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

TL;DR

This paper introduces a novel survival tree algorithm that uses copula-graphic estimators and permutation tests to handle dependent censoring, improving flexibility and interpretability in survival analysis.

Contribution

It presents a new survival tree method based on copula-graphic estimators and permutation tests, relaxing the independent censoring assumption and enhancing modeling flexibility.

Findings

Good control of type I error and power in simulations

Effective handling of dependent censoring in survival data

Comparable or improved performance over traditional logrank-based trees

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.