# Re: st: Meta-analysis of rates?

 From Tom Trikalinos To statalist@hsphsun2.harvard.edu Subject Re: st: Meta-analysis of rates? Date Tue, 14 Sep 2004 12:50:34 +0300

Sona,

Meta-analysis of proportions may be a bit tricky. You can do it in STATA, though, using e.g. _meta_.
1. One way is to use the Freeman-Tukey arcsin transform to stabilize variances:
Let "n" be the nominator and "N" the denominator for the proportion.
Then p=n/N.
- if n=0 & N<50, compute p as p = 1/(4*N)
- if n=N & N<50, compute p as p = (n-0.25)/N

The effect size would be "pTransformed"
. gen pTransformed = asin(sqrt(n/(N+1))) + asin(sqrt((n+1)/(N+1))) // which is about the same as ". gen Theta = 2* asin(sqrt(n/N))" for large n, N

The SE would be:
. gen SEpTransf = sqrt(1/(N+1))

. meta pTransformed SEpTransf // select the proper options for meta-analysis, or for the forrest plot

Then you can transform the Summary estimate and the CI boundaries back to proportions using

gen AnyProportion = (sin(AnyPTransformed / 2))^2

2. Another way (provided that proportions are not really close to 0 or 1, and that N is large) is to compute a sample size-weighted summary as
pSummary = sum(n)/sum(N), where the variance would be sqrt(pSummary*(1-pSummary)/sum(N)).

You can make the forrest plot manually. You assume no heterogeneity.

Hope this helps.

Tom

On Sep 13, 2004, at 9:47 PM, Sona Saha wrote:

Hi,

Is anyone familiar with any routines or commands in STATA that allow for a meta-analysis of rates?

The metan, meta and metacum commands require 2 groups for analysis. Ideally, I would very much like to pool these rates with options for random or fixed effects models, evaluating heterogeneity and the ability to create Forrest plots. However, I have not found a routine that will take data for just one group per study. If you have any suggestions or advice that would be much appreciated.

Thank you!

Regards,
Sona

Sona R. Saha, MPH
Division of Public Health Biology
& Epidemiology
School of Public Health
University of California, Berkeley
140 Warren Hall #7360
Berkeley, CA 94720

Phone: 510 642-6265
Fax: 510 643-7316
Email: ssaha@berkeley.edu

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