Balanced Functional Module Detection in Genomic Data
High dimensional genomic data can be analyzed to understand the effects of multiple variables on a target variable such as a clinical outcome, risk factor or diagnosis. Of special interest are functional modules, cooperating sets of variables affecting the target. Graphical models of various types are often useful for characterizing such networks of variables. In other applications such as social networks, the concept of balance in undirected signed graphs characterizes the consistency of associations within the network. To extend this concept to applications where a set of predictor variables influences an outcome variable, we define balance for functional modules. This property specifies that the module variables have a joint effect on the target outcome with no internal conflict, an efficiency that evolution may use for selection in biological networks. We show that for this class of graphs, observed correlations directly reflect paths in the underlying graph. Consequences of the balance property are exploited to implement a new module discovery algorithm, bFMD, which selects a subset of variables from highdimensional data that compose a balanced functional module. Our bFMD algorithm performed favorably in simulations as compared to other module detection methods that do not consider balance properties. Additionally, bFMD detected interpretable results in a real application for RNA-seq data obtained from The Cancer Genome Atlas (TCGA) for Uterine Corpus Endometrial Carcinoma using the percentage of tumor invasion as the target outcome of interest. bFMD detects sparse sets of variables within highdimensional datasets such that interpretability may be favorable as compared to other similar methods by leveraging balance properties used in other graphical applications.