Stouffer's test in a large scale simultaneous hypothesis testing

In microarray data analysis, we are often required to combine several dependent partial test results. To overcome this, many suggestions have been made in previous literature; Tippett's test and Fisher's omnibus test are most popular. Both tests have known null distributions when the partial tests are independent. However, for dependent tests, their (even, asymptotic) null distributions are unknown and additional numerical procedures are required. In this paper, we revisited Stouffer's test based on z-scores and showed its advantage over the two aforementioned methods in the analysis of large-scale microarray data. The combined statistic in Stouffer's test has a normal distribution with mean 0 from the normality of the z-scores. Its variance can be estimated from the scores of genes in the experiment without an additional numerical procedure. We numerically compared the errors of Stouffer's test and the two p-value based methods, Tippett's test and Fisher's omnibus test. We also analyzed our microarray data to find differentially expressed genes by non-genotoxic and genotoxic carcinogen compounds. Both numerical study and the real application showed that Stouffer's test performed better than Tippett's method and Fisher's omnibus method with additional permutation steps.