Estimation of the censoring distribution in clinical trials.

Clinical studies with time to event endpoints typically report the median follow-up (i.e., censoring) time for the subjects in the trial, alongside the median time to event. The reason for this is to provide information about the opportunity for subjects in the study to experience the event of interest (Betensky, 2015 [1]). The median follow-up time is often calculated from the Kaplan-Meier estimate for time to censoring. In most clinical studies, the censoring time is a composite measure, defined as the minimum of time to drop-out from the study and time to administrative end of study. The time to drop-out component may or may not be observed; it is observed only if drop-out occurs before the event and the end of the study. However, the time to end of study is observed for each subject, as it is the time from entry to the study to the calendar date that is administratively set as the end of the study. It is known even for subjects who have the event prior to the end of the study. This decomposition of the censoring time into a time that is itself potentially censored and a time that is fully observed raises the interesting question of whether estimation of the censoring distribution could be improved through a decoupling of these times. We demonstrate in simulations that consideration of censoring in this way yields reduced variability under some circumstances and should be used in practice. We illustrate these concepts through application to a meningioma study.