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# Re: st: A little problem with clustered data

 From "Mark Schaffer" To statalist@hsphsun2.harvard.edu Subject Re: st: A little problem with clustered data Date Fri, 30 Apr 2004 16:53:41 +0100

```Ronan,

From:           	Ronán Conroy <rconroy@rcsi.ie>
To:             	"statalist hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Date sent:      	Fri, 30 Apr 2004 12:01:45 +0100
Subject:        	st: A little problem with clustered data
Send reply to:  	statalist@hsphsun2.harvard.edu

> I would like to show you the results of two logistic regressions and get
> ideas on how to carry the analysis forward.
>
> The situation is this: a survey was run in 38 hospitals. The survey used two
> depression scales. Half the hospitals received the first scale, the other
> half the second.
>
> Not all patients completed a depression scale. The researcher suspected that
> one of the scales was less likely to be returned (it was more threatening
> than the other). So he ran a logistic regression, which confirmed his
> suspicions.
>
> . logistic depress_scale_ok which_scale
>
> Logistic regression                            Number of obs   =       1206
>                                                LR chi2(1)      =      13.09
>                                                Prob > chi2     =     0.0003
> Log likelihood = -758.99238                    Pseudo R2       =     0.0086
>
> ---------------------------------------------------------------------------
> depress_sc~k | Odds Ratio   Std. Err.      z    P>|z|  [95% Conf. Interval]
> -------------+-------------------------------------------------------------
>  which_scale |   1.560516   .1927593     3.60   0.000   1.22497    1.987975
> ---------------------------------------------------------------------------
>
> However, when he used -svyset- to set the PSU to hospital, to account for
> patient clustering within hospitals, this is what happens (same point
> estimate, but much wider confidence intervals)
>
> . svylogit depress_scale_ok which_scale if which_scale <3, or
>
> Survey logistic regression
>
> pweight:  <none>                               Number of obs    =      1206
> Strata:   <one>                                Number of strata =         1
> PSU:      hospital_number                      Number of PSUs   =        38
>                                                Population size  =      1206
>                                                F(   1,     37)  =      3.15
>                                                Prob > F         =    0.0839
>
> ---------------------------------------------------------------------------
> depress_sc~k | Odds Ratio   Std. Err.      t    P>|t|  [95% Conf. Interval]
> -------------+-------------------------------------------------------------
>  which_scale |   1.560516    .390986     1.78   0.084  .9392774    2.592642
> ---------------------------------------------------------------------------
>
>
> So it would seem that the variation between hospitals in the rate of return
> is greater than the variation you would expect from a binomial process. This
> accords with the researcher's experience. Some hospitals took a dislike to
> the depression scales, and this was more likely to happen with the more
> threatening one.

Two related thoughts from a non-biostatistician...

First, clustered standard errors rely on the number of clusters going
off to infinity for the asymptotics to work.  38 clusters isn't bad,
but it's not a lot either.  Part of the problem might be caused by
finite sample issues.

Second, the idea behind clustered SEs is to get SEs that are valid in
the presence of arbitrary within-group correlation.  Why not go down
the alternative route of specifying the form of within-group
correlation, e.g., xtlogit with fixed or random effects?  Apologies
if the answer is obvious and I'm displaying my ignorance of things
biostatistical.

--Mark

>
> My question, finally, is what next? Clearly, one source of variability in
> the return of completed depression scales is whether the hospital thinks
> that it is a useful exercise or not. But are hospitals allocated the second
> scale more likely to withhold their collaboration? How much of the poorer
> return rate is the unwillingness of patients to fill in the scale, and how
> much is the way in which the hospital handles the task of administering the
> scale and making sure it is returned?
>
> A good two-pipe problem, as my old metaphysics tutor used to say.
>
>
> Ronan M Conroy (rconroy@rcsi.ie)
> Lecturer in Biostatistics
> Royal College of Surgeons
> Dublin 2, Ireland
> +353 1 402 2431 (fax 2764)
>
> --------------------
> Just say no to drug reps
> http://www.nofreelunch.org/
>
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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
44-131-451-3485 CERT administrator
http://www.som.hw.ac.uk/cert

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