Bryon Aragam

Personalized Regression Enables Sample-Specific Pan-Cancer Analysis

Motivation In many applications, inter‐sample heterogeneity is crucial to understanding the complex biological processes under study. For example, in genomic analysis of cancers, each patient in a cohort may have a different driver mutation, making it difficult or impossible to identify causal mutations from an averaged view of the entire cohort. Unfortunately, many traditional methods for genomic analysis seek to estimate a single model which is shared by all samples in a population, ignoring this inter‐sample heterogeneity entirely. In order to better understand patient heterogeneity, it is necessary to develop practical, personalized statistical models. Results To uncover this inter‐sample heterogeneity, we propose a novel regularizer for achieving patient‐specific personalized estimation. This regularizer operates by learning two latent distance metrics—one between personalized parameters and one between clinical covariates—and attempting to match the induced distances as closely as possible. Crucially, we do not assume these distance metrics are already known. Instead, we allow the data to dictate the structure of these latent distance metrics. Finally, we apply our method to learn patient‐specific, interpretable models for a pan‐cancer gene expression dataset containing samples from more than 30 distinct cancer types and find strong evidence of personalization effects between cancer types as well as between individuals. Our analysis uncovers sample‐specific aberrations that are overlooked by population‐level methods, suggesting a promising new path for precision analysis of complex diseases such as cancer. Availability and implementation Software for personalized linear and personalized logistic regression, along with code to reproduce experimental results, is freely available at github.com/blengerich/personalized_regression.

Precision Lasso: accounting for correlations and linear dependencies in high-dimensional genomic data

Abstract Motivation Association studies to discover links between genetic markers and phenotypes are central to bioinformatics. Methods of regularized regression, such as variants of the Lasso, are popular for this task. Despite the good predictive performance of these methods in the average case, they suffer from unstable selections of correlated variables and inconsistent selections of linearly dependent variables. Unfortunately, as we demonstrate empirically, such problematic situations of correlated and linearly dependent variables often exist in genomic datasets and lead to under-performance of classical methods of variable selection. Results To address these challenges, we propose the Precision Lasso. Precision Lasso is a Lasso variant that promotes sparse variable selection by regularization governed by the covariance and inverse covariance matrices of explanatory variables. We illustrate its capacity for stable and consistent variable selection in simulated data with highly correlated and linearly dependent variables. We then demonstrate the effectiveness of the Precision Lasso to select meaningful variables from transcriptomic profiles of breast cancer patients. Our results indicate that in settings with correlated and linearly dependent variables, the Precision Lasso outperforms popular methods of variable selection such as the Lasso, the Elastic Net and Minimax Concave Penalty (MCP) regression. Availability and implementation Software is available at https://github.com/HaohanWang/thePrecisionLasso. Supplementary information Supplementary data are available at Bioinformatics online.