EMPIRICAL LIKELIHOOD INFERENCE FOR THE COX MODEL WITH TIME-DEPENDENT COEFFICIENTS VIA LOCAL PARTIAL LIKELIHOOD

Area of Science:

• Statistics
• Biostatistics
• Survival Analysis

Background:

• Time-dependent coefficients in Cox models are crucial for analyzing evolving risk factors.
• Existing methods for confidence regions may lack precision and fail to capture coefficient function dynamics.

Purpose of the Study:

• To develop novel empirical likelihood (EL) based confidence regions and bands for time-dependent regression coefficients in Cox models.
• To evaluate the finite sample performance and accuracy of the proposed EL methods.

Main Methods:

• Utilizing local partial likelihood smoothing to formulate the empirical likelihood ratio.
• Applying strong approximation methods for deriving simultaneous confidence bands.
• Developing pointwise confidence regions for time-dependent regression coefficients.

Main Results:

• Empirical likelihood methods provide satisfactory finite sample performance for both pointwise and simultaneous confidence regions/bands.
• EL confidence regions are demonstrated to be tighter and more effective at capturing coefficient function curvature compared to asymptotic normal distribution-based methods.
• The proposed methods were successfully applied to gastric cancer and primary biliary cirrhosis datasets.

Conclusions:

• The developed empirical likelihood approach offers a superior method for constructing confidence regions in time-dependent Cox models.
• These findings advance the analysis of time-varying effects in survival data, offering improved precision and interpretability.