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Abstract:
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As a consequence of large p small n 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. We studied F_S-test developed with the concept of James-Stein shrinkage to estimate the variance. Under a statistical model providing a theoretical justification of F_S, we derive F_S-test as an empirical Bayes likelihood ratio test. Furthermore, modifying the priors leads to a new test, the F_{MAP} test. An approximation to F_{MAP}, F_{SS}, is derived which was seen to shrink both means and the variances and which has a numerically identical average power as F_{MAP}. Simulation studies show that, the proposed F_{SS} test improves upon many other tests including the classical F test, F_S-test, the test of Wright and Simon, moderated t-test, SAM, Efron's t-test and B-statistics.
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