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Graphical models are commonly used to discover associations within gene orprotein networks for complex diseases such as cancer. Most existing methodsestimate a single graph for a population, while in many cases, researchers areinterested in characterizing the heterogeneity of individual networks acrosssubjects with respect to subject-level covariates. Examples include assessmentsof how the network varies with patient-specific prognostic scores orcomparisons of tumor and normal graphs while accounting for tumor purity as acontinuous predictor. In this paper, we propose a novel edge regression modelfor undirected graphs, which estimates conditional dependencies as a functionof subject-level covariates. Bayesian shrinkage algorithms are used to inducesparsity in the underlying graphical models. We assess our model performancethrough simulation studies focused on comparing tumor and normal graphs whileadjusting for tumor purity and a case study assessing how blood proteinnetworks in hepatocellular carcinoma patients vary with severity of disease,measured by HepatoScore, a novel biomarker signature measuring diseaseseverity.

Bayesian Edge Regression in Undirected Graphical Models to Characterize Interpatient Heterogeneity in Cancer