On the use of permutation in and the performance of a class of nonparametric methods to detect differential gene expression

Recently a class of nonparametric statistical methods, including the empirical Bayes (EB) method, the significance analysis of microarray (SAM) method and the mixture model method (MMM), have been proposed to detect differential gene expression for replicated microarray experiments conducted under two conditions. All the methods depend on constructing a test statistic Z and a so-called null statistic z. The null statistic z is used to provide some reference distribution for Z such that statistical inference can be accomplished. A common way of constructing z is to apply Z to randomly permuted data. Here we point our that the distribution of z may not approximate the null distribution of Z well, leading to possibly too conservative inference. This observation may apply to other permutation-based nonparametric methods. We propose a new method of constructing a null statistic that aims to estimate the null distribution of a test statistic directly.