Consider the gene ranking problem of replicated microarray time course experiments where there are multiple biological conditions, and genes of interest are those whose temporal profiles are different across conditions. We derive the multi-sample multivariate empirical Bayes statistic for rank- ing genes in the order of differential expression, from both longitudinal and cross-sectional replicated developmental microarray time course data. Our longitudinal multi-sample model assumes that time course replicates are i.i.d. multivariate normal vectors. On the other hand, we construct our cross-sectional model using a normal regression framework with any appro- priate basis for the design matrices. In both cases, we use natural conjugate priors in our empirical Bayes setting which guarantee closed form solutions for the posterior odds. Our simulations and two case studies using pub- lished worm and mouse microarray time course datasets indicate that the proposed approaches work well.

Keywords: longitudinal; cross-sectional; microarray time course; gene ranking; empirical Bayes.