Meta-analysis using correlation coefficients as effect size

[Isha Chaudhry]

Hi,

I am performing meta-analysis for the first time and using correlation coefficient as the effect size. I am using correlation coefficient because I am trying to investigate the association between predictor and independent variables and correlation coefficient would be an appropriate measure showing the strength of such associations.
I have transformed betas, odds ratio and proportion of variance statistics across studies to generate correlation coefficient as a consistent effect size.
I have a few questions and will appreciate the assistance.

1. While transforming standardized betas to correlation coefficient, I used the following imputation formula by Peterson and Brown (2005).
r=.98ꞵ+.05λ

Question - There are a few studies where standardized beta value is >1 and if calculating correlation coefficient using the formula mentioned above, the resultant r value is also greater than 1 which is an invalid value since -1<r<1. Please advise how to proceed in such cases.

2. When specifying my dataset for meta analysis, I use the following code and get the error that confidence intervals are not symmetric.
Code: meta set r CI1 CI2, studylabel(Author)

meta set assumes that confidence intervals for effect sizes are based on the normal distribution, and therefore they should be symmetric.

I computed the relative difference between CI upper limit – effect size and effect size – CI lower limit and found the maximum difference as 0.11. I was wondering if it is ok to include this value as civartolerance when specifying the above code. To give context, the correlation coefficients calculated are based on standardized betas where X variable were not normally distributed for most studies.

meta setr CI1 CI2, civartolerance(0.110) studylabel(Author)

Thank you.

Regards,
Isha

[George Ford]

https://www.stata.com/statanow/meta-analysis-correlations/?utm_source=20250113statanow&utm_medium=email&utm_campaign=stata18&utm_content=meta_corr

[Nick Cox]

Here is that link again from George Ford

https://www.stata.com/statanow/meta-...tent=meta_corr

[Tiago Pereira]

A potentially better approach is to convert all betas and log-odds ratios into standardized mean differences (SMDs). Both SMDs and correlation coefficients have limitations, but SMDs are generally easier to work with (i.e., they are not constrained within a finite range).