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I wanted to obtain the mean and median survival times using survfit and Surv but due to the small event size, I can't obtain them. How should I proceed with analysing this survival data?

sfit <- survfit(Surv(time_to_event, event) ~ 1, data = df)
sfit
Call: survfit(formula = Surv(time_to_event, event) ~ 1, data = df)

      n  events  median 0.95LCL 0.95UCL 
     62      15      NA      NA      NA 
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With only 15 events out of 62 cases, it seems likely that your Kaplan-Meier curve hasn't even reached the median survival yet. See this page for a similar situation.

Unless the very last time is an event (which can't be the case if you haven't yet reached the median survival), the mean survival will be a truncated value calculated out only to some particular time. The survfit() function does allow for such mean survivals, but you have to specify what type of upper time limit you want (your call to the software might have specified "none" for that mean calculation) and they aren't always very informative in any event.

The best way to present the data is to show the Kaplan-Meier curve with confidence limits. You could consider showing values and CI for a survival time you have reached, perhaps 80% survival.

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