Screening for changes in gene expression across biological conditions using microarrays is now a common tool in biology. Efficient use of these data for identifying important biological hypotheses is inherently a statistical problem. In this paper we present a broad Bayesian multilevel framework for developing computationally fast shrinkage-based screening tools for this purpose. Our scheme makes it easy to adapt the choice of statistics to the goals of the analysis and to the genomic distributions of signal and noise. We empirically investigate the extent to which these shrinkage-based statistics improve performance, and the conditions under which such improvements takes place. Our evaluation uses both extensive simulations and controlled biological experiments. The experimental data include a so-called spike-in experiment, in which the target biological signal is known, and a two-sample experiment, which illustrates the typical conditions in which the methods studied are applied.

Our results emphasize two important practical concerns that are not receiving sufficient attention in applied work in this area. First, while shrinkage strategies based on multilevel models are able to improve selection performance, they require careful verification of the assumptions on the relationship between signal and noise. Incorrect specification of this relationship can negatively affect a selection procedure. Because this inter-gene relationship is generally identifiable in genomic experiments, we suggest a simple diagnostic plot to assist model checking. Secondly, no statistic performs optimally across two common categories of experimental goals: selecting genes with large changes, and selecting genes with reliably measured changes. Therefore, careful consideration of analysis goals is critical in the choice of the approach taken.