Measures of explained variation under the mixture cure model for survival data

Explained variation is well understood under linear regression models and has been extended to models for survival data. In this article, we consider the mixture cure models. We propose two approaches to define explained variation under the mixture cure models, one based on the Kullback-Leibler information gain and the other based on residual sum of squares. We show that the proposed measures have desired properties as measures of explained variation, similar to those under other regression models. A simulation study is conducted to demonstrate the properties of the proposed measures. They are also applied to real data analyses to illustrate the use of explained variation.