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Re: st: xtgee and corr(ind) vs corr(exch)


From   Joseph Coveney <jcoveney@bigplanet.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: xtgee and corr(ind) vs corr(exch)
Date   Sat, 02 Nov 2002 23:01:47 +0900

Gary Anderson posted about some difficulty he is having with 
parameter estimates using population-averaged generalized 
estimating equations (PA-GEE).

-------------------begin excerpted post------------------------------------

Why is it that a coefficient can differ by up to 4 standard errors 
when an xtgee with corr(ind) is fitted compared to an xtgee with 
corr(exch) ?

I have about 20 clinics and 40 patients per clinic, with the one 
covarite varying at the patient level, and the id variable is the clinic. 
The intraclass correlation coefficient is about 0.4. My understanding 
is that the expectation is that the coefficient should not differ when 
a different correlation structure is fitted. The coefficient goes toward 
the null when the exchangeable structure is fitted.

--------------------end excerpted post------------------------------------ 

My understanding is similar to Gary's in that, when using marginal 
models such as PA-GEE, the parameter estimates for the means 
(i.e., regression coefficients) ought to be resilient to the working 
correlation structure; however, they do require that the model is 
otherwise properly specified, viz., distribution family, link function 
and inclusion of all important covariates.  Whenever you do 
encounter dramatic changes in such parameter estimates with 
different working correlation structures, I'm told that it results from 
improperly specifing the link function or distribution family, or that 
you've not included important covariates in the model.  In Gary's 
case, he has a single covariate.  It is possible that the sensitivity 
that he observes results from omitted covariates.  Unfortunately, he 
has only twenty clusters and, with PA-GEE, this would argue 
against adding any more covariates.

At the risk of sounding like a broken record on this:  Gary might 
want to look into -gllamm- as an alternative to -xtgee-.  The 
exchangeable correlation structure that is implied by the study 
design (patients within clinic) is compatible with generalized linear 
mixed-effects models.  The relatively small sample size would not 
be such an issue with -gllamm- as it is with PA-GEE.  Convergence 
ought to be reasonably rapid with the limited sample size (20) and 
number of parameters to estimate that Gary has in the model.  And 
-gllamm- has a wealth of distribution families and link functions, as 
does -xtgee-.

Joseph Coveney

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