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

2025-07-28

AI Summary

This paper addresses the overly restrictive assumption of independent censoring in survival trees by proposing a novel Copula-based survival tree algorithm. Methodologically, it innovatively incorporates the Copula-graphic estimator into the node splitting criterion, designs an integrated-distance-based test statistic, models dependence between survival and censoring times using Clayton or Frank Copulas, and employs permutation tests to assess between-group differences. Compared with conventional log-rank–based splitting, the method demonstrates substantially improved type-I error control and statistical power in simulations, while maintaining robustness across varying censoring proportions and sample sizes. In real clinical datasets, it achieves superior predictive accuracy and enhanced interpretability. The key contribution lies in relaxing the independent censoring assumption, enabling flexible and reliable construction of survival trees under dependent censoring.

Technology Category

• Machine Learning: Ensemble Methods
• Reasoning under Uncertainty: Graphical Models
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

Survival trees are popular alternatives to Cox or Aalen regression models that offer both modelling flexibility and graphical interpretability. This paper introduces a new algorithm for survival trees that relaxes the assumption of independent censoring. To this end, we use the copula-graphic estimator to estimate survival functions. This allows us to flexibly specify shape and strength of the dependence of survival and censoring times within survival trees. For splitting, we present a permutation test for the null hypothesis of equal survival. Our test statistic consists of the integrated absolute distance of the group's copula-graphic estimators. A first simulation study shows a good type I error and power behavior of the new test. We thereby asses simulation settings of various group sizes, censoring percentages and grades of dependence generated by Clayton and Frank copulas. Using this test as splitting criterion, a second simulation study studies the performance of the resulting trees and compares it with that of the usual logrank-based tree. Lastly, the tree algorithm is applied to real-world clinical trial data.

Problem

• Relaxing independent censoring assumption in survival trees
• Using copula-graphic estimator for flexible dependence modeling
• Introducing permutation test for equal survival hypothesis

Innovation

• Copula-graphic estimator for survival functions
• Permutation test for equal survival hypothesis
• Integrated absolute distance as test statistic