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RE: st: Relationship of Nelson-Aalen and Kaplan-Meier

From   "Hugh Robinson" <>
To   <>
Subject   RE: st: Relationship of Nelson-Aalen and Kaplan-Meier
Date   Tue, 22 Apr 2008 12:34:37 -0600

Thanks Maarten.

Unfortunately Stata will give me either a standard error for the
Nelson-Aalen estimator, or a standard error for the Kaplan-Meier
survival estimate.  The two are not equal as they're calculated a little
bit differently.  KM survival variance is calculated using Greenwood's
formula and the variance of the NA hazard function is the sum of (# of
events/ # at risk). 
Kaplan Meier estimates got to zero during periods when no subjects are
at risk.  Because of small samples sizes I would like to use the
Nelson-Aalen estimator but still need to come up with a survival
estimate and standard deviation.  The Nelson-Aalen hazard function can
be converted to a survival estimate that approximates KM survival using
Skm = exp(-Hna).  

I'm wondering how to get an equivalent measure of KM survival variance
from the Nelson-Aalen hazard function.  I've found several texts that
discuss the equivalence of the survival estimates but can't find
anything that discusses how the variances equate.

Thanks again.


-----Original Message-----
[] On Behalf Of Maarten buis
Sent: Tuesday, April 22, 2008 2:37 AM
Subject: Re: st: Relationship of Nelson-Aalen and Kaplan-Meier

These are discussed in the methods and formulas section of the manual
entry on -sts-. Anyhow, you can let Stata do the computations by typing
-sts list-.

Hope this helps,

--- Hugh Robinson <> wrote:

> 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
> *
> *   For searches and help try:
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> *
> *

Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

visiting address:
Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

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