Meta-analyzing partial correlation coefficients using Fisher's z transformation.

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Robbie C M van Aert

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Robbie C M van Aert: Department of Methodology and Statistics, Tilburg University, Tilburg, The Netherlands. ORCID

PMID: 37421188 DOI: 10.1002/jrsm.1654

The partial correlation coefficient (PCC) is used to quantify the linear relationship between two variables while taking into account/controlling for other variables. Researchers frequently synthesize PCCs in a meta-analysis, but two of the assumptions of the common equal-effect and random-effects meta-analysis model are by definition violated. First, the sampling variance of the PCC cannot assumed to be known, because the sampling variance is a function of the PCC. Second, the sampling distribution of each primary study's PCC is not normal since PCCs are bounded between -1 and 1. I advocate applying the Fisher's z transformation analogous to applying Fisher's z transformation for Pearson correlation coefficients, because the Fisher's z transformed PCC is independent of the sampling variance and its sampling distribution more closely follows a normal distribution. Reproducing a simulation study by Stanley and Doucouliagos and adding meta-analyses based on Fisher's z transformed PCCs shows that the meta-analysis based on Fisher's z transformed PCCs had lower bias and root mean square error than meta-analyzing PCCs. Hence, meta-analyzing Fisher's z transformed PCCs is a viable alternative to meta-analyzing PCCs, and I recommend to accompany any meta-analysis based on PCCs with one using Fisher's z transformed PCCs to assess the robustness of the results.

Fisher's z transformation meta-analysis partial correlation coefficient sampling variance

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VI.Veni.211G.012/Dutch Research Council (NWO)

Computer Simulation

Meta-Analysis as Topic

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