[R-meta] Convert Multilevel Models Estimates

[Bernard Fernou]

Hi everyone,

I have a question about the conversion of estimates produced by multilevel
models into standard Pearson's correlation coefficient.

In our meta-analysis, we face two major difficulties:
First, although the large majority of the included studies are conducted at
the single-level (i.e., includes only one DV assessment by patient), some
used  some repeated-measures tasks (i.e., due to the combined use of fMRI
scan, they assessed the DV in multiple trials per patient).
Second, although we are primarily interested in a continuous outcome, some
studies assessed a related outcome that is binary (the IV is
systematically continuous). This binary outcome will not be included in our
primary analysis but - in an exploratory analysis - we would we would like
to merge all effect sizes, produced by both continuous and binary outcomes.

For most of these repeated measure tasks, we obtained raw data from study
authors.
(1) When the DV of these repeated-measure tasks was continuous, we
aggregated the results at the participant level and ran standard pearson's
correlation (we compared results to those obtained by standardizing the
linear mixed model estimate and we obtained very similar results ~ maximum
+/- 0.05).
(2) However, when the DV of these repeated measures tasks was binary,
things were most complicated.  Our first intention was :
- to run generalized linear mixed models
- to extract log odds ratio and associated confidence interval using the
code provided below
- to convert the 95% CI into sampling variance using the Cochrane
handook's formula
- to convert this log odds ratio into correlation coefficient using the
compute.es package (where n1 and n2 were assumed to be respectively 50% of
the sample size of level 2 units).
Because these steps involve a lot of transformations, we have also tried to
aggregate data at the patient-level (i.e., the binary DV becomes an index
resulting from the sum of yes/no answers) and to run Pearson's correlations
between:
- the IV and this index
- the IV and the deciles of this index

These last two correlations give very similar results. However, they
diverge quite largely compared to the correlation coefficient obtained by
transforming the coefficient estimates of the GLMM into correlation (this
difference reaches r = +0.18 in a study). This is not dramatic but it
raises questions about our approach.

Is there a recommended procedure in our situation or should we simply
report the results produced by the different approaches in several
sensitivity analyses?

Thank you very much for your help!

Regards,
BF


GLMM_Model<-glmer(DV~IV+(1|Patient)+(1|Trial), family=binomial, dataset)

ConfidenceInterval <- confint(GLMM_Model,parm="beta_")

Estimate <-fixef(GLMM_Model)

Var=((CIup-CIlow)/3.92)^2

lores(lor=LogOR, var.lor= Var, n.1=0.5*Level2units, n.2= 0.5*Level2units ,
dig=3)

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