An empirical likelihood method for semiparametric linear regression with right censored data

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Modeling

Background:

• Semiparametric linear regression models are frequently used for analyzing survival data.
• The Buckley-James estimator is a common method but has limitations, particularly with variance estimation.
• Existing empirical likelihood methods may not fully address the complexities of censored data and unknown error distributions.

Purpose of the Study:

• To develop a new empirical likelihood method for semiparametric linear regression with right censored survival data.
• To address challenges associated with unknown error distributions and variance estimation in survival analysis.
• To extend the empirical likelihood method to incorporate auxiliary information.

Main Methods:

• The proposed method is based on the Buckley-James estimating equation.
• It utilizes empirical likelihood principles, similar to those for complete data.
• The method is extended to integrate auxiliary information for enhanced analysis.

Main Results:

• The new empirical likelihood method avoids the need for variance estimation, a known issue with the Buckley-James estimator.
• Simulation studies demonstrate competitive performance compared to the synthetic data empirical likelihood method.
• The method is successfully applied to the Stanford heart transplantation dataset.

Conclusions:

• The developed empirical likelihood method offers a robust alternative for semiparametric regression with censored survival data.
• It provides a valuable tool for biostatisticians and researchers dealing with complex survival data.
• The incorporation of auxiliary information further enhances the method's applicability.