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Can someone help me find a way to estimate the variance of the Kaplan-Meier estimate with dependent observations? Specifically, I have failure time data from patients with several different observations for each patient (and different patients may have different number of observations). The observations for different patients are assumed to be independent but observations from the same patient are expected to be dependent.

I was suggested two publications, "Kaplan-Meier Analysis of Dental Implant Survival: A Strategy for Estimating Survival with Clustered Observations" and "The Kaplan-Meier Estimate for Dependent Failure Time Observations", the second of which is cited by the first.

However I was unable to make sense of these. The first has errors and the second seems far more rigorous but the equation for the variance does not make sense (double integration on a 1-form).

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  • $\begingroup$ How does the dependence manifest itself in your case? Can you describe your situation in more detail? $\endgroup$ – cardinal Dec 21 '11 at 15:27
  • $\begingroup$ @cardinal Of course, should have remembered that. Added details to the question now. $\endgroup$ – Anton Dec 21 '11 at 16:05
  • $\begingroup$ So, do the failures happen one after another, i.e., similar to a renewal process, or do they happen simultaneously? For the latter, I'm imagining something like time to organ failure (each organ being considered individually) for a terminally ill patient (forgive the imagery), whereas the former might be something like, time between epileptic seizures. $\endgroup$ – cardinal Dec 21 '11 at 17:24
  • $\begingroup$ @cardinal They are individual and may or may not happen simultaneously. $\endgroup$ – Anton Dec 22 '11 at 10:20
  • $\begingroup$ @Anton if the events concern different outcomes, then you simply produce Kaplan Meier curves for each outcome. Or are you interesting in estimating a multidimensional KM that can covary for specific outcomes at different points in time? $\endgroup$ – AdamO Feb 1 '18 at 19:32

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