Copula Based Fusion of Clinical and Genomic Machine Learning Risk Scores for Breast Cancer Risk Stratification

TL;DR

This study demonstrates that modeling the joint relationship between clinical and genomic risk scores using copulas improves breast cancer risk stratification and identifies high-risk patient subgroups more effectively.

Contribution

The paper introduces a copula-based method to fuse clinical and genomic risk scores, capturing their dependency structure for better risk stratification in breast cancer.

Findings

Gaussian copula best fits the joint distribution (bootstrap p=0.997)

High-risk patients in both scores have significantly worse survival

Copula-based fusion improves identification of high-risk subgroups

Abstract

Clinical and genomic models are both used to predict breast cancer outcomes, but they are often combined using simple linear rules that do not account for how their risk scores relate, especially at the extremes. Using the METABRIC breast cancer cohort, we studied whether directly modeling the joint relationship between clinical and genomic machine learning risk scores could improve risk stratification for 5-year cancer-specific mortality. We created a binary 5-year cancer-death outcome and defined two sets of predictors: a clinical set (demographic, tumor, and treatment variables) and a genomic set (gene-expression $z$-scores). We trained several supervised classifiers, such as Random Forest and XGBoost, and used 5-fold cross-validated predicted probabilities as unbiased risk scores. These scores were converted to pseudo-observations on $(0,1)^2$ to fit Gaussian, Clayton, and Gumbel copulas. Clinical models showed good discrimination (AUC 0.783), while genomic models had moderate performance (AUC 0.681). The joint distribution was best captured by a Gaussian copula (bootstrap $p=0.997$), which suggests a symmetric, moderately strong positive relationship. When we grouped patients based on this relationship, Kaplan-Meier curves showed clear differences: patients who were high-risk in both clinical and genomic scores had much poorer survival than those high-risk in only one set. These results show that copula-based fusion works in real-world cohorts and that considering dependencies between scores can better identify patient subgroups with the worst prognosis.