  This paper discusses the problem of identifying differentially expressed
groups of genes from a microarray experiment. The groups of genes are
externally defined, for example, sets of gene pathways derived from biological
databases. Our starting point is the interesting Gene Set Enrichment Analysis
(GSEA) procedure of Subramanian et al. [Proc. Natl. Acad. Sci. USA 102 (2005)
15545--15550]. We study the problem in some generality and propose two
potential improvements to GSEA: the maxmean statistic for summarizing
gene-sets, and restandardization for more accurate inferences. We discuss a
variety of examples and extensions, including the use of gene-set scores for
class predictions. We also describe a new R language package GSA that
implements our ideas.
