Network hub gene detection using the entire solution path information

Gene co-expression networks typically comprise modules and their associated hub genes, which are regulating numerous downstream interactions within the network. Methods for hub screening, as well as data-driven estimation of hub co-expression networks using graphical models, can serve as useful tools for identifying these hubs. Graphical model-based penalization methods typically have one or multiple regularization terms, each of which encourages some favorable characteristics (e.g. sparsity, hubs, and power-law) to the estimated complex gene network. It is common practice to find a single optimal graphical model corresponding to a specific value of the regularization parameter(s). However, instead of doing this, one could aggregate information across several graphical models, all of which depend on the same data set, along the solution path in the hub gene detection process. We propose a novel method for detecting hub genes that utilizes the information available in the solution path. Our procedure is related to stability selection, but we replace resampling with a simple statistic. This procedure amalgamates information from each node of the data-driven graphical models into a single influence statistic, similar to Cook's distance. We call this statistic the Mean Degree Squared Distance (MDSD). Our simulation and empirical studies demonstrate that the MDSD statistic maintains a good balance between false positive and true positive hubs. An R package MDSD is publicly available on GitHub under the General Public License https://github.com/markkukuismin/MDSD.