“…It is particularly challenging to quantify inter-node connection strength precisely with a unified metric, especially when involving group (e.g., patients versus healthy controls) differences in biological networks (Gambardella et al, 2013;Yates and Mukhopadhyay, 2013;Ruan et al, 2015). In an attempt to accommodate changes in nodes and edges which lead to network differences, we previously developed statistics to test the group difference for weighted biological networks (Ji et al, 2016), for pathways with chain structure (Ji et al, 2015;Yuan et al, 2016a) and for directed biological networks (Yuan et al, 2016b). Nevertheless, these methods have little capacity to adjust for potential confounding factors and covariates (e.g., age, sex, batch effect), which served as a motivation for the current investigation into network regression techniques to infer the effect of a biological network as a whole (i.e., treating the whole network as the independent variables), accounting for the potential confounders through a regression model.…”