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

Music City Center 

Graphical models are powerful tools to investigate complex dependency structures in high-throughput datasets. However, most existing graphical models make one of two canonical assumptions: (1) a homogeneous graph with a common network for all subjects or (2) an assumption of normality especially in the context of Gaussian graphical models. Both assumptions are restrictive and can fail in certain applications such as proteomic networks. We propose an approach termed robust Bayesian graphical regression (rBGR) to estimate heterogeneous graphs for non-normally distributed data. rBGR is a flexible framework that accommodates non-normality by random marginal transformations and constructs covariate-dependent graphs to accommodate heterogeneity via graphical regressions. We formulate a new characterization of dependencies, conditional sign independence with covariates, with an efficient sampler. Simulation studies show that rBGR outperforms existing graphical models for data from various levels of non-normality in both edge and covariate selection. We use rBGR to access proteomic networks and find protein-protein interactions that are differentially associated with immune cell abundance.

Bayesian graphical models

Cancer

Conditional sign independence

Covariate-dependent graphs

Protein-protein interactions 

Biometrics Section