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

arXiv: https://arxiv.org/abs/2101.09587 · HTML: https://mlsanity.com/paper/2101.09587/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2021.

## Built on by (most cited first, 2 of 2)

- [Convex Estimation of Gaussian Graphical Regression Models with Covariates](https://mlsanity.com/paper/2410.06326/) (2024)
- [Patient-Specific Models of Treatment Effects Explain Heterogeneity in Tuberculosis](https://mlsanity.com/paper/2411.10645/) (2024)

## Abstract (arXiv)

Graphical models are commonly used to discover associations within gene or protein networks for complex diseases such as cancer. Most existing methods estimate a single graph for a population, while in many cases, researchers are interested in characterizing 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 paper, we propose a novel edge regression model for undirected graphs, which estimates conditional dependencies as a function of subject-level covariates. Bayesian shrinkage algorithms are used to induce sparsity in the underlying graphical models. We assess our model performance through simulation studies focused on comparing tumor and normal graphs while adjusting for tumor purity and a case study assessing how blood protein networks in hepatocellular carcinoma patients vary with severity of disease, measured by HepatoScore, a novel biomarker signature measuring disease severity.