Assessing Differential Gene Expression with Small Sample Sizes in Oligonucleotide Arrays Using a Mean‐Variance Model

Summary The identification of the genes that are differentially expressed in two‐sample microarray experiments remains a difficult problem when the number of arrays is very small. We discuss the implications of using ordinary t ‐statistics and examine other commonly used variants. For oligonucleotide arrays with multiple probes per gene, we introduce a simple model relating the mean and variance of expression, possibly with gene‐specific random effects. Parameter estimates from the model have natural shrinkage properties that guard against inappropriately small variance estimates, and the model is used to obtain a differential expression statistic. A limiting value to the positive false discovery rate (pFDR) for ordinary t ‐tests provides motivation for our use of the data structure to improve variance estimates. Our approach performs well compared to other proposed approaches in terms of the false discovery rate.