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How to calculate life time expectancy when not all patients have died. Kaplan-Meier provides a survival curve which is similar to cumulative distribution function but not the actual expectancy.

For reference: http://lifelines.readthedocs.org/en/latest/Quickstart.html

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    $\begingroup$ If you want to estimate an expected value in the face of censoring I think you'll probably need some parametric assumption $\endgroup$ – Glen_b -Reinstate Monica Dec 13 '15 at 7:13
  • $\begingroup$ Can you please elaborate? $\endgroup$ – iddober Dec 13 '15 at 16:59
  • $\begingroup$ If few of the observations are (right) censored, you can get somewhat defensible bounds on the mean by considering the case where all events occur just at the censoring time (giving a lower bound on the mean survival time) and then the case where you assume that the censored values follow the survival curves for the general population. Depending on the exact situation, these might at least give good bounds to the mean. $\endgroup$ – AlaskaRon Dec 19 '15 at 0:13
  • $\begingroup$ Here is a good reference. $\endgroup$ – Randel Feb 13 '17 at 20:35
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The average lifetime is the same as the area under the survival curve.

With a Kaplan-Meier estimate (a non-parametric estimate of 1-F rather than of F), for example, the estimate of the survival curve will only hit zero when/if there's at least one death after the last censoring time.

Typically if you have censored data, there's censored observations that last beyond your last recorded death. In that case the survival curve never reaches 0 and you don't have a bound on the mean lifetime.

This is why you can't generally get expected lifetime from a Kaplan-Meier. [You can compute an expected lifetime within some time interval -- so you could compute expected lifetime in the study period for example and some packages will provide that or something similar.]

With a parametric survival curve, it will eventually go to zero; while it's possible to have a survival curve that doesn't have a finite expectation, for many typical choices it will have a finite expectation.

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