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<p>The Cox regression is a popular model for analyzing survival data with predictors. However, its effectiveness can decline when multicollinearity is present, resulting in unreliable estimates from the standard maximum partial likelihood approach. In this study, we develop improved shrinkage estimators inspired by the Liu method to enhance the accuracy of coefficient estimation. Specifically, we develop several estimators, including linear shrinkage, Stein, positive Stein, pretest, and shrinkage pretest estimators, that leverage prior knowledge about the model parameters. We derive their asymptotic properties and assess their performance through extensive Monte Carlo simulations. We further illustrate how to evaluate the estimation strategies on survival data. Our findings reveal notable improvements, demonstrating the practical benefits of these estimators for researchers.</p>

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Combating multicollinearity in the Cox model using improved Liu estimators

  • 期刊论文

  • 发表日期：

    2026年5月2日

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  • Seyed Amirhossein Tabatabaei Shirazi,
  • Mahdi Emadi,
  • Mohammad Arashi,
  • Solmaz Seifollahi

摘要

The Cox regression is a popular model for analyzing survival data with predictors. However, its effectiveness can decline when multicollinearity is present, resulting in unreliable estimates from the standard maximum partial likelihood approach. In this study, we develop improved shrinkage estimators inspired by the Liu method to enhance the accuracy of coefficient estimation. Specifically, we develop several estimators, including linear shrinkage, Stein, positive Stein, pretest, and shrinkage pretest estimators, that leverage prior knowledge about the model parameters. We derive their asymptotic properties and assess their performance through extensive Monte Carlo simulations. We further illustrate how to evaluate the estimation strategies on survival data. Our findings reveal notable improvements, demonstrating the practical benefits of these estimators for researchers.