Fisher transformation based Confidence Intervals of Correlations in Fixed- and Random-Effects Meta-Analysis

TL;DR

This paper introduces improved confidence interval methods for correlation meta-analyses, enhancing accuracy in fixed- and random-effects models through advanced variance estimators and extensive simulation validation.

Contribution

It proposes novel confidence interval approaches based on enhanced variance estimators, outperforming existing methods in coverage accuracy for correlation meta-analyses.

Findings

New intervals show better coverage in simulations

Robust estimators outperform traditional methods

Effective in both fixed- and random-effects models

Abstract

Meta-analyses of correlation coefficients are an important technique to integrate results from many cross-sectional and longitudinal research designs. Uncertainty in pooled estimates is typically assessed with the help of confidence intervals, which can double as hypothesis tests for two-sided hypotheses about the underlying correlation. A standard 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. Results from previous studies (Field, 2005; Hafdahl and Williams, 2009), however, indicate that in random-effects models the performance of the HOVz confidence interval can be unsatisfactory. To this end, we propose improvements of the HOVz approach, which are based on enhanced variance estimators for the main effect estimate. In order to study the coverage of the new confidence intervals in both fixed- and random-effects meta-analysis models, we perform an extensive simulation study, comparing them to established approaches. Data were generated via a truncated normal and beta distribution model. The results show that our newly proposed confidence intervals based on a Knapp-Hartung-type variance estimator or robust heteroscedasticity consistent sandwich estimators in combination with the integral z-to-r transformation (Hafdahl, 2009) provide more accurate coverage than existing approaches in most scenarios, especially in the more appropriate beta distribution simulation model.