[R-meta] random effects MA with correlations

[Viechtbauer, Wolfgang (SP)]

Dear F.,

It is impossible to say which estimator (REML, DL, PM, etc.) is optimal in any particular case (if, by optimal, we mean: 'closest to the true value').

We also cannot say that one of these estimators is better on average (i.e., in the sense of being a UMVUE -- https://en.wikipedia.org/wiki/Minimum-variance_unbiased_estimator). In some circumstances, one is better, while under other circumstances, another is better.

A lot has been written about 'tau^2' estimators. These days, I feel like this is one of the least important issues in a meta-analysis. There are exceptions where it matters, but in most cases, conclusions won't change depending on the estimator. I personally prefer ML/REML because these methods automatically can be generalized to more complex models, while other estimators do not.

As for the Hartung-Knapp method: Use it. It really should be the default (too late to change this now in metafor, but I should have done this from the beginning).

Not sure what other arguments you are concerned about, but you probably do not have to mess with them.

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On Behalf Of F.Anagnostopoulos
Sent: Thursday, 13 September, 2018 8:59
To: r-sig-meta-analysis using r-project.org
Subject: [R-meta] random effects MA with correlations

Dear all,

Regarding  the  use of  proper procedures to estimate between-study variance/heterogeneity  (tau-squared) and its CIs, when performing random effects meta-analysis with correlation coefficients as effect sizes, using R, the "metafor" package implements REML by default when estimating tau-squared, while "metacor" uses DSL by default for examining random effects with correlation coefficients. Others suggest the Paule- Mandel method.

Thus, which is the optimal method in this case, especially when the number of studies= 20, the mean sample size=250, average r = 0.525 (95% CI= 0.411- 0.622), tau-squared= 0.10, I-squared= 98%, and correlations are converted  to Fisher's  z values? . 
Moreover, is it necessary  to apply the Hartung- Knapp method  to adjust test statistics and CIs? Should we  pay special attention to any "arguments" used in "metafor" package, when dealing with correlations?
Thanks in advance.

F. Agnew