title: A novel nonparametric measure of explained variation for survival data with an easy graphical interpretation.
abstract: BACKGROUND
  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.
  
  
  CONCLUSIONS
  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.
authors.affiliation: Institute of Medical Statistics, Informatics and Epidemiology, University of Cologne, Germany.
authors.forename: Verena
authors.initials: V
authors.lastname: Weiß
authors.affiliation: Department of Nuclear Medicine, University of Cologne, Germany.
authors.forename: Matthias
authors.initials: M
authors.lastname: Schmidt
authors.affiliation: Institute of Medical Statistics, Informatics and Epidemiology, University of Cologne, Germany.
authors.forename: Martin
authors.initials: M
authors.lastname: Hellmich
mesh_terms: D000704:Analysis of Variance; D003627:Data Interpretation, Statistical; D006801:Humans; D053208:Kaplan-Meier Estimate; D015233:Models, Statistical; D018709:Statistics, Nonparametric; D013964:Thyroid Neoplasms / Q000401:mortality*
keywords: explained variation; nonparametric; novel measure; survival data; test of significance