[R-meta] Questions about fitting a multilevel meta-analysis model with effect sizes measured as different outcome

[CHIU, Man Hey]

Dear Dr. Viechtbauer and All,


I am writing this letter to seek for your help on multilevel meta-analysis
using the metafor package you have developed.


In our meta-analysis, we chose to conduct a mutilevel meta-analysis due to
multiple effect sizes from a single study (i.e., dependence).


Thus, we are thinking about a 3-level random effect meta-analysis model
with level 1 being sampling biases, level 2 being the variation of effect
sizes measured as different outcomes within the same studies and level 3
being the variation between studies across the whole dataset.



During running the analyses, we have encountered a specific problem about
the organization of the data file that is entered into the model. We have
one column 'StudyName' representing each study, 'Outcome' representing each
outcome within a study (p.s. different studies can have the same outcome)
and 'EffectID' representing each unique effect size across all studies
(p.s. if the whole dataset has 300 effect sizes, there would be 300
different EffectID.)


And I wonder whether the 'Outcome' (the first line of code below) or the
'EffectID' (the second line of code below) should be used to get our
desired outcome:



(1) rma.mv(yi=Hedge.g, V = Variances, data=df, slab=StudyName, random =
list(~1|Outcome, ~1|StudyName))



(2) rma.mv(yi=Hedge.g, V = Variances, data=df, slab=StudyName, random =
list(~1|EffectID, ~1|StudyName))


I have read the demonstration of doing the multilevel meta-analysis on
sample dataset dat.konstantopoulos2011, the 'school' column can have the
same code which may be reused in different districts. Yet, actually, every
school should be unique. In contrast, in my case, different studies can
share the same outcomes. Since my case is different than the example that
you showed, I am not so sure how should I fit my dataset to the model.



Another question would be whether the order of specific effect inside
list() would matter. As the following two line of code would give the same
result, how does the function know which level 2 and level 3 is? Since
level 2 should be clustered in level 3, why don't we have to specify the
level 2 and level 3?



>rma.mv(yi=Hedge.g, V = Variances, data=df, slab=StudyName, random =
list(~1|Outcome, ~1|StudyName))


>rma.mv(yi=Hedge.g, V = Variances, data=df, slab=StudyName, random =
list(~1|StudyName, 1|Outcome))



The final question we have encountered would be about adding moderators to
the above function. Since in multilevel-meta analysis, there might be
covariates on the level 2 outcome and level 3 study respectively, e.g.,
similar outcome may be measured across different studies. Would the
function automatically detect the covariate as a level 2 covariate when
that value is different across the outcomes in a specific cluster (i.e.
study) or do we have to specify the level of covariates?


Thank you in advance for your time and help, we really appreciate your
input on these questions~



Regards,

Heidi Chiu

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