Bayesian Graphical Models for Differential Pathways

Graphical models can be used to characterize the dependence structure for a set of random variables. In some applications, the form of dependence varies across different subgroups. This situation arises, for example, when protein activation on a certain pathway is recorded, and a subgroup of patients is characterized by a pathological disruption of that pathway. A similar situation arises when one subgroup of patients is treated with a drug that targets that same pathway. In both cases, understanding changes in the joint distribution and dependence structure across the two subgroups is key to the desired inference. Fitting a single model for the entire data could mask the differences. Separate independent analyses, on the other hand, could reduce the effective sample size and ignore the common features. In this paper, we develop a Bayesian graphical model that addresses heterogeneity and implements borrowing of strength across the two subgroups by simultaneously centering the prior towards a global network. The key feature is a hierarchical prior for graphs that borrows strength across edges, resulting in a comparison of pathways across subpopulations (differential pathways) under a unified model-based framework. We apply the proposed model to data sets from two very different studies: histone modifications from ChIP-seq experiments, and protein measurements based on tissue microarrays.