  Substantial statistical research has recently been devoted to the analysis of
large-scale microarray experiments which provide a measure of the simultaneous
expression of thousands of genes in a particular condition. A typical goal is
the comparison of gene expression between two conditions (e.g., diseased vs.
nondiseased) to detect genes which show differential expression. Classical
hypothesis testing procedures have been applied to this problem and more recent
work has employed sophisticated models that allow for the sharing of
information across genes. However, many recent gene expression studies have an
experimental design with several conditions that requires an even more involved
hypothesis testing approach. In this paper, we use a hierarchical Bayesian
model to address the situation where there are many hypotheses that must be
simultaneously tested for each gene. In addition to having many hypotheses
within each gene, our analysis also addresses the more typical multiple
comparison issue of testing many genes simultaneously. We illustrate our
approach with an application to a study of genes involved in obstructive sleep
apnea in humans.
