  In recent years, network models have gained prominence for their ability to
capture complex associations. In statistical omics, networks can be used to
model and study the functional relationships between genes, proteins, and other
types of omics data. If a Gaussian graphical model is assumed, a gene
association network can be determined from the non-zero entries of the inverse
covariance matrix of the data. Due to the high-dimensional nature of such
problems, integrative methods that leverage similarities between multiple
graphical structures have become increasingly popular. The joint graphical
lasso is a powerful tool for this purpose, however, the current AIC-based
selection criterion used to tune the network sparsities and similarities leads
to poor performance in high-dimensional settings. We propose stabJGL, which
equips the joint graphical lasso with a stable and accurate penalty parameter
selection approach that combines the notion of model stability with
likelihood-based similarity selection. The resulting method makes the powerful
joint graphical lasso available for use in omics settings, and outperforms the
standard joint graphical lasso, as well as state-of-the-art joint methods, in
terms of all performance measures we consider. Applying stabJGL to proteomic
data from a pan-cancer study, we demonstrate the potential for novel
discoveries the method brings. A user-friendly R package for stabJGL with
tutorials is available on Github at https://github.com/Camiling/stabJGL.
