Unequal group covariances in microarray data analysis

초록

In testing for differential expression for gene sets, such as genetic pathways, we often face the problem of singular covariance matrices (if n< p) and of unequal covariance matrices between groups. To deal with this singularity problem, we can apply a shrinkage covariance estimation method and this leads to a regularized version of Hotelling's T2. However, the Welch-type regularized Hotelling's T2 lacks sensitivity when the covariances are equal. To overcome this problem, we introduce a moderated regularized Hotelling's T2 that is based on weighing by the probability that the covariances are equal given data. When a non-trivial proportion of gene sets has unequal covariance matrices, the false discovery rate (FDR) estimate based on the proposed statistic is shown to perform better than the existing methods over wider range of data conditions.