Developing individualized prediction rules for disease risk and prognosis has played a key role in modern medicine. When new genomic or biological markers become available to assist in risk prediction, it is essential to assess the improvement in clinical usefulness of the new markers over existing routine variables. Net reclassification improvement (NRI) has been proposed to assess improvement in risk reclassification in the context of comparing two risk models and the concept has been quickly adopted in medical journals (Pencina et al., Stat Med 27:157-172, 2008). We propose both nonparametric and semiparametric procedures for calculating NRI as a function of a future prediction time [Formula: see text] with a censored failure time outcome. The proposed methods accommodate covariate-dependent censoring, therefore providing more robust and sometimes more efficient procedures compared with the existing nonparametric-based estimators (Pencina et al., Stat Med 30:11-21, 2011; Uno et al., Comparing risk scoring systems beyond the roc paradigm in survival analysis, 2009). Simulation results indicate that the proposed procedures perform well in finite samples. We illustrate these procedures by evaluating a new risk model for predicting the onset of cardiovascular disease.