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

## TL;DR

This paper introduces a new method for improving survival analysis by better capturing both strong and weak signals in high-dimensional data.

## Contribution

A novel class of post-selection shrinkage estimators for the Cox model that improves estimation by incorporating weak signals.

## Key findings

- The proposed estimators show improved accuracy in simulations with weak signals.
- The method outperforms existing approaches on real-world biomedical datasets.

## Abstract

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.