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I'm analyzing Trisomy 18 patients who underwent cardiac surgery. They all had surgery at different points in time, and they have all been followed-up until present day. This means that follow-up times vary depending on how long ago surgery was performed. It also means that #at risk increases over time assuming no events.

For a patient who underwent surgery 1 month ago and is still alive, how does the Kaplan-Meier model/function distinguish between this situation versus the patient having been followed for 1 month then right-censored?

If the data you enter is composed only of variables TIME (months) and EVENT (1/0), wouldn't the KM function assume they all entered at time = 0 and give you a "# at risk at time = 0" of n? (As opposed to a "# at risk at time = 0" of 1, which is the first surgery performed). How do you deal with this?

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    $\begingroup$ Are you interested in survival after birth or survival after surgery? $\endgroup$
    – Todd D
    Jul 18, 2022 at 5:19

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If you define time = 0 as the date of surgery (which seems most appropriate here), then the time represented along the horizontal axis of the Kaplan-Meier (KM) plot is the duration of time since surgery. Thus for your question:

For a patient who underwent surgery 1 month ago and is still alive, how does the Kaplan-Meier model/function distinguish between this situation versus the patient having been followed for 1 month then right-censored?

the answer is that there is no distinction.

If the data you enter is composed only of variables TIME (months) and EVENT (1/0), wouldn't the KM function assume they all entered at time = 0 and give you a "# at risk at time = 0" of n?

Yes, and that's exactly what you want. All $n$ of your subjects are at risk as of the date of surgery. The subsequent survival curve represents the fraction still surviving at times elapsed since surgery, with censoring taken into account appropriately.

In this situation it doesn't make much sense to define time = 0 as the date that the study started. If you want to take the calendar date of surgery into account, for example because of improvements in surgical technique over time, you can use a Cox model and include the calendar date of surgery as a predictor.

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