This paper analyses a case in censored failure time data problems where some observations are potentially censored. The traditional models for failure time data implicitly assume that the censoring status for each observation is deterministic. Therefore, they cannot be applied directly to the potentially censored data. We propose an estimator that uses resampling techniques to approximate censoring probabilities for individual observations. A Monte Carlo simulation study shows that the proposed estimator properly corrects biases that would otherwise be present had it been assumed that either all potentially censored observations are censored or that no censoring has occurred. Finally, we apply the estimator to a health insurance claims database. Copyright © 2004 John Wiley & Sons, Ltd.