Re: st: Meta-analysis of rates?

[Tom Trikalinos <ttrikalin@mac.com>]

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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