# Fusion of Tree-induced Regressions for Clinico-genomic Data

arXiv: https://arxiv.org/abs/2411.02396 · HTML: https://mlsanity.com/paper/2411.02396/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2024.

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

- [How important are the genes to explain the outcome - the asymmetric Shapley value as an honest importance metric for high-dimensional features](https://mlsanity.com/paper/2603.05317/) (2026)

## Abstract (arXiv)

Cancer prognosis is often based on a set of omics covariates and a set of established clinical covariates such as age and tumor stage. Combining these two sets poses challenges. First, dimension difference: clinical covariates should be favored because they are low-dimensional and usually have stronger prognostic ability than high-dimensional omics covariates. Second, interactions: genetic profiles and their prognostic effects may vary across patient subpopulations. Last, redundancy: a (set of) gene(s) may encode similar prognostic information as a clinical covariate. To address these challenges, we combine regression trees, employing clinical covariates only, with a fusion-like penalized regression framework in the leaf nodes for the omics covariates. The fusion penalty controls the variability in genetic profiles across subpopulations. We prove that the shrinkage limit of the proposed method equals a benchmark model: a ridge regression with penalized omics covariates and unpenalized clinical covariates. Furthermore, the proposed method allows researchers to evaluate, for different subpopulations, whether the overall omics effect enhances prognosis compared to only employing clinical covariates. In an application to colorectal cancer prognosis based on established clinical covariates and 20,000+ gene expressions, we illustrate the features of our method.