From "Mark Schaffer" To statalist@hsphsun2.harvard.edu, Ricardo Ovaldia Subject Re: st: Mantel-Haenszel vs. clustered logistic - please help Date Fri, 23 May 2003 17:08:50 +0100

```Ricardo,

Date sent:      	Fri, 23 May 2003 06:15:22 -0700 (PDT)
From:           	Ricardo Ovaldia <ovaldia@yahoo.com>
To:             	statalist@hsphsun2.harvard.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.

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
>
> 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
44-131-451-3494 direct
44-131-451-3008 fax