In medical research, it is often of interest to evaluate the predictive performance of a biomarker. Statistical approaches based on the Receiver Operating Characteristic (ROC) curve and its summary measures, such as the area under the curve (AUC) and the Youden index, are widely used to evaluate the prognostic performance of these biomarkers. In time-to-event studies, ROC analysis poses additional challenges due to change in disease status over time and the presence of censored individuals. To address these issues, time-dependent ROC curves were introduced. In this paper, we propose a non-parametric estimator of the time-dependent two-way partial AUC for right-censored data. We also discuss the partial Youden index and the associated optimal biomarker cutoff estimator for the right-censored data. We conduct an extensive simulation study to investigate the finite sample performance of the proposed estimators. The simulation study indicates that the proposed non-parametric estimators efficiently account for right censoring. Finally, we illustrate the proposed methods using two real data sets, one from the Primary Biliary Cirrhosis study and the other from the Molecular Taxonomy of Breast Cancer International Consortium trial.
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