[R-sig-ME] Dependence of Effect Sizes in meta analysis metafor (some statistical theory questions included)

[Mike Cheung]

Hello,

 There are several types of dependence in a meta-analysis. The effect sizes
can be conditionally dependent because the same samples (participants) are
used in the analysis. There are formulas to estimate the amount the
dependence (sampling covariances among effect sizes) when enough summary
statistics are given. The second type of dependence is the covariances
among the true effect sizes at the population level. Both of them are
assumed in a multivariate random-effects meta-analysis. If the later
(covariances among the true effect sizes) is assumed zero, it becomes a
multivariate fixed-effects meta-analysis.

 A third type of dependence happens when there are multiple effect sizes
reported by the same study. One typical issue is that we may not have
enough information to estimate the sampling covariances among effect sizes.
Thus, the multivariate meta-analysis cannot be used. If we take the
assumptions that (1) the amount of dependence is random and (2) the effect
sizes are conditionally independent after controlling for the random
effects, we may use a three-level meta-analysis to model it. This is
basically what the note means.

 Some researchers further suggested to use the three-level meta-analysis to
conduct the multivariate meta-analysis because there is no need to
calculate the conditional sampling covariances among the effect sizes.
Under some assumptions (see the following links), this approach works. On
the other hand, the three-level meta-analysis is a special case of the
multivariate meta-analysis by imposing a few constraints. Since the
multivariate and three-level meta-analyses are related, I would suggest
studying both of them at the same time and see which one fits better for
your data and research questions.

 The followings are some excerpts from my book that are related to my
points.


https://books.google.com.sg/books?id=sp3TBgAAQBAJ&pg=PA121&dq=5.1.1+Types+of+dependence&hl=en&sa=X&ei=YUmOVfWKHpOGuASOsbTABg&redir_esc=y#v=onepage&q=5.1.1%20Types%20of%20dependence&f=false


https://books.google.com.sg/books?id=sp3TBgAAQBAJ&pg=PA195&dq=6.4+Relationship+between+the+multivariate+and+the+three-level+meta-analyses&hl=en&sa=X&ei=bEiOVZibL8ytuQS_moGwCg&redir_esc=y#v=onepage&q=6.4%20Relationship%20between%20the%20multivariate%20and%20the%20three-level%20meta-analyses&f=false


 Regards,
Mike

-- 
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 Mike W.L. Cheung               Phone: (65) 6516-3702
 Department of Psychology       Fax:   (65) 6773-1843
 National University of Singapore
 http://courses.nus.edu.sg/course/psycwlm/internet/
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On Sat, Jun 27, 2015 at 2:50 PM, Theodore Lytras <thlytras at gmail.com> wrote:

> Στις Σαβ 27 Ιουν 2015 06:05:39 Drwecki, Brian B έγραψε:
> > Hello all,
> >
> > I apologize for the long post, but I want to be thorough.
> >
> > My Goal: To conduct the appropriate mixed-effects (random effects meta
> > analysis model+ one fixed effects moderator with two categorical levels)
> > meta analysis where 11 of 38 papers/studies present effects for both
> levels
> > of my Fixed Effects moderator (i.e. these 11 studies provide 2 effect
> sizes
> > each =  22 total estimates; each pair of effects is dependent and
> violates
> > assumptions of independence).
> [snip, snip]
>
> Hello,
>
> Maybe you can check package "robumeta" and the associated paper:
>
> Hedges LV, Tipton E, Johnson MC. Robust variance estimation in
> meta-regression
> with dependent effect size estimates. Res Synth Method. 2010;1(1):39–65.
> http://onlinelibrary.wiley.com/doi/10.1002/jrsm.5/abstract
>
> I've recently dealt with a similar meta-analysis situation, with
> hierarchical
> dependence (multiple effect estimates clustered within the same study), and
> this approach worked well for me.
>
> As a plus, you can have "robumeta" play nice ball with "metafor":
>
> http://blogs.edb.utexas.edu/pusto/2014/04/21/a-meta-sandwich/
>
> Hope this helps!
>
> Kind regards,
>
> Theodore Lytras
>
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