# [R] life table and Kaplan-Meier

peter dalgaard pdalgd at gmail.com
Wed Jul 13 16:05:55 CEST 2011

```On Jul 13, 2011, at 07:23 , stat999 wrote:

> Hello, I have a question about the function lifetab in package KMsurv.
> The description of the output value surv says "the estimated survival
> function at the start of the intervals".
>
> Are these estimates the ones calculated via Kaplan-Meier probability of
> survival ?

You really should do your own reading of the underlying theory... However, without studying the package too carefully, I's expect the answer to be "not quite". (And do notice that the  "KM" in KMsurv are not Kaplan and Meier, but Klein and Moeschberger.)

K-M assumes that you have precise times of death and censoring, whereas life tables have more coarse-grained information, usually number of deaths during certain time intervals and population size at start and end of each interval. So for a life table, you'd calculate the survival for a time interval as 1 - (#deaths/#atrisk), with #atrisk typically calculated as roughly the average of the population size at the endpoints. Then you can calculate the longer time survival by multiplying the interval survivals together.

If you reduce the interval length so much that, in the limit,  there is at most one death per interval, then the lifetable procedure turns into the K-M estimator (which, for the same reason, is sometimes called the product-limit estimator).

Another difference is that with K-M, you usually have only right censored data (the same person followed from time 0 till death or lost-to-followup), whereas lifetables don't even assume that the time intervals refer to the same individuals (and in "synthetic cohorts",  they are typically completely separate).

[The above is somewhat oversimplified; trying to the details right seemed like overkill.]

--
Peter Dalgaard
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com

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