Network-regularized Sparse Logistic Regression Models for Clinical Risk Prediction and Biomarker Discovery

TL;DR

This paper introduces a novel network-regularized sparse logistic regression framework that incorporates prior biological knowledge for improved clinical risk prediction and biomarker discovery, with efficient algorithms and demonstrated effectiveness.

Contribution

It proposes a new penalty for network-regularized sparse logistic regression that considers absolute coefficient differences, enhancing performance over traditional methods.

Findings

The new model outperforms existing methods in simulated and real data.

The algorithms are efficient and avoid matrix inversion, speeding up computation.

Incorporating prior network information improves biomarker identification.

Abstract

Molecular profiling data (e.g., gene expression) has been used for clinical risk prediction and biomarker discovery. However, it is necessary to integrate other prior knowledge like biological pathways or gene interaction networks to improve the predictive ability and biological interpretability of biomarkers. Here, we first introduce a general regularized Logistic Regression (LR) framework with regularized term $\lambda \|\bm{w}\|_1 + \eta\bm{w}^T\bm{M}\bm{w}$, which can reduce to different penalties, including Lasso, elastic net, and network-regularized terms with different $\bm{M}$. This framework can be easily solved in a unified manner by a cyclic coordinate descent algorithm which can avoid inverse matrix operation and accelerate the computing speed. However, if those estimated $\bm{w}_i$ and $\bm{w}_j$ have opposite signs, then the traditional network-regularized penalty may not perform well. To address it, we introduce a novel network-regularized sparse LR model with a new penalty $\lambda \|\bm{w}\|_1 + \eta|\bm{w}|^T\bm{M}|\bm{w}|$ to consider the difference between the absolute values of the coefficients. And we develop two efficient algorithms to solve it. Finally, we test our methods and compare them with the related ones using simulated and real data to show their efficiency.