Penalized Empirical Likelihood for the Sparse Cox Regression Model.

Area of Science:

• Statistics
• Biostatistics
• Machine Learning

Background:

• Penalized regression methods for sparse Cox models often rely on partial likelihood.
• High-dimensional data presents challenges for variable selection and coefficient estimation in these models.

Purpose of the Study:

• To propose a novel bias-corrected empirical likelihood method for sparse Cox models with high-dimensional data.
• To enhance predictor variable selection and regression coefficient estimation accuracy.

Main Methods:

• Developed a bias-corrected empirical likelihood approach.
• Incorporated appropriate penalty functions for high-dimensional settings.
• Proved theoretical properties of the estimator for large samples.

Main Results:

• The proposed penalized empirical likelihood method demonstrates superior performance over partial likelihood.
• Achieved better accuracy in selecting correct predictors.
• Avoided introducing additional model errors compared to existing methods.

Conclusions:

• The bias-corrected empirical likelihood method offers an effective alternative for sparse Cox models with high-dimensional data.
• This method provides improved variable selection and estimation accuracy.
• The approach is validated using the primary biliary cirrhosis dataset.