To quantify the ability of a marker to predict the onset of a clinical outcome in the future, time-dependent estimators of sensitivity, specificity, and ROC curve have been proposed accounting for censoring of the outcome. In this paper, we review these estimators, recall their assumptions about the censoring mechanism and highlight their relationships and properties. A simulation study shows that marker-dependent censoring can lead to important biases for the ROC estimators not adapted to this case. A slight modification of the inverse probability of censoring weighting estimators proposed by Uno et al. (2007) and Hung and Chiang (2010a) performs as well as the nearest neighbor estimator of Heagerty et al. (2000) in the simulation study and has interesting practical properties. Finally, the estimators were used to evaluate abilities of a marker combining age and a cognitive test to predict dementia in the elderly. Data were obtained from the French PAQUID cohort. The censoring appears clearly marker-dependent leading to appreciable differences between ROC curves estimated with the different methods.