Testing for undetected withdrawal in a follow-up study of times to events

Undetected withdrawal of units from a study inflates the length of time remaining between the last recorded event and the end of the study. Treating these times as right-censored observations may give misleading results. A test is given for excessive remaining times assuming homogeneous Poisson processes, using approximations to the sum of Beta random variables. The distortion of trend tests by wrongly including these times in the analysis is examined and found to be substantial. On the other hand, the loss of power through unnecessarily dropping the time after the last event from the analysis is relatively insignificant, so the safest course is to discard these times. Tests for use when only one event per unit can be recorded are also considered. Simple randomization tests are shown to be effective in this case.