Bayesian Hierarchical Varying-sparsity Regression Models with Application to Cancer Proteogenomics.

Identifying patient-specific prognostic biomarkers is of critical importance in developing personalized treatment for clinically and molecularly heterogeneous diseases such as cancer. In this article, we propose a novel regression framework, Bayesian hierarchical varying-sparsity regression (BEHAVIOR) models to select clinically relevant disease markers by integrating proteogenomic (proteomic+genomic) and clinical data. Our methods allow flexible modeling of protein-gene relationships as well as induces sparsity in both protein-gene and protein-survival relationships, to select ge-nomically driven prognostic protein markers at the patient-level. Simulation studies demonstrate the superior performance of BEHAVIOR against competing method in terms of both protein marker selection and survival prediction. We apply BEHAV-IOR to The Cancer Genome Atlas (TCGA) proteogenomic pan-cancer data and find several interesting prognostic proteins and pathways that are shared across multiple cancers and some that exclusively pertain to specific cancers.