A note on patient follow-up time distribution in clinical trial simulations with survival endpoints

In this short note, we highlight a frequent issue in the specification of patient follow-up time distribution in clinical trial simulations. This issue arises from confusing two distinct concepts, namely the potential follow-up time and the loss-to-follow-up (LTFU) time, where the latter is inherently shorter than or equal to the former for survival endpoint trials. We provide a simple analytical formula to determine the LTFU time distribution based on the accrual, survival and potential follow-up time distributions. A grid method based on piecewise uniform distribution is suggested to reconstruct the potential follow-up time distribution from the targeted LTFU time distribution.