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Graphical models are powerful tools to investigate complex dependencystructures in high-throughput datasets. However, most existing graphical modelsmake one of the two canonical assumptions: (i) a homogeneous graph with acommon network for all subjects; or (ii) an assumption of normality especiallyin the context of Gaussian graphical models. Both assumptions are restrictiveand can fail to hold in certain applications such as proteomic networks incancer. To this end, we propose an approach termed robust Bayesian graphicalregression (rBGR) to estimate heterogeneous graphs for non-normally distributeddata. rBGR is a flexible framework that accommodates non-normality throughrandom marginal transformations and constructs covariate-dependent graphs toaccommodate heterogeneity through graphical regression techniques. We formulatea new characterization of edge dependencies in such models called conditionalsign independence with covariates along with an efficient posterior samplingalgorithm. In simulation studies, we demonstrate that rBGR outperforms existinggraphical regression models for data generated under various levels ofnon-normality in both edge and covariate selection. We use rBGR to assessproteomic networks across two cancers: lung and ovarian, to systematicallyinvestigate the effects of immunogenic heterogeneity within tumors. Ouranalyses reveal several important protein-protein interactions that aredifferentially impacted by the immune cell abundance; some corroborate existingbiological knowledge whereas others are novel findings.

Robust Bayesian Graphical Regression Models for Assessing Tumor Heterogeneity in Proteomic Networks