[R-meta] Multivariate meta-analysis with unknown covariances?

schlegei schlegei at hu-berlin.de
Thu Aug 10 18:54:28 CEST 2017

for my master thesis, I want to conduct a multivariate meta-analysis 
with the R-package metafor.
Unfortunately, I‘m not sure if it is possible to conduct this analysis 
based on my data set.

To illustrate my problem, a few words about my research question: I 
investigate the efficacy of gestalt therapy (a psychotherapeutic 
approach) for people with a mental disorder according to DSM-IV/ICD-10 
(my focus is on symptom reduction). My literature research resulted in 
12 randomized controlled trials (RCTs).
 From this 12 studies, I extracted 28 outcomes and calculated the effect 
sizes and variances (standardized mean differences). I assume outcomes 
from the same study are dependent. Unfortunately, in no study 
correlations/covariances between the sampling errors of the outcomes are 
reported. So the within study covariance structure is totally missing.
Because I included studies about people with different mental disorders, 
my outcomes are pretty heterogeneous: Only one questionnaire (Beck‘s 
Depression Inventory) was used in 4 studies, apart from that the 
outcomes don‘t overlap between the studies.

Summed up, my data set consists of the following variables:
ES_ID = idenfification number for every effect size (I have 28 effect 
study = every study gets one number (I included 12 studies)
outcome = every questionnaire/outcome gets one letter (I included 24 
different outcomes)
yi = effect size
vi = variance of the effect size

Is it possible to conduct a multivariate meta-analysis based on this 
data set?

My supervisor told me, the missing within study covariances can be 
easily estimated with the R-package metafor. Up until now, I do not 
understand how. Following the discussions on stackexchange and this 
mailing list (e.g. 
it seems to me that estimating the whole covariance structure is not 
that easy and is attended by some disadvantages/assumptions . This also 
coincides with other articles I have read about multivariate 
meta-analysis and in which missing covariances are described as a major 
problem. When I contacted my supervisor, he just told me that the 
literature I read is out-dated and repeated that the problem of missing 
covariances can be solved with metafor (unfortunately, he didn‘t 
recommend up-to-date articles to me).

Right now, I feel a bit locked in a stalemate. Is there a simple, 
up-to-date solution for my problem with the missing covariances that I 
have overseen?
If yes: I would be extremely happy about any tip!
If no: Do you think, it makes sense to conduct a multivariate 
meta-analysis based on my data set or is it more appropriate to choose 
one effect size per study (univariate meta-analysis)? If it is possible 
to conduct a multivariate meta-analysis based on my data: Is there a 
strategy – like making a rough guess of the correlations or using robust 
methods – that you would recommend?

I would be really happy to hear a response,
Isabel Schlegel

More information about the R-sig-meta-analysis mailing list