Penalized Cox Regression Models for High-Dimensional Survival Analysis: An Application to Breast Cancer Microarray Data

Abstract

Survival analysis provides a statistical framework for examining the relationship between time to event outcomes and explanatory variables. The Cox proportional hazards (Cox PH) model is widely used for this purpose, but its performance deteriorates in high-dimensional settings, where the number of predictors is large and strong collinearity is present. Penalized Cox regression methods have been developed to address these limitations by incorporating regularization into the estimation process. This study applies penalized Cox regression models to breast cancer microarray survival data obtained from the Gene Expression Omnibus dataset GSE20685, which contains gene expression measurements for 54,682 genes across 327 patients. The aim of this study is to fit and compare Ridge, LASSO, and Elastic Net Cox models with the classical Cox PH model. Model performance is evaluated using root mean square error (RMSE), with emphasis placed on test set results to assess predictive generalization. The results show that penalized Cox regression models consistently outperform the Cox PH model on the test set across all evaluated predictor dimensions. While the Cox PH model fails to produce reliable predictions when the number of predictors is large, the penalized models remain stable and effective. Among the penalized approaches, Ridge regression demonstrates the most robust performance in ultra-high-dimensional settings, whereas LASSO and Elastic Net provide competitive performance at lower and moderate dimensional levels through feature selection. These findings highlight the importance of regularization for survival modelling in high-dimensional genomic data and demonstrate that penalized Cox regression offers a more reliable alternative to the classical Cox PH model for microarray-based survival prediction.