Kaplan Meier survival estimate at t=infinite

Question

Since the KM estimator does not allow for any other state other than the event of interest is it safe to assume that $S(t=\infty) = 0$ ? Or can it be that $S(t=\infty) > 0$

Answer 1

When different from zero at the largest event time (i.e. when the largest observation is censored), the Kaplan-Meier estimator is usually undefined from that point on. There exist methods for completing the Kaplan-Meier estimator (for example, see here). In any case, the underlying survival function decreases to zero, $S(\infty) = 0$ even if $\hat{S}(\text{largest event time}) \neq 0$. Models that allow for $S(\infty) \neq 0$ are called cure models.

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EDIT related to your comment below

The first sentence of this paper, which shows how to fit a cure model, says "In survival analysis, it is usually assumed that if complete follow-up were possible for all individuals, each would eventually experience the event of interest." That is, $S(\infty) = 0$, by assumption. Almost any other paper on cure models starts in the same way.

Answer 2

The Kaplan-Meier method computes the actual observed percent survival at each time a subject dies in your experiment. It describes your data, taking into account censoring. No theoretical model. No extrapolation.

Any assumption about survival at infinite times needs to be based on a model, so is beyond Kaplan and Meier.

Of course, it is hard to imagine any model of survival that doesn't end up at zero survival at long time points :)