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st: Relationship of Nelson-Aalen and Kaplan-Meier


From   "Hugh Robinson" <hugh.robinson@umontana.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Relationship of Nelson-Aalen and Kaplan-Meier
Date   Mon, 21 Apr 2008 16:14:50 -0600

Can anyone tell me how to calculate the variance of a Kaplan-Meier
survival estimate derived from the Nelson-Aalen hazard function?
 
For instance, Stata provides a Standard Error of 0.08 for a cumulative
NA hazard of 0.22.  The hazard function is easily converted to the
Kaplan-Meier equivalent  as S= exp(-H).  In this case the equivalent
Kaplan-Meier S = exp(-0.22)=0.80.  However I am unclear as how to
calculate the equivalent variance.  According to Cleves et al, Stata
uses the Greenwood method to calculate standard error for Kaplan-Meier
estimates.  A second source suggests that variance should be the same
for both and calculated as the sum of (# of events/# at risk) for each
time step.


Thanks.
HR


Hugh S Robinson Ph.D.
Postdoctoral Researcher
Wildlife Biology Program
College of Forestry and Conservation
University of Montana
Missoula, MT 59802
(406) 243-4128


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