Evaluating a New Risk Marker's Predictive Contribution in Survival Models

Although the area under the receiver operating characteristic (ROC) curve (AUC) is the most popular measure of the performance of prediction models, it has limitations, especially when it is used to evaluate the added discrimination of a new risk marker in an existing risk model. Pencina et al. (2008) proposed two indices, the net reclassification improvement (NRI) and integrated discrimination improvement (IDI), to supplement the improvement in the AUC (IAUC). Their NRI and IDI are based on binary outcomes in case-control settings, which do not involve time-to-event outcome. However, many disease outcomes are time-dependent and the onset time can be censored. Measuring discrimination potential of a prognostic marker without considering time to event can lead to biased estimates. In this paper, we extended the NRI and IDI to time-to-event settings and derived the corresponding sample estimators and asymptotic tests. Simulation studies showed that the time-dependent NRI and IDI have better performance than Pencina's NRI and IDI for measuring the improved discriminatory power of a new risk marker in prognostic survival models.