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

## TL;DR

This paper introduces a new survival tree algorithm using a copula-graphic estimator to handle dependent censoring, improving survival analysis in clinical data.

## Contribution

A novel permutation test based on the copula-graphic estimator is introduced for survival tree construction under dependent censoring.

## Key findings

- The new permutation test shows good type I error and power in simulations with varying group sizes and censoring.
- Survival trees using the new test outperform logrank-based trees in certain simulation scenarios.
- The method is successfully applied to real clinical trial data.

## Abstract

Survival trees are popular alternatives to Cox or Aalen regression models that offer both modeling 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 groups' copula‐graphic estimators. A first simulation study shows a good type I error and power behavior of the new test. We thereby assess simulation settings of various group sizes, censoring percentages, and grades of dependence generated by Clayton and Frank copulas. Using this test as a 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.