# Restricted mean survival in a study without administrative censoring

Suppose a safety study is to be conducted where subjects can be followed interminably. Subjects are censored randomly d/t loss to follow-up or withdrawal of consent, assume it’s non-informative. Is the restricted mean survival a consistent estimator without condiditons on the censoring process? If so does it actually converge to the mean survival?

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I believe this will depend only on the method used to estimate the survival curve. A consistent/unbiased estimate of S(t) that is correct for 0 \leq t \leq w, where w is the restriction time, will lead to a consistent/unbiased estimate of restricted mean survival. If w is a good amount less than the maximum uncensored time, the Kaplan-Meier estimate of S(t) will do the trick.

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