Survival model predictive accuracy and ROC curves

The predictive accuracy of a survival model can be summarized using extensions of the proportion of variation explained by the model, or R 2: commonly used for continuous response models, or using extensions of sensitivity and specificity, which are commonly used for binary response models. In this article we propose new time-dependent accuracy summaries based on time-specific versions of sensitivity and specificity calculated over risk sets. We connect the accuracy summaries to a previously proposed global concordance measure, which is a variant of Kendall's tau. In addition, we show how standard Cox regression output can be used to obtain estimates of time-dependent sensitivity and specificity, and time-dependent receiver operating characteristic (ROC) curves. Semiparametric estimation methods appropriate for both proportional and nonproportional hazards data are introduced, evaluated in simulations, and illustrated using two familiar survival data sets.