Explained Variation in Survival Analysis

Several measures of explained variation have been suggested for the Cox proportional hazards regression model. We have categorized these measures into three classes which correspond to three different definitions of multiple R2 of the general linear model. In an empirical study we compared the performance of these measures and classified them by their adherence to a set of criteria which we think should be met by a measure of explained variation for survival data. We suggest that currently there is no uniformly superior measure, particularly as the concepts of either uncensored or censored populations may lead to different choices. For uncensored populations, a measure by Kent and O'Quigley and the squared rank correlation between survival time and the predictor from a Cox regression model appear recommendable choices. For the latter, censored survival times are terminated using a very recent data augmentation algorithm for multiple imputation under proportional hazards. With censored populations, Schemper's measure, V2, could be considered. We give an introductory example, discuss aspects of application and stress the desirability of routinely evaluating explained variation in studies of survival.