Geoff McLachlan, University of Queensland
On Simple Mixture Models in High-Dimensional Testing in the Detection of Differentially Expressed Genes

An important problem in microarray experiments is the detection of genes that are differentially expresse in a given number of classes. As there are usually thousands of genes to be considered simultaneously, one encounters high-dimensional testing problems. We provide a straightforward and easily implemented method for estimating the posterior probability that an individual gene is null (not differentially expressed).  The problem can be expressed in a two-component mixture framework.  Current methods of implementing this approach either have some limitations due to the minimal assumptions made or with the computationally intensive nature of more specific assumptions. By converting to a z-score the value of the test statistic used to test the significance of each gene, we propose a simple two-component normal mixture that models adequately the distribution of this score. The approach provides an estimate of the local false discovery rate (FDR) for each gene, which is taken to be the posterior probability that the gene is null.  Genes with the local FDR less than a specified threshold C are taken to be differentially expressed.  For a given C, this approach also provides estimates of the implied overall errors such as the (global) FDR and the false negative/positive rates.