A multivariate empirical Bayes statistic for replicated microarray time course data

August, 2004
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Yu Chuan Tai and Terence P. Speed

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 $1_k$, the vector of $k$ $1$s. The importance of moderation in this context is explained. Together with the $MB$-statistic we have the one-sample $\widetilde{T}^2$ statistic, a variant of the one-sample Hotelling $T^2$. Both the $MB$-statistic and $\widetilde{T}^2$ 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, $\widetilde{T}^2$ 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.

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