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

Abstract

It is well established that interpatient heterogeneity in cancer may significantly affect genomic data analyses and in particular, network topologies. Most existing graphical model methods estimate a single population-level graph for genomic or proteomic network. In many investigations, these networks depend on patient-specific indicators that characterize the heterogeneity of individual networks across subjects with respect to subject-level covariates. Examples include assessments of how the network varies with patient-specific prognostic scores or comparisons of tumor and normal graphs while accounting for tumor purity as a continuous predictor. In this article, we propose a novel edge regression model for undirected graphs, which estimates conditional dependencies as a function of subject-level covariates. We evaluate our model performance through simulation studies focused on comparing tumor and normal graphs while adjusting for tumor purity. In application to a dataset of proteomic measurements on plasma samples from patients with hepatocellular carcinoma (HCC), we ascertain how blood protein networks vary with disease severity, as measured by HepatoScore, a novel biomarker signature measuring disease severity. Our case study shows that the network connectivity increases with HepatoScore and a set of hub proteins as well as important protein connections are identified under different HepatoScore, which may provide important biological insights to the development of precision therapies for HCC.

Keywords:

• Bayesian adaptive shrinkage
• Gene regulatory network
• Nonstatic graph
• Tumor heterogeneity
• Undirected graphical models

Supplementary Materials

The supplementary materials additionally detail the steps of the MCMC algorithm used for edge regression as well as the derivation of the algorithm. The supplementary materials also present more simulation settings and results as well as more implementation details for the methods in simulations. Additional result analyses for our HCC case study are also provided in the supplementary materials.

Acknowledgments

This work was supported by NSF grants 1550088 and 1463233, plus NIH grants P30-CA-016672, CA-160736, CA-158113, CA-178744, CA-183793, CA220299, CA-221707, CA-239342, CA-244845, P30-CA46592, and ULI-TR001878, and start-up funds from the U-M Rogel Cancer Center and University of Michigan School of Public Health. We thank the associate editor and referees whose constructive comments greatly improved this paper.

Notes

1 Available in the R package JGL.

2 Available in the R package LASICH.

3 Implementation requested from the authors.

4 https://odin.mdacc.tmc.edu/∼cbpeterson/software.html.

Additional information

Funding

This work was supported by NSF grants 1550088 and 1463233, plus NIH grants P30-CA-016672, CA-160736, CA-158113, CA-178744, CA-183793, CA220299, CA-221707, CA-239342, CA-244845, P30-CA46592, and ULI-TR001878, and start-up funds from the U-M Rogel Cancer Center and University of Michigan School of Public Health. We thank the associate editor and referees whose constructive comments greatly improved this paper.