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

arXiv: https://arxiv.org/abs/2511.17605 · HTML: https://mlsanity.com/paper/2511.17605/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 49 references that are in the map.
- First posted on arXiv 18 Nov 2025.

## Builds on (most cited first, 2 of 2)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [IGNIS: A Robust Neural Network Framework for Constrained Parameter Estimation in Archimedean Copulas](https://mlsanity.com/paper/2505.22518/) (2025)

## Built on by (most cited first, 1 of 1)

- [Comparing Two Categorical Gini Correlations with Applications to Classification Problems](https://mlsanity.com/paper/2605.17763/) (2026)

## Abstract (arXiv)

Clinical and gene-expression models predict breast cancer outcomes, but simple linear fusion ignores dependence between their risk scores. Using METABRIC, we tested whether modeling the joint distribution of clinical and gene-expression scores improved stratification of 5-year cancer-specific mortality. We defined clinical and mRNA-expression predictor views, trained classifiers, and obtained out-of-fold probabilities through 5-fold cross-validation. The scores were transformed into pseudo-observations on (0,1)^2 and used to fit Gaussian, Clayton, Gumbel, and Frank copulas. The clinical model discriminated better than the gene-expression model (AUC 0.783 vs 0.721). Frank had the smallest goodness-of-fit statistic, with Gaussian performing similarly. Copula fusion did not improve ROC-AUC over the clinical model. However, joint score groups showed clear survival differences, with patients scoring high on both views having the poorest outcomes. Competing-risks analysis showed the same pattern for cancer-death incidence. We also conducted an external evaluation in independent TCGA data using shared predictors and a harmonized 5-year overall-mortality endpoint. Copula-fused, individual, and simple-fusion scores showed comparable discrimination with overlapping confidence intervals. All received the same METABRIC-based recalibration. No gene met the prespecified stability criterion under repeated cross-validated permutation importance, so gene-level findings were treated as exploratory. Copulas provide an explicit, interpretable description of dependence between clinical and gene-expression risk scores and support descriptive joint-group analyses. This methodological study does not establish superior prediction, validated clinical risk categories, or clinical utility.