Optimal Tests Shrinking Both Means and Variances Applicable to Microarray Data Analysis

Abstract

<p>As a consequence of “large p small n” characteristic for microarray data, hypothesis tests based on individual genes often result in low average power. There are several proposed tests that attempt to improve power. Among these, FS test developed using the concept of James-Stein shrinkage to estimate the variances, showed a striking average power improvement. In this paper, we derive the FS test as an empirical Bayes likelihood ratio test, providing a theoretical justification. To shrink the means also, we modify the prior distributions leading to the optimal Bayes test which is called MAP test (where MAP stands for Maximum Average Power). Also an FSS statistic is derived as an approximation to MAP and can be computed instantaneously. The FSS shrinks both the means and the variances and has a numerically identical average power as MAP. Simulation studies show that the proposed test performs uniformly better in average power than the other tests in the literature including the classical F test, FS test, the test of Wright and Simon, moderated t-test, SAM, Efron’s t test and B statistics. A theory is established which indicates that the proposed test is optimal in power when controlling the false discovery rate (FDR).</p>