Measures of explained variation for survival data

The predictive power of a set of prognostic variables in a survival time model is a concept distinct from the statistical significance of the variables or the adequacy of the model fit. In this paper we discuss the importance of quantifying the predictive power of a prognostic model, and suggest measures of explained variation as a possible quantification. The important features of our approach are that (1) the measures are completely model-based; (2) a specification of the time range of interest is easily incorporated; and (3) the null models used for comparison are derived as mixtures of the predicted distributions.