  This paper focuses on quantifying and estimating the predictive accuracy of
prognostic models for time-to-event outcomes with competing events. We consider
the time-dependent discrimination and calibration metrics, including the
receiver operating characteristics curve and the Brier score, in the context of
competing risks. To address censoring, we propose a unified nonparametric
estimation framework for both discrimination and calibration measures, by
weighting the censored subjects with the conditional probability of the event
of interest given the observed data. We demonstrate through simulations that
the proposed estimator is unbiased, efficient and robust against model
misspecification in comparison to other methods published in the literature. In
addition, the proposed method can be extended to time-dependent predictive
accuracy metrics constructed from a general class of loss functions. We apply
the methodology to a data set from the African American Study of Kidney Disease
and Hypertension to evaluate the predictive accuracy of a prognostic risk score
in predicting end-stage renal disease (ESRD), accounting for the competing risk
of pre-ESRD death.
