Fusion of Tree-induced Regressions for Clinico-genomic Data

TL;DR

This paper introduces a novel fusion approach combining tree-based models and penalized regression to improve cancer prognosis by effectively integrating clinical and high-dimensional genomic data, addressing heterogeneity and redundancy.

Contribution

The method uniquely combines clinical covariates with omics data using tree-induced regressions and fusion penalties, with theoretical guarantees and practical application to colorectal cancer prognosis.

Findings

The proposed method outperforms traditional models in prognostic accuracy.

It effectively captures subpopulation heterogeneity in genetic effects.

The shrinkage limit aligns with a ridge regression benchmark.

Abstract

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.