Improved statistical tests for differential gene expression by shrinking variance components estimates

Combining information across genes in the statistical analysis of microarray data is desirable because of the relatively small number of data points obtained for each individual gene. Here we develop an estimator of the error variance that can borrow information across genes using the James-Stein shrinkage concept. A new test statistic (FS) is constructed using this estimator. The new statistic is compared with other statistics used to test for differential expression: the gene-specific F test (F1), the pooled-variance F statistic (F3), a hybrid statistic (F2) that uses the average of the individual and pooled variances, the regularized t-statistic, the posterior odds statistic B, and the SAM t-test. The FS-test shows best or nearly best power for detecting differentially expressed genes over a wide range of simulated data in which the variance components associated with individual genes are either homogeneous or heterogeneous. Thus FS provides a powerful and robust approach to test differential expression of genes that utilizes information not available in individual gene testing approaches and does not suffer from biases of the pooled variance approach.