Permutation Tests Based on the Copula-Graphic Estimator and Their Use for Survival Tree Construction

Area of Science:

• Biostatistics
• Machine Learning
• Survival Analysis

Background:

• Survival trees offer flexibility and interpretability, but often assume independent censoring.
• Existing models like Cox and Aalen regression have limitations in handling complex censoring patterns.

Purpose of the Study:

• To develop a novel survival tree algorithm that relaxes the assumption of independent censoring.
• To introduce a copula-graphic estimator for flexible modeling of survival and censoring time dependencies.
• To evaluate the performance of the new algorithm against existing methods.

Main Methods:

• Utilized a copula-graphic estimator to estimate survival functions, allowing flexible specification of dependence.
• Developed a permutation test based on the integrated absolute distance of copula-graphic estimators for group comparisons.
• Conducted simulation studies to assess type I error, power, and tree performance under various dependence scenarios (Clayton, Frank copulas).

Main Results:

• The new permutation test demonstrated good type I error and power behavior in simulations.
• Survival trees built with the new splitting criterion showed competitive performance compared to logrank-based trees.
• The algorithm was successfully applied to real-world clinical trial data.

Conclusions:

• The proposed survival tree algorithm effectively handles dependent censoring, offering a more flexible and realistic approach.
• The copula-graphic estimator and permutation test provide a robust framework for survival analysis with dependent censoring.
• This method has practical implications for analyzing clinical trial data where censoring may not be independent.