Edit: 11/3/2019 – I’m thinking of creating a BibTeX database of all the links related to meta-analysis in this thread. If anyone is interested, I’d be happy to share it on github.
I’m adding some especially relevant citations related to the assumption of normality in meta-analytic procedures:
Especially useful is Table 3: (Eight main assumptions made by conventional methods for meta‐analysis)
The recommendation in the discussion section was the use of logistic regression.
Blockquote
Comparing these results to those in Section 2.1 (μˆ=0.65 with standard error 0.20), this analysis is in reasonable agreement with the conventional analysis presented above. Given the small study sizes, and so the crudeness of the conventional methods, it is perhaps surprising that the inferences from the logistic regression are so similar. The alternative common‐effect Mantel‐Haenszel method used in the Cochrane Review has also slightly, but to a lesser extent, diluted the estimated treatment effect.
Calling the DerSimonian Laird procedure “unreliable” is serious.
I strongly recommend this paper by David Hoaglin. It is probably the best article I’ve seen on the technical issues related to logistic regression and generalized linear mixed effects models for meta-analysis to date.
Further elaboration of various versions of the Generalized Mixed Effects Model model for meta-analysis using logistic regression.
The authors of the original DerSimonian Laird Meta-analysis technique reflect on its widespread use and modify it with robust variance estimates.
An empirical evaluation of meta-analytic procedures. Suffice it to say GRADE criterion undervalue “low quality” studies and overvalue “high quality” ones.