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Re: st: Compare observed - expected survival functions


From   Enzo Coviello <enzo.coviello@tin.it>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Compare observed - expected survival functions
Date   Sat, 08 May 2004 15:36:44 +0200

At 09.35 07/05/04 -0700, you wrote:
Dear statalisters,

Is it possible to evaluate the fit of a survival model
by comparing the predicted survival function with the
observed (Kaplan-Meier estimate). I think this questio
n was asked long time ago but I found no answers in
the archives. I also think that this kind of test is
refered as "one-sample logrank test" but I am not
sure. I am asking this on behalf of a coleague of mine
but I am also curious.
Any help, thoughts or pointers to relevant literature
will be much appreciated.
Hi Nikos,

I found that a very good paper on this subject is the Tech. Report 63 that you can download from the site of prof. T. Therneau.
Here Therneau says that one-sample log rank is equivalent to the test for intercept = 0 in a Poisson model where the offset term is log(n_expected). So typing
- poisson depvar, exposure(n_expected)

should yield the result you are looking for.
Actually I believe that, to this aim, even the simpler strate with smr(varname) option should be equivalent.

Formulas in this paper to estimate the expected survival function based on reference rates are implemented in -stexpect- a new Stata macro that you can download from SSC archive. Type findit stexpect or ssc desc stexpect for more details.
I know that prof. Dickman also developed a new ado to estimate expected survival based on probability of death and applying a life table approach.

Paul Dickman also wrote a wonderful paper on Stat. in Med. 2004 23: 51-64 where he presents different regression models for relative survival, all of them can be estimated using Stata. My preferred method is achievable using the glm command with a new link function specified in the rs.ado.
Briefly, a nice model to compare observed to expected survival could be:
glm depvar indepvars, f(poisson) l(rs n_expected) lnoffset(personyears)

rs.ado and more details can be found at Paul Dickman site www.paul.dickman.com.

Hope this could be useful.

Enzo

Enzo Coviello
Dipartimento di Prevenzione ASL BA/1
via L. Barbera 27
70055 MINERVINO MURGE (BA)
Italy
tel - fax +390883691053
(home) +390883695055
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