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10Statistical Methods for Identifying DifferentiallyExpressed Gene CombinationsYen-Yi Ho, Leslie Cope, Marcel Dettling, and Giovanni ParmigianiSummaryIdentification of coordinate gene expression changes across phenotypes or biological conditionsis the basis of the ability to decode the role of gene expression regulatory networks. Statistically, theidentification of these changes can be viewed as a search for groups (most typically pairs) of geneswhose expression provides better phenotype discrimination when considered jointly than whenconsidered individually. Such groups are defined as being jointly differentially expressed. In thischapter several approaches for identifying jointly differentially expressed groups of genes arereviewed of compared on a set of simulations.Key Words: High-order interactions; liquid correlation; microarray data; entropy; joint differentialexpression; correlation.1. IntroductionGene-expression microarrays quantify the levels of thousands of RNA transcriptssimultaneously (1). A common experimental design is the comparison ofsamples from different phenotypes or biological conditions, with the goal ofidentifying differences in expression. Standard analysis approaches are constructedconsidering each gene in turn and investigating the hypothesis that theone-dimensional (1D) gene-specific distributions are the same across conditions(2,3). In biological processes, RNA transcript levels interact with each other, andit is of interest to consider more than one gene at a time, to explore functionalrelationships between genes that are associated with phenotypes. Statistically,this means testing more general hypotheses formulated in terms of joint distributionsof pairs or larger subgroups of genes (4).The following artificial examples illustrate two archetypical cases of jointdifferential expression. Figure 1 shows two genes with joint association on theFrom: Methods in Molecular Biology, vol. 408: Gene Function AnalysisEdited by: M. Ochs © Humana Press Inc., Totowa, NJ171