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Re: st: comparing rates


From   Chris Rohlfs <car@uchicago.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: comparing rates
Date   Mon, 8 Sep 2003 14:40:30 -0500 (CDT)

yes.  sorry; i wasn't thinking.

On Mon, 8 Sep 2003, Roger Harbord wrote:

> --On 08 September 2003 11:27 -0500 Chris Rohlfs <car@uchicago.edu> wrote:
> 
> > ricardo,
> >
> > don't worry about controlling for practice.  you've already controlled for
> > it with the doctor id (i.e., they're perfectly multicollinear).  so just
> > run:
> >
> > 	clogit referred, group(doctorid)
> >
> > and any possible confounding effects of "practice" will be captured &
> > controlled for by doctorid.
> >
> > chris
> 
> Hmm, but Ricardo is interested in comparing the referral rates between 
> practices and that command isn't going to do that.
> 
> Presumably each physician belongs to only one practice. Ricardo is 
> concerned that referral rates may vary between physicians WITHIN a 
> practice, i.e. that observations on patients seen by different physicians 
> within the same practice are not independent -  or put another way, there 
> may be more variation between physicians in the same practice than would be 
> expected by chance if all physicians in a practice had identical referral 
> rates. This means there may be overdispersion.  I can't see that -clogit- 
> is useful as there's no matching and there's no information on differences 
> between practices within physicians so a fixed-effects model is no use.
> 
> The simplest analysis is:
> . logistic referred practice
> However this ignores the possibility of overdispersion and is therefore 
> likely to be anticonservative (P-value too small).
> 
> To allow for the within-physician correlation you could use -xtlogit- to 
> fit a model with a between-physician variance component.  Either a 
> random-effects model:
> . xtlogit referred practice, i(doctorid) or
> Or a population-averaged model:
> . xtlogit referred practice, i(doctorid) or pa
> Both are likely to give similar results though the second is less likely to 
> run into numerical problems.
> 
> Another approach would be to use -glm- with the -scale- option to fit a 
> logistic regression model with a multiplicative overdispersion factor.  To 
> do this in Stata you need to first -collapse- the data to give grouped 
> binomial data:
> . collapse (sum) referred (count) npatients=referred, by(practice doctorid)
> . glm referred practice, family(binomial npatients) scale(x2) eform
> 
> This gives the same point estimate as the -logistic- command above but 
> increases the standard error to allow for the overdispersion.  I'd be 
> surprised if the results were much different to the -xtlogit- analyses 
> above.  If they do i'd probably prefer the -xtlogit- model.
> 
> Ricardo's idea about computing rates for each physician and weighting 
> appropriately would be yet another possibility (esp. if followed by a 
> variance-stabilising transformation) but would be an 'old-fashioned' 
> approach as modern software makes the more correct analyses above easier 
> than summarising, weighting, transforming...
> 
> Hope this helps,
> Roger.
> ----------------------------------------------------
> Roger Harbord     mailto:roger.harbord@bristol.ac.uk
> Department of Social Medicine, University of Bristol
> 
> > On Mon, 8 Sep 2003, Ricardo Ovaldia wrote:
> >
> >> Dear all,
> >>
> >> I have received only one reply to my post (please see
> >> my original post below), so either of two things is
> >> possible: (1) there is not a good answer or (2) my
> >> question was no clear. So let me ask a slightly
> >> different question.
> >>
> >> Can I simply take the number of referrals at one
> >> practice and divide by the number of patients seen at
> >> that practice (referral rate for practice 1) and
> >> compare it to the rate of  the other practice without
> >> taking in account that some physicians within practice
> >> may refer more than others? Or, should I compute the
> >> referral rate for each physician, and then combine
> >> these rates within practice by weighting them some
> >> how?  If so how can I do this in Stata? what kind of
> >> weights should I use?
> >>
> >> Thank you,
> >> Ricardo.
> >>
> >>
> >>
> >> --- Ricardo Ovaldia <ovaldia@yahoo.com> wrote:
> >> > Dear all,
> >> >
> >> > We are interested in comparing the referral rates
> >> > for
> >> > two physician practices.   The fist group has 20
> >> > physicians and the second group has 22 physicians.
> >> > Each physician saw a variable number of similar
> >> > patients some saw as few as 4 and others as many as
> >> > 43. The physician either referred the patient to a
> >> > specialist or did not.
> >> >
> >> > If I compute the referral rate for each physician
> >> > group and compare them, I concerned because the
> >> > observations are not independent. I suspect that
> >> > some
> >> > doctors are more likely to refer patients than
> >> > other.
> >> > I though that I could use &#33192;logit- to group by
> >> > doctor&#30196; ID:
> >> >
> >> > . clogit referred practice, group(doctorid)
> >> >
> >> > This did not work because the &#26420;ractice-
> >> variable
> >> > does
> >> > not vary within doctor ID, so it is dropped from the
> >> > model (omitted due to no within-group variance).
> >> >
> >> > Any suggestions will be greatly appreciated.
> >> >
> >> > Thank you,
> >> > Ricardo.
> >> >
> >> >
> >> > =====
> >> > Ricardo Ovaldia, MS
> >> > Statistician
> >> > Oklahoma City, OK
> >> >
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