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Re: st: Meta-analysis of rates greater than 1 (when the event number is greater than the sample size)


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Meta-analysis of rates greater than 1 (when the event number is greater than the sample size)
Date   Wed, 20 Apr 2011 09:40:06 +0100

Your rate is manifestly not a proportion bounded by 0 and 1, so it can
be confirmed that Freeman-Tukey transformations and the method you
cite do not apply. It is not just that they "do not seem to work";
they are quite wrong. For example, any number greater than 1 has a
square root that is also greater than one, so the arcsine of that is
undefined. Similarly if p, supposedly a proportion, is greater than 1,
then 1 - p < 0 and sqrt(p (1 - p)) is a complex number without
statistical interpretation here

A more positive answer to your question might be forthcoming from
people who use meta-analysis routinely. Such people might be helped by
your indicating which Stata program or programs you imagine using.

Nick

On Wed, Apr 20, 2011 at 8:55 AM, Wang, Alberta L
<Alberta.L.Wang@uth.tmc.edu> wrote:

> Is anyone familiar with how to perform a meta-analysis of rates in Stata when the number of events is greater than the sample size (i.e., when the rate is greater than 1)?
>
> The data I'm working with has one group per study. To further explain, I am performing a meta-analysis of partner notification outcome rates--for example, the number of sex partners notified per index patient.  The index patient is the patient diagnosed with a STI who is notifying his/her sex partners of possible exposure. The number of partners notified (number of events) can be higher than the number of index patients (sample size) because one index patient can notify more than one sex partner.
>
> I tried using the Freeman-Tukey arcsin transformation and back transformation method for meta-analysis of proportions as described in the archives (http://www.stata.com/statalist/archive/2004-09/msg00386.html). However, this method does not seem to work when the rate is greater than 1.
>

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