Re: st: Mantel-Haenszel vs. clustered logistic - please help

[Constantine Daskalakis <c_daskalakis@entwhistle.jci.tju.edu>]

> > Dear all,
> >
> > I am analyzing data from the 306 women at 4 outpatient
> > clinics in Oklahoma. Each woman was asked if they
> > performed monthly breast exams and other additional
> > data (covariates) such as race was collected. We would
> > like to characterize women according to these
> > covariates. I am concerned about the these women are
> > from different clinics and would like to take this
> > into account.
> >
> > My first though was to performed a logistic regression
> > clustering on clinic.
>
> > Summary:
> >
> > The raw OR:           1.97  (1.10,3.54) p= 0.0138
> > Mantel-Haenszel OR:   2.94  (1.44,5.98) p= 0.0018
> > Cluster logistic OR:  1.97  (0.77,5.06) p= 0.158
> >
> > Regards,
> > Ricardo
There are two issues here.

1. Do you need to control for clinic in your model? This is necessary if 
the clinics have varying rates of SBE (ie, clinic is a confounder).

The logistic regressions do not control for this. The MH does. You can get 
comparable results by including appropriate dummy variables for clinic in 
your logistic models.

Looking at your results, it seems that you do need to control for clinic.

2. Do you need to control for the clustering (ie, correlation of 
observations) within clinics?

Usual logistic regression assumes that all observations are independent. 
This may not be for observations that come from the same clinic (ie, the 
outcomes for two women of the same clinic may be more similar that the 
outcomes for two women from different clinics). The cluster/robust options 
account for this lack of independence.

I don't agree with Mark that "clustering on clinic is not a good idea." It 
does not matter how many clusters you have, as long as you account for the 
within-cluster correlation. The robust variance certainly does not treat 
the data as 4 observations. This is how I'd explain it.

Without clustering (ie, independence for all observations), you have 306 
observations.

With perfect clustering (ie, perfect correlation within each clinic, but 
independence across clinics), you have 4 observations.

The cluster/robust option will essentially correctly fall somewhere in 
between, depending on the actual degree of correlation in your data. This 
is as it should be, no? You don't really have info from 306 independent 
observations, but less (depending on how correlated they are).

Looking at your results, it seems that there's a non-trivial within-clinic 
correlation. -logit- uses the "independence" working correlation to correct 
for clustering. You can use -xtlogit- (with exchangeable correlation) to 
get more efficient estimates, ie, tighter standard errors.






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________________________________________________________________

Constantine Daskalakis, ScD
Assistant Professor,
Biostatistics Section, Thomas Jefferson University,
125 S. 9th St. #402, Philadelphia, PA 19107
   Tel: 215-955-5695
   Fax: 215-503-3804
   Email: c_daskalakis@mail.jci.tju.edu
   Webpage: http://www.kcc.tju.edu/Science/SharedFacilities/Biostatistics

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