# A novel nonparametric measure of explained variation for survival data with an easy graphical interpretation

## TL;DR

This paper introduces a new nonparametric measure to assess how well survival models fit data, with a clear visual interpretation.

## Contribution

A novel nonparametric measure of explained variation for survival data with graphical interpretation is proposed.

## Key findings

- The new measure is based on the Kaplan-Meier estimator and is nonparametric.
- The measure allows for different weighting options and a significance test.
- The method was applied to a dataset of papillary thyroid carcinoma patients.

## Abstract

Introduction: For survival data the coefficient of determination cannot be used to describe how good a model fits to the data. Therefore, several measures of explained variation for survival data have been proposed in recent years.

Methods: We analyse an existing measure of explained variation with regard to minimisation aspects and demonstrate that these are not fulfilled for the measure.

Results: In analogy to the least squares method from linear regression analysis we develop a novel measure for categorical covariates which is based only on the Kaplan-Meier estimator. Hence, the novel measure is a completely nonparametric measure with an easy graphical interpretation. For the novel measure different weighting possibilities are available and a statistical test of significance can be performed. Eventually, we apply the novel measure and further measures of explained variation to a dataset comprising persons with a histopathological papillary thyroid carcinoma.

Conclusion: We propose a novel measure of explained variation with a comprehensible derivation as well as a graphical interpretation, which may be used in further analyses with survival data.