Network-regularized Sparse Logistic Regression Models for Clinical Risk Prediction and Biomarker Discovery
This work addresses the need for more interpretable and predictive biomarkers in clinical settings, though it appears incremental as it builds upon existing regularization frameworks.
The authors tackled the problem of improving clinical risk prediction and biomarker discovery from molecular data by integrating prior biological knowledge, introducing a novel network-regularized sparse logistic regression model with a penalty based on absolute coefficient values to address issues with traditional methods when coefficients have opposite signs, and demonstrated its efficiency through simulations and real data comparisons.
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 $λ\|\bm{w}\|_1 + η\bm{w}^T\bm{M}\bm{w}$, 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 $λ\|\bm{w}\|_1 + η|\bm{w}|^T\bm{M}|\bm{w}|$ 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.