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I am performing survival analysis (Kaplan-Meier, Cox-regression) for 1500 patients. I noticed that I have missing values for 15 patients in regards to their time-to-event and their dichotomous outcome-event. I know they were alive at the time of inclusion but cannot make any further statements.

I thought about excluding these patients or censoring them at the index event. Are there any other suggestions how to proceed here?

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Since you have such a healthy sample, I wouldn't be concerned of excluding 15 patients due to missing information. You lack both the outcome and its timing. You could confidently censor them at a follow-up point, if you have any. I wouldn't keep them in the risk set unless you are 100% they are in it, just to be accurate (although, from a practical point of view, I wouldn't expect these 15 out of 1500 patients to substantially affect estimates).

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