Summary The predictive accuracy of a survival model can be summarized using extensions of the proportion of variation explained by the model, or R2, 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.