Metaprop meta analysis, Variance of the synthesized proportion.

[Don Vicendese]

Hi All,

I am using metaprop to meta-analyse proportions from 8 studies using a random effects approach. Metaprop is a user written Stata package.
Meta prop uses an exact binomial method to estimate the included studies' proportions of interest and their standard errors along with 95% confidence intervals.
However, for the overall synthesized proportion, the estimated proportion is given along with its 95% CI but not its standard error. As I am using a random effects approach, metaprop also give a measure of heterogeneity and the between study variance.

Does anyone know how to extract this from metaprop easily. I can calculate it by summing the product of the study specific weights and their estimated standard errors but I am hoping that there may be a more direct method using metaprop.

Thanks for taking the time to consider this,

Don

[David Fisher]

Hi Don,

Most Stata commands, whether built-in or user-written, will return a set of objects -- text, numeric values and/or matrices -- for the user to make use of with subsequent commands; see help return. In the case of metaprop, these returned objects may be seen by typing return list. The values you asked for are stored in r(seES) [standard error] and r(tau2) [between-study heterogeneity variance]. Depending on how you plan to use them, you may wish to store them in regular local or global macros or Stata scalars, e.g. scalar seES = r(seES).

Best wishes,

David.

[Don Vicendese]

Hi David,

Thanks for taking the time to reply. However - I had checked this already but it doesn't seem to be there. There is an r(ES) for the estimate. I checked the ereturn list as well but there are no matrices. It is possible to calculate the variance for the pooled estimate. I use the output from a random effect meta-analysis to calculate the weights for each study = inverse(study_variance + tau^2). These are summed and the result inverted to get the variance of the pooled estimate. For fixed effects there is no tau^2 to worry about.

I would have expected this to be part of the output. I will write to the authors.

Thanks again,

Don

[David Fisher]

Hi Don,

I thought that was odd, as I was sure that I had see the standard error being reported when I tried on my own installation.

But I eventually worked out that the problem is the ftt option. It seems that r(seES) is not returned when that option is used, but it is returned otherwise. Unfortunately, I'm not sure if I can help you, as the Freeman-Tukey transformation is quite complicated, and the code of metaprop.ado is far from clearly written. I think contacting the authors is a good idea. Unless you could possibly "reverse-engineer" the standard error using the confidence interval and/or the tau-squared estimate?

Best wishes,

David.

[Don Vicendese]

Hi David,

I use the output from a random effect meta-analysis to calculate the weights for each study = inverse(study_variance + tau^2). These are summed and the result inverted to get the variance of the pooled estimate. For fixed effects there is no tau^2 to worry about. Unless I am misunderstanding something, I can't see why this can't be returned.

There was one other thing I find curious - probably due to my lack of understanding. After the included study proportions are normalized using the asin formulation, the variance for the transformed variable is calculated as 1/(n + .5), where n is sample size for the proportion which is calculated as r/n where r is the number of successes. I find this curious as, if we have two studies with the same n but different r, the normalized proportion will have the same variance. So when it is back transformed, two studies in the meta_analysis with different proportions have the same standard error.

I need to use the ftt (asin transform) option as some of my studies have zero proportions.

I have written to the authors. They are clear about their methods and formulas in their paper Metaprop: a Stata command to perform meta-analysis of binomial data. Of course all methods have their limitations and this paper discusses them - Seriously misleading results using inverse of Freeman-Tukey double arcsine transformation in meta-analysis of single proportons , Schwarzer et al.

Regards,

Don