Nonparametric analysis of replicated microarray experiments

Microarrays are part of a new class of biotechnologies which allow the monitoring of expression levels of thousands of genes simultaneously. In microarray data analysis, the comparison of gene-expression profiles with respect to different conditions and the selection of biologically interesting genes are crucial tasks. Multivariate statistical methods have been applied to analyze these large data sets. In particular, Dudoit et al. [2002] developed methods using t-statistics with p-values calculated through permutations, and with the Westfall and Young [1993] step-down approach to correct for multiple testing. Thomas et al. [2001] developed a regression modelling approach. Following the idea of Efron et al. [2000] and Tusher et al. [2001], Pan [2002] proposed a Normal mixture modelling approach that relaxes many strong assumptions on the null distributions of the test statistics. This paper makes two contributions to the analysis of microarray data. The first is the introduction of a new method for the calculation of the cut-off point and the acceptance region, and the second is the replacement of the based Normal mixture density estimators proposed by Pan et al. [2002], with less restrictive kernel nonparametric ones. A useful modification is suggested in order to increase the performance of the kernel estimator on the tail of the distribution. We apply our approach to leukemia data of Golub et al. [1999] and compare our results to those of Pan [2002].