An efficient method for identifying statistical interactors in gene association networks

Network reconstruction is a main goal of many biological endeavors. Graphical Gaussian models (GGMs) are often used since the underlying assumptions are well understood, the graph is readily estimated by calculating the partial correlation (paCor) matrix, and its interpretation is straightforward. In spite of these advantages, GGMs are limited in that interactions are not accommodated as the underlying multivariate normality assumption allows for linear dependencies only. As we show, when applied in the presence of interactions, the GGM framework can lead to incorrect inference regarding dependence. Identifying the exact dependence structure in this context is a difficult problem, largely because an analogue of the paCor matrix is not available and dependencies can involve many nodes. We here present a computationally efficient approach to identify bivariate interactions in networks. A key element is recognizing that interactions have a marginal linear effect and as a result information about their presence can be obtained from the paCor matrix. Theoretical derivations for the exact effect are presented and used to motivate the approach; and simulations suggest that the method works well, even in fairly complicated scenarios. Practical advantages are demonstrated in analyses of data from a breast cancer study.