[R-meta] correlational meta-analyses and Egger's regression test

Hi Catia,

I don't know of any studies on this. But the statistical theory here is
pretty straight-forward, so perhaps it's not necessary to do simulations to
confirm.

For the sample Pearson correlation coefficient r, the (estimated) standard
error is (1 - r^2) / sqrt(N - 1), which is strongly correlated with the
point estimator. This implies that there will tend to be an asymmetric
funnel plot and non-zero slope to Egger's regression (or the
multi-level/multi-variate extensions thereof) even in the absence of
selective reporting. To avoid this artifact, Wolfgang suggests using
1 / sqrt(N - 1) as the predictor in Egger's regression because then it will
be independent of the effect size estimator. Alternately, you could do the
analysis using Fisher's z transformation. The z transformed correlation has
standard error 1 / sqrt(N - 3), which will be independent of the effect
size estimator.

James

On Sat, Jan 22, 2022 at 11:53 AM C?tia Margarida Oliveira <

Hello,

I am running a correlational meta-analysis and I was wondering if there are
guidelines for which measure to use as a predictor in Egger's test with
multilevel models. I have encountered a few sources (e.g. the paper by
James - Testing for funnel plot asymmetry of standardized mean differences)
on how using measures of variance may be problematic with logs odds ratios
and standardised mean difference effect size estimates, but does anyone
know if there's such research for meta-analyses examining correlations?

The only reference I found was here:
https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2020-May/002086.html

Thank you,

Catia

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