Identifying patient-specific prognostic biomarkers is of critical importance in developing personalized treatment for clinically and molecularly heterogeneous diseases such as cancer. 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 and induce sparsity in both protein-gene and protein-survival relationships to select genomically driven prognostic protein markers at the patient-level. Simulation studies demonstrate the superior performance of BEHAVIOR against a competing method in terms of both protein marker selection and survival prediction.