Multiple Augmented Reduced Rank Regression for Pan-Cancer Analysis

TL;DR

This paper introduces maRRR, a novel flexible matrix regression method for integrating multiple high-dimensional datasets, such as pan-cancer gene expression data, to improve analysis power and uncover shared or specific variation.

Contribution

It proposes a new structured nuclear norm-based framework that unifies and extends existing methods for multi-cohort data analysis, including a novel approach for single dataset regression and factorization.

Findings

Significant power gains in multi-dataset analysis demonstrated through simulations.

Effective prediction and imputation of gene expression data across cancer types.

New biological insights into mutation-driven and shared variation across cancers.

Abstract

Statistical approaches that successfully combine multiple datasets are more powerful, efficient, and scientifically informative than separate analyses. To address variation architectures correctly and comprehensively for high-dimensional data across multiple sample sets (i.e., cohorts), we propose multiple augmented reduced rank regression (maRRR), a flexible matrix regression and factorization method to concurrently learn both covariate-driven and auxiliary structured variation. We consider a structured nuclear norm objective that is motivated by random matrix theory, in which the regression or factorization terms may be shared or specific to any number of cohorts. Our framework subsumes several existing methods, such as reduced rank regression and unsupervised multi-matrix factorization approaches, and includes a promising novel approach to regression and factorization of a single dataset (aRRR) as a special case. Simulations demonstrate substantial gains in power from combining multiple datasets, and from parsimoniously accounting for all structured variation. We apply maRRR to gene expression data from multiple cancer types (i.e., pan-cancer) from TCGA, with somatic mutations as covariates. The method performs well with respect to prediction and imputation of held-out data, and provides new insights into mutation-driven and auxiliary variation that is shared or specific to certain cancer types.