# Re: st: comparing rates

 From Roger Harbord To statalist@hsphsun2.harvard.edu Subject Re: st: comparing rates Date Mon, 08 Sep 2003 20:16:55 +0100

```--On 08 September 2003 11:27 -0500 Chris Rohlfs <car@uchicago.edu> wrote:

```
```ricardo,

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,

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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