A colleague of mine wishes to conduct a network meta-analysis of correlation coefficients for a set of imaging tests (eg ultrasound, computed tomography, magnetic resonance imaging, and so forth).
He has collected correlation coefficients (R), R-squared, and Fisher z. He pushes me to embark in a formal network meta-analysis (eg a frequentist one with the netmeta R package).
However, after some thoughts, I think it is a logical paradox, in the sense that in my opinion the transitivity assumption (see figure below) does not apply to correlation coefficients in the same fashion it applies to clinical trials with unambiguous endpoint definitions or to diagnostic test accuracy studies with clear labeling of healthy and diseased subjects.
Indeed, I fear that the correlation obtained when comparing test A and B, and that obtained when comparing B and C, cannot inform on the comparison between A and C, as the latter may depend on completely different cases.
I have also searched in Google and PubMed for "network meta-analysis" and "correlation", but did not find any meaningful reference.
According, my recommendation would simply to stick to a univariate meta-analysis approach, or otherwise use a multivariate meta-analysis one, for instance with mvmeta in Stata or R.
Am I correct?