Forward regression for Cox models with high-dimensional covariates.

Area of Science:

• Statistics
• Biostatistics
• Machine Learning

Background:

• Forward regression is a classical variable screening method, but its application is limited in high-dimensional settings due to computational complexity and theoretical uncertainties.
• Existing research shows forward regression with an extended Bayesian information criterion (EBIC) can identify predictors in linear models, but its use in survival analysis remains unexplored.

Purpose of the Study:

• To introduce and investigate a novel forward variable selection procedure for high-dimensional Cox proportional hazards models.
• To establish theoretical guarantees for the selection consistency of this procedure in survival data settings.

Main Methods:

• A sequential variable selection approach is proposed, utilizing the increment of partial likelihood to identify important predictors.
• An extended Bayesian information criterion (EBIC) is employed as a stopping rule for the forward selection process.
• New theoretical results on partial likelihood are developed to prove sure screening properties.

Main Results:

• The proposed forward regression method consistently identifies all relevant predictors in high-dimensional Cox models.
• The order of variable entry is determined by the magnitude of the partial likelihood increment.
• The method demonstrates practical utility through simulations and analysis of lung cancer survival data.

Conclusions:

• This study presents the first partial likelihood-based forward regression for high-dimensional survival analysis.
• The developed method offers a theoretically sound and practically useful tool for variable selection in complex survival data.
• The findings have implications for biomarker discovery in cancer research and other survival-related studies.