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....@cbs.dk  Priv: pda...@gmail.com

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