Abstract: In high-dimensional survival analysis, complex relationships involving both linear and nonlinear effects are prevalent. Traditional linear Cox proportional hazards models often fail to capture these complex nonlinearities, while purely neural network-based methods struggle with overfitting and a lack of interpretability in high-dimensional settings. This paper proposes a Deep Partial Linear Cox Model with adaptive Minimax Concave Penalty (MCP) regularization, termed DMCOX. While preserving the interpretability of the classic Cox model, the proposed method integrates deep neural networks into the Partial Linear Cox Model (PLCM) framework. It leverages the universal approximation capability of neural networks to flexibly capture the non-linear effects of low-dimensional covariates, while simultaneously introducing MCP regularization to achieve unbiased estimation and precise feature selection for high-dimensional linear covariates. A hybrid optimization objective combining MCP regularization and neural network approximation is constructed, and an alternating optimization algorithm based on coordinate descent and gradient-based updates is designed for model solving. Extensive numerical simulation experiments demonstrate that DMCOX outperforms traditional Cox models, simple deep learning-based models, and methods using Lasso, SCAD, or L0 penalties. Under various censoring rates and non-linear complexity scenarios, DMCOX exhibits superior predictive accuracy (C-index) and variable selection performance (Recall, F1-score), effectively overcoming overfitting and underfitting issues. Furthermore, the application of the model to real-world high-grade serous ovarian cancer (HGSOC) data, combined with SP-LIME for feature screening and interpretability analysis, successfully identified key prognostic gene features such as TAP1, CXCL9, and COL11A1. The model achieved predictive performance superior to existing methods, validating its effectiveness and clinical potential in precision medicine and biomarker discovery.

Key words: high-dimensional survival analysis, deep neural networks, partial linear Cox model, MCP regularization