Threshold-free measure for assessing the performance of risk prediction with censored data

The area under the receiver operating characteristic curve (AUC) is a popular threshold-free metric to retrospectively measure the discriminatory performance of medical tests. In risk prediction or medical screening, main interests often focus on accurately predicting the future risk of an event of interest or prospectively stratifying individuals into risk categories. Thus, AUC might not be optimal in assessing the predictive performance for such purposes. Alternative accuracy measures have been proposed, such as the positive predictive value (PPV). Yuan et al. (2015) proposed a threshold-free metric, the average positive predictive value (AP), which is the area under the PPV versus true positive fraction (TPF) curve, when the outcome is binary disease status. In this thesis, we propose the time-dependent AP when the outcome is censored event time. Empirical estimates of the time-dependent AP (AP_t0) are developed, where the inverse weighted probability technique is applied to deal with censoring. In addition, inference procedures — using bootstrap and perturbation resampling—are proposed to construct confidence intervals. We conduct simulation studies to investigate the performance of the proposed estimation and inference procedures in finite samples. The method is also illustrated through a real data analysis.