CLEAR-test: Combining inference for differential expression and variability in microarray data analysis

A common goal of microarray experiments is to detect genes that are differentially expressed under distinct experimental conditions. Several statistical tests have been proposed to determine whether the observed changes in gene expression are significant. The t-test assigns a score to each gene on the basis of changes in its expression relative to its estimated variability, in such a way that genes with a higher score (in absolute values) are more likely to be significant. Most variants of the t-test use the complete set of genes to influence the variance estimate for each single gene. However, no inference is made in terms of the variability itself. Here, we highlight the problem of low observed variances in the t-test, when genes with relatively small changes are declared differentially expressed. Alternatively, the z-test could be used although, unlike the t-test, it can declare differentially expressed genes with high observed variances. To overcome this, we propose to combine the z-test, which focuses on large changes, with a χ2 test to evaluate variability. We call this procedure CLEAR-test and we provide a combined p-value that offers a compromise between both aspects. Analysis of three publicly available microarray datasets reveals the greater performance of the CLEAR-test relative to the t-test and alternative methods. Finally, empirical and simulated data analyses demonstrate the greater reproducibility and statistical power of the CLEAR-test and z-test with respect to current alternative methods. In addition, the CLEAR-test improves the z-test by capturing reproducible genes with high variability.