Proportional hazard model estimation under dependent censoring using copulas and penalized likelihood

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Modeling

Background:

• Estimating survival probabilities is crucial in medical research, but informative censoring complicates standard Cox proportional hazard models.
• Existing methods may not adequately handle the dependence between event and censoring times, leading to biased results.

Purpose of the Study:

• To develop a robust method for Cox proportional hazard model estimation with informative right censored data.
• To ensure the baseline hazard function is smooth and non-negative, improving model reliability.
• To provide theoretical guarantees for the proposed estimation method.

Main Methods:

• Utilizing maximum penalized likelihood estimation to model the dependence between censoring and event times via a copula function.
• Employing a roughness penalty function to constrain the baseline hazard to be a smooth function.
• Developing a specialized iterative algorithm combining Newton's method for regression coefficients and a multiplicative algorithm for the baseline hazard.

Main Results:

• The proposed method effectively handles informative right censoring by modeling dependencies with copulas and ensuring a smooth baseline hazard.
• Asymptotic properties for both regression coefficient and baseline hazard estimates are theoretically established.
• Simulation studies demonstrate the superior performance of the proposed method compared to existing maximum likelihood approaches.

Conclusions:

• The developed maximum penalized likelihood method offers a reliable approach for survival data with informative censoring.
• The method's ability to produce smooth, non-negative baseline hazards enhances its applicability in biostatistical analyses.
• Application to a dementia patient dataset highlights the practical utility of this advanced survival analysis technique.