[R-meta] Transformation for ICC as outcome?

Andrew McAleavey @ndrew@mc@|e@vey @end|ng |rom gm@||@com
Fri Jun 10 11:24:14 CEST 2022


tl;dr: What is the proper transformation to apply to ICC values as the
outcome of a meta-analysis?

More detail:

I work in an area where it is substantively interesting to evaluate the
intraclass correlation coefficient (ICC) from hierarchical models as an
estimate of the relative impact of clustering level. Most frequently my
field looks at patient outcomes in psychotherapy clustered within
psychotherapists, but the same design is often used for group effects of
group psychotherapy, clinic/center effects etc. The ICC, computed through
variance components, is a conventional way to indicate whether these
clustering levels make a difference in treatment outcome.

From what I can tell, previous meta-analyses of these ICCs have not
transformed the outcome variable at all, and the values tend to be quite
low in published papers (.003 to .04 are common, slightly larger values
occasionally). The lack of transformation seems strange to me, given that
these ICCs are ratios of variance components. In fact, not only are these
ICC values are bounded at (or close to) 0, but when estimates are this
small, publication bias should be a huge factor due to non-convergence of
ML estimates (primary studies would tend to simply omit this clustering
factor if the model didn't converge or the effect was extremely small, so
the file-drawer is essentially infinitely large). Without transforming the
outcome, tests for publication bias would also be problematic, since there
is no possibility for symmetry in a funnel plot (for example), right?

Despite this, I haven't seen any examples of meta-analyses of ICC values in
other fields that transform the ICC values first. So maybe this is not a
big deal? Admittedly, it is hard to search for meta-analyses of ICC values
as the outcome, and I haven't found that many outside my area at all -
probably there are more I am not familiar with.

My question is this:

Does it make sense to transform ICC values prior to meta-analytic
aggregation, and if so, what transformation makes the most sense?

I've had logit and double-arcsine transformations recommended already since
they apply for ratio/proportion outcomes. I am just not sure if I am
missing some reason why ICC values should not be treated that way.

Any advice or links would be appreciated!

Andrew McAleavey
Helse Førde, Norway

Andrew McAleavey
andrew.mcaleavey using gmail.com
He / him

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