Estimating the survival function based on the semi-Markov model for dependent censoring.

Area of Science:

• Statistics
• Survival Analysis
• Biostatistics

Background:

• Dependent censoring complicates survival function estimation.
• Semi-Markov models offer flexibility for complex event sequences.
• Accurate survival function estimation is crucial for clinical and reliability studies.

Purpose of the Study:

• To develop and evaluate a nonparametric maximum likelihood estimator (NPMLE) for the survival function under dependent censoring within a semi-Markov framework.
• To assess the asymptotic properties and finite-sample performance of the proposed NPMLE.
• To provide a consistent estimator for the asymptotic covariance function.

Main Methods:

• Utilized a semi-Markov model to account for complex event dependencies.
• Developed a nonparametric maximum likelihood estimator (NPMLE).
• Established asymptotic normality and efficiency of the NPMLE.
• Proposed a uniformly consistent estimator for the asymptotic covariance function.

Main Results:

• The proposed NPMLE is asymptotically normal and achieves nonparametric efficiency.
• Simulation studies indicate the NPMLE has a smaller mean squared error compared to existing estimators.
• Pointwise confidence intervals derived from the NPMLE demonstrate reasonable coverage probabilities.
• A uniformly consistent estimator for the asymptotic covariance function was developed.

Conclusions:

• The novel NPMLE provides a statistically sound and efficient method for survival function estimation under dependent censoring in semi-Markov models.
• The estimator offers superior finite-sample performance and reliable confidence intervals.
• The findings are validated through simulation and a real-world data example.