bayes methods for ranking and selection of genes with largest effect sizes have been proposed (Noma et al., 2010; Biostatistics 11: 281–289). The hierarchical mixture model incorporates the differential and non-differential components and allows information borrowing across differential genes with separation from nuisance, non-differential genes. In this article, we develop empirical Bayes ranking methods via a semiparametric hierarchical mixture model. A nonparametric prior distribution, rather than parametric prior distributions, for effect sizes is specified and estimated using the “smoothing by roughening” approach of Laird and Louis (1991; Computational Statistics and Data Analysis 12: 27–37). We present applications to childhood and infant leukemia clinical studies with microarrays for exploring genes related to prognosis or disease progression. Copyright © 2012 John Wiley & Sons, Ltd.