Using weighted permutation scores to detect differential gene expression with microarray data

A class of nonparametric statistical methods, including a nonparametric empirical Bayes (EB) method, the Significance Analysis of Microarrays (SAM) and the mixture model method (MMM) have been proposed to detect differential gene expression for replicated microarray experiments. They all depend on constructing a test statistic, for example, a t-statistic, and then using permutation to draw inferences. However, due to special features of microarray data, using standard permutation scores may not estimate the null distribution of the test statistic well, leading to possibly too conservative inferences. We propose a new method of constructing weighted permutation scores to overcome the problem: posterior probabilities of having no differential expression from the EB method are used as weights for genes to better estimate the null distribution of the test statistic. We also propose a weighted method to estimate the false discovery rate (FDR) using the posterior probabilities. Using simulated data and real data for time-course microarray experiments, we show the improved performance of the proposed methods when implemented in MMM, EB and SAM.