[R] metafor - Meta-Analysis of rare events / beta-binomial regression

[Viechtbauer Wolfgang (STAT)]

I would say the issue of how to deal with 'double-zero' studies is far from settled. For example, under the (non-central) hypergeometric model, studies with no events have a flat likelihood, so they are automatically excluded. That may go against our intuition (for various reasons, some of them are aptly described on page 1098 in Kuss, 2015), but from a likelhood perspective, it is correct. And since the Mantel-Haenszel and Peto's method are also based on the hypergeometric model, they should also exclude double-zero studies. Now I am not so sure if we are ready to completely scrap these methods altogether simply because they exclude double-zero studies.

However, for 2x2 table data, I am all in favor of using methods that make more realistic distributional assumptions than the 'standard' approach that assumes that the sampling distribution of the log(odds ratio) is normal and has a known sampling variance. That's why metafor includes rma.glmm() for fitting appropriate unconditional mixed-effects logistic and the conditional mixed-effects logistic (i.e., hypergeometric) model to such data. And for fixed-effects models, there are also rma.mh() and rma.peto() for the Mantel-Haenszel and Peto's method.

I may also eventually include the beta-binomial model, but I need to give this some more thought. If you already want to start using this model, you will find implementions thereof in VGAM, aods3, and gamlss.

Best,
Wolfgang

-- 
Wolfgang Viechtbauer, Ph.D., Statistician | Department of Psychiatry and    
Neuropsychology | Maastricht University | P.O. Box 616 (VIJV1) | 6200 MD    
Maastricht, The Netherlands | +31 (43) 388-4170 | http://www.wvbauer.com    

> -----Original Message-----
> From: R-help [mailto:r-help-bounces at r-project.org] On Behalf Of Markus
> Kösters
> Sent: Friday, November 27, 2015 14:38
> To: 'Michael Dewey'; r-help at r-project.org
> Subject: Re: [R] metafor - Meta-Analysis of rare events / beta-binomial
> regression
> 
> Dear Michael,
> 
> Thank you very much for your input, that is very much appreciated. I have
> not considered that method, because it's rather outlawed in general. But
> it is also included in Kuss and if I understood correctly, the collapsing
> method (and the Cochrane method) both performed not too bad under FEM
> assumption and had weaknesses in REM. I usually prefer a REM approach,
> but in this case that may not be that important.
> I will also read the mmeta paper and documentation.
> 
> Thanks a lot!
> 
> Markus
> 
> -----Ursprüngliche Nachricht-----
> Von: Michael Dewey [mailto:lists at dewey.myzen.co.uk]
> Gesendet: Freitag, 27. November 2015 13:32
> An: Markus Kösters; r-help at r-project.org
> Betreff: Re: [R] metafor - Meta-Analysis of rare events / beta-binomial
> regression
> 
> Dear Markus
> 
> This is not a direct answer to your question, I will leave that to
> Wolfgang but two thoughts:
> 
> 1 - if all the studies have very sparse data @article{bradburn07,
>     author = {Bradburn, M J and Deeks, J J and Berlin, J A and Localio, A
> R},
>     title = {Much ado about nothing: a comparison of the performance of
>        meta--analytical methods with rare events},
>     journal = {Statistics in Medicine},
>     year = {2007},
>     volume = {26},
>     pages = {53--77},
>     keywords = {meta-analysis, fixed effects, random effects} } suggests,
> surprisingly, that just collapsing the tables may be adequate
> 
> 2 - there is a CRAN package mmeta which uses beta-binomial in a Bayesian
> perspective. I did not find the documentation very explicit but there is
> a paper in JSS.
> 
> On 26/11/2015 13:39, Markus Kösters wrote:
> > Dear all,
> >
> > I am currently writing a protocol for a meta-analysis which will
> > analyze suicidal events. Recently, O. Kuss has (DOI 10.1002/sim.6383)
> > published a paper that suggest using beta-binomial regression methods
> > to incorporate double-zero studies. He states that  Methods that
> > ignore information from double-zero studies or use continuity
> > corrections should no longer be used.  It seems obvious to me that
> > excluding studies with zero events will bias the results and I am
> > willing to follow his advice. However, I am not a a biometrician, I
> > have to admit that I am at a loss if and how it is possible to fit
> > such model within the metafor package. Can someone help me or should I
> > use the Yusuf Peto odds ratio method as suggested in the Cochrane
> handbook?
> >
> > Many thanks in advance,
> >
> > Markus