Non-parametric estimation of gap time survival functions for ordered multivariate failure time data

Area of Science:

• Biostatistics
• Survival Analysis
• Biomedical Data Science

Background:

• Analyzing sequential event times (gap times) in biomedical studies, such as cancer progression or renal failure, presents statistical challenges.
• Common issues include right censoring and dependent failure times within subjects, complicating the analysis of multiple gap times.
• Induced dependent censoring and non-identifiable marginal distributions are key hurdles in modeling subsequent gap times.

Purpose of the Study:

• To propose a novel non-parametric method for estimating conditional gap-time specific survival functions.
• To address the statistical complexities associated with analyzing second and subsequent gap times in longitudinal biomedical data.
• To provide a robust statistical framework for understanding event sequences in the presence of censoring and dependency.

Main Methods:

• Development of a non-parametric approach for constructing one-sample estimators of conditional gap-time specific survival functions.
• Theoretical analysis demonstrating uniform consistency of the estimators.
• Asymptotic analysis showing weak convergence to a zero-mean Gaussian process with a consistently estimable covariance function.

Main Results:

• The proposed estimators are uniformly consistent.
• Standardized estimators converge weakly to a zero-mean Gaussian process, with a consistently estimable covariance function.
• Simulation studies confirm the appropriateness of asymptotic approximations for finite sample sizes, supported by methods for confidence bands.

Conclusions:

• The developed non-parametric method offers a statistically sound approach for analyzing sequential gap times in biomedical research.
• The method effectively handles dependent censoring and non-identifiable distributions, providing reliable survival function estimates.
• The approach is validated through simulations and demonstrated on a renal failure dataset, highlighting its practical utility.