In biomedical studies, statistical approaches based on the Receiver Operating Characteristic (ROC) analysis have been extensively used in the evaluation of classification performance of markers and construction of classifiers. In this article, we investigate time-dependent ROC approaches for censored survival data. While most existing studies have been focused on uncensored and right-censored data, insufficient attention has been paid to other censoring schemes. This study advances from existing studies by investigating more diverse censoring schemes and developing ROC measurements under such censoring. Both estimation and inference are investigated. We conduct simulation and find satisfactory performance of the proposed approaches. We apply the proposed approaches to two real data sets, compare the prognostic power of markers, and investigate whether their linear combinations have better prognostic performance. We also explore graphical tools that can assist diagnostics and efficiently monitor the classification performance. Copyright © 2011 John Wiley & Sons, Ltd.