Survival analysis for the missing censoring indicator model using kernel density estimation techniques

Area of Science:

• Statistics
• Survival Analysis
• Biostatistics

Background:

• Missing data in censoring indicators poses challenges in survival analysis.
• Existing estimators may not fully address the complexities of random censorship with missing indicators.

Purpose of the Study:

• To develop and analyze a new estimator for the survival function in the presence of missing censoring indicators.
• To derive asymptotic properties, including large sample results and consistency, for a novel cumulative hazard function estimator.

Main Methods:

• Utilized an inverse probability-of-non-missingness weighted approach.
• Employed kernel estimation for the conditional probability of non-missingness.
• Derived almost sure representations, uniform strong consistency, bias, variance, and mean squared error.

Main Results:

• Established large sample results for the inverse probability-of-non-missingness weighted cumulative hazard function estimator.
• Demonstrated uniform strong consistency with a rate of convergence for the proposed estimator.
• The derived survival function estimator is asymptotically efficient.

Conclusions:

• The novel estimator provides a robust method for survival function estimation with missing censoring indicators.
• The derived asymptotic properties support its theoretical validity and efficiency.
• Numerical studies confirm its competitive performance against existing methods.