With regard to the last part, if you think that the effects are influenced
by clinic (i.e., not only do the intercepts differ, but the slopes differ by
clinic). You can model this in logistic regression by including interaction
terms. The M-H procedure provides two tests of homogeneity of the ORs, (a
MH test and the breslow-day test) which will test whether the ORs differ
across the clinic strata. This is equivalent to including interaction terms
in your logistic regression model.
Paul
-----Original Message-----
From: Mark Schaffer [mailto:[email protected]]
Sent: Friday, May 23, 2003 12:09 PM
To: [email protected]; Ricardo Ovaldia
Subject: Re: st: Mantel-Haenszel vs. clustered logistic - please help
Ricardo,
Date sent: Fri, 23 May 2003 06:15:22 -0700 (PDT)
From: Ricardo Ovaldia <[email protected]>
Subject: st: Mantel-Haenszel vs. clustered logistic - please
help
To: [email protected]
Send reply to: [email protected]
> 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.
If I understand correctly what you are doing, clustering on clinic is
not a good idea. The reason is that you have only 4 clinics, i.e.,
only 4 clusters.
In the construction of cluster-robust standard errors, this is like
having only 4 observations. Roughly speaking, in the construction of
the "sandwich" matrices, the clusters are aggregated and treated as
an "average" observation. Apologies for the gross abuse of
terminology, but it gets the point across - you can't do very much
that's sensible with only 4 observations.
Hope this helps.
--Mark
> But I later though to use a
> stratified analysis and compute a Mantel-Haenszel odds
> ratio. However, I get very deferent results from these
> methods and I am confused on which to use. Here is an
> example:
>
> nrace: 0=African American 1=Caucasian
> breast-exam: 0=No 1=Yes
>
>
> Mantel-Haenszel:
> . mhodds breast_exam nrace,by(clinic)
>
> Maximum likelihood estimate of the odds ratio
> Comparing nrace==1 vs. nrace==0
> by clinic
>
>
----------------------------------------------------------------------------
---
> clinic | Odds Ratio chi2(1) P>chi2
> [95% Conf. Interval]
>
----------+-----------------------------------------------------------------
---
> CWC | 3.966102 7.27 0.0070
> 1.34348 11.70839
> FN | 0.000000 1.26 0.2621
> . .
> Freeway | 3.446154 4.76 0.0291
> 1.05511 11.25567
> MB | 2.153846 0.40 0.5286
> 0.18671 24.84655
>
----------------------------------------------------------------------------
---
>
> Mantel-Haenszel estimate controlling for clinic
>
> ----------------------------------------------------------------
> Odds Ratio chi2(1) P>chi2 [95%
> Conf. Interval]
>
> ----------------------------------------------------------------
> 2.937339 9.71 0.0018
> 1.442772 5.980127
>
> ----------------------------------------------------------------
>
> Test of homogeneity of ORs (approx): chi2(3) =
> 4.12
> Pr>chi2 =
> 0.2483
>
>
> Clustered logistic:
>
> . xi:logistic breast_exam i.nrace,cluster(clinic)
> i.nrace _Inrace_0-1 (naturally
> coded; _Inrace_0 omitted)
>
> Logistic regression
> Number of obs = 306
> Wald
> chi2(1) = 2.00
> Prob
> > chi2 = 0.1578
> Log pseudo-likelihood = -160.29912
> Pseudo R2 = 0.0186
>
> (standard errors adjusted
> for clustering on clinic)
>
----------------------------------------------------------------------------
--
> | Robust
> breast_exam | Odds Ratio Std. Err. z P>|z|
> [95% Conf. Interval]
>
-------------+--------------------------------------------------------------
--
> _Inrace_1 | 1.971711 .947687 1.41 0.158
> .7686353 5.057856
>
----------------------------------------------------------------------------
--
>
>
> 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
>
>
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Prof. Mark E. Schaffer
Director
Centre for Economic Reform and Transformation
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS UK
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