[R-meta] random effects MA with correlations

[Guido Schwarzer]

I agree with Wolfgang on all comments. I would like to add some thoughts 
on the use of the Hartung-Knapp method.

The Hartung-Knapp method is not a viable option in meta-analyses with 
very few studies (Bender et al., 2018); this is quite common in the 
medical field. The reason is that the Hartung-Knapp method uses a 
quantile from the t-distribution with 'number of studies minus 1' 
degrees of freedom - in the extreme case of two studies one uses a 
quantile of 12.71 (compared to 1.96 for the normal approximation).

Furthermore, in very rare situations with "too homogeneous" study 
results the Hartung-Knapp method might lead to a smaller confidence 
interval than the fixed effect meta-analysis (Schwarzer et al., 2016). 
This seems somewhat counterintuitive.

Best wishes,
Guido

P.S. I do not have a preference for any tau2 estimator. R package meta 
uses the (nowadays criticized) DerSimonian-Laird estimator as default 
for historic reasons / to be in agreement with RevMan 5 from Cochrane.

References:

Bender R, Friede T, Koch A, et al. (2018): Methods for evidence 
synthesis in the case of very few studies, Research Synthesis Methods, 
https://doi.org/10.1002/jrsm.1297

Wiksten A, Rücker G, Schwarzer, G (2016): Hartung-Knapp method is not 
always conservative compared with fixed-effect meta-analysis, Statistics 
in Medicine, 35, 2503-15