Efficient Post-Shrinkage Estimation Strategies in High-Dimensional Cox's Proportional Hazards Models

Regularization methods such as LASSO, adaptive LASSO, Elastic-Net, and SCAD are widely employed for variable selection in statistical modeling. However, these methods primarily focus on variables with strong effects while often overlooking weaker signals, potentially leading to biased parameter estimates. To address this limitation, Gao, Ahmed, and Feng (2017) introduced a corrected shrinkage estimator that incorporates both weak and strong signals, though their results were confined to linear models. The applicability of such approaches to survival data remains unclear, despite the prevalence of survival regression involving both strong and weak effects in biomedical research. To bridge this gap, we propose a novel class of post-selection shrinkage estimators tailored to the Cox model framework. We establish the asymptotic properties of the proposed estimators and demonstrate their potential to enhance estimation and prediction accuracy through simulations that explicitly incorporate weak signals. Finally, we validate the practical utility of our approach by applying it to two real-world datasets, showcasing its advantages over existing methods.