# Meta-analysis of proportions - how to analyze possible moderators and publication bias?

I am performing a meta-analysis study of proportions in Stata using the metaprop command. My data includes 10 studies for which I have the variables: study, ntotal, nobserved, region, age. Using metaprop is not a problem, but I want to add two additional analyses:

1. an analysis of the possible moderators region, mean age and studysize (ntotal)

I read about the metareg command, but I suspect its handling of binominal data is different than metaprop? And I fear this to influence the validity of its usage compared to Forest plots based on the metaprop command. I run the code:

// Generate logged proportion for regression analysis
gen logp = log(nobserved/ntotal)

// Try test for covariates.
metareg logp ntotal age region, wsse(logp)


Is this at all a valid approach for the regression analysis?

1. Funnelplot for possible publication bias

Next problem is the funnelplot. I have access to all data of the included studies, and hence I can calculate proportions and the corresponding standard error:

proportion agree, over(studyName)

and putting these values in variables prop and SEp.

I log the propability, and run the metabias command:

gen logp = log(prop)

// Funnel plot and Egger
metabias logp SEp, graph(begg)


My question is: Are the statistical approach and usage of meta-analysis commands above valid?

• Two comments. (1) with 10 studies three moderators at once is unlikely to show anything convincing, even one is optimistic, (2) I do not see where you calculate the standard errors of your transformed proportions but this may be because I do not speak Stata. – mdewey Mar 23 '18 at 13:51
• Indeed, you can easily do this if you use R instead. – Joe_74 Mar 23 '18 at 16:33
• Thank you both. The standard errors are automatically produced by the proportion command. I copy the se for each study into a separate dataset used in the meta analysis. I have tried R many years ago (but not for meta analysis), but everybody at the research department I work at now use Stata... – Alex Mar 27 '18 at 9:02
• @mdewey why will the regression analysis not work with three moderators? I believe I've seen several published examples of this approach... – Alex Mar 27 '18 at 9:04
• You can fit the model but unless you are lucky the standard errors will be large and you will have only vague conclusions. – mdewey Mar 27 '18 at 20:07