Large-scale simultaneous inference with applications to the detection of differential expression with microarray data

An important problem in microarray experiments is the detection of genes that are differentially expressed in agiven mumber of classes. We consider a straightforward and easily implemented method for estimating the posterior probability that an individual gene is null. The problem can be expressed in a two-component mixture framework, using an empirical Bayes approach. Current methods of implementing this approach either have some limitations due to the minimal assumptions made or with more specific assumptions are computationally intensive. By converting to a z-score the value of the test statistic used to test the significance of each gene, we can use a simple two-component normal mixture to model adequately the distribution of this score. In the context of the application of this approach to a well known breast cancer data set, we consider some of the issues associated with the problem of the detection of differential expression, including the case where there is need for the use of an empirical null distribution in place of the standard normal (the theoretical null) and the case where none of the genes might be differentially expressed. We also describe briefly some initial results on a cluster analysis approach to this problem, which attempts to model the joint distribution of the individual gene expressions. This latter approach thus has to make distributional assumptions which are note necessary with the former approach based on the z-scores. However, in the case where the distributional assumptions are valid, it has the potential to provide a more powerful analysis.