A Multivariate Empirical Bayes Statistic for Replicated Microarray Time Course Data

In this paper we derive a one-sample multivariate empirical Bayes statistic (the MB-statistic) to rank genes in the order of differential expression from replicated microarray time course experiments . We do this by testing the null hypothesis that the expectation of a k-vector of a gene’s expression levels is a multiple of 1k, the vector of k 1s. The importance of moderation in this context is explained. Together with the MB-statistic we have the one-sample T̃ 2 statistic, a variant of the one-sample Hotelling T 2. Both the MB-statistic and T̃ 2 statistic can be used to rank genes in the order of evidence of nonconstancy, incorporating any correlation structure among time point samples and the replication. In a simulation study we show that the one-sample MB-statistic, T̃ 2 statistic, and moderated Hotelling T 2 statistic achieve the smallest number of false positives and false negatives, and all perform equally well. Several special and limiting cases of the MB-statistic are derived, and two-sample versions are described. AMS 2000 subject classifications. Primary 62M10; secondary 62C12, 92D10.