Article
Fisher transformation-based confidence intervals of correlation coefficients in meta-analyses
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Authors
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Thilo Welz
- TU Dortmund University, Dortmund, Germany
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Markus Pauly
- TU Dortmund University, Dortmund, Germany
| Published: | February 26, 2021 |
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Outline
Text
Background: In the fields of Psychology and Sociology investigators often consider meta-analyses with Pearson correlation coefficients as effect measure of interest. A classical approach to construct confidence intervals for the main effect is the Hedges-Olkin-Vevea Fisher-z (HOVz) approach, which is based on the Fisher-z transformation. This approach has been analyzed in various papers, such as [1] and [2]. Their results indicate that in random-effects models with substantial amounts of heterogeneity the coverage of the HOVz confidence interval can be unsatisfactory.
Methods: We propose improvements to the HOVz approach, which are based on enhanced variance estimators for the main effect estimate. In particular, we propose using either the Knapp-Hartung variance estimate or one of the robust heteroscedasticity consistent (HC) variance estimators. These approaches have proven fruitful in our previous research on mixed-effects meta-regression [3]. Furthermore, we propose a data-dependent wild bootstrap based approach for constructing confidence intervals. In order to study the performance of the new confidence intervals in both fixed- and random-effects meta-analysis models, we performed an extensive simulation study, comparing our new approaches to established procedures such as HOVz and Hunter-Schmidt.
Results: The simulation results indicate that our new confidence intervals improve upon the HOVz and Hunter-Schmidt approaches with regard to control of nominal coverage. Especially the confidence intervals based on the Knapp-Hartung and HC-estimators performed well and were more robust to substantial amounts of between-study heterogeneity.
Conclusion: Based on our simulation results we recommend using one of our newly proposed approaches for constructing confidence intervals, when performing meta-analyses of correlations, over the classical HOVz or Hunter-Schmidt type intervals. Especially the confidence intervals based on the Knapp-Hartung and HC-estimators are to be recommended. Our proposed methods are easy to implement in practice.
The authors declare that they have no competing interests.
The authors declare that an ethics committee vote is not required.
References
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- Hafdahl AR, Williams MA. Meta-analysis of correlations revisited: Attempted replication and extension of field's (2001) simulation studies. Psychological Methods. 2009;14(1):24.
- 2.
- Field AP. Is the meta-analysis of correlation coefficients accurate when population correlations vary? Psychological methods. 2005;10(4):444.
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- Welz T, Pauly M. A simulation study to compare robust tests for linear mixed-effects meta-regression. Research Synthesis Methods. 2020;11(3):331-342..
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- Schulze R. Meta-analysis – A comparison of approaches. Hogrefe; 2004.
