How to synthesize randomized controlled trial data with meta-analytic structural equation modeling: A comparison of various d-to-rpb conversions.

Meta-analytic structural equation modeling (MASEM) allows a researcher to simultaneously examine multiple relations among variables by fitting a structural equation model to summary statistics from multiple studies. Consider, for example, a mediation model with a predictor (X), mediator (M), and outcome variable (Y). In such a model, X can be a dichotomous variable, allowing researchers to examine the direct and indirect effects of an intervention as in randomized controlled trials (RCTs). However, the natural choice of a meta-analysis of RCTs would involve standardized mean differences as effect sizes, whereas MASEM requires correlation matrices as input. This can be solved by converting standardized mean differences (Cohen's d or Hedges' g) to point-biserial correlations (r_pb). Possible conversion formulas vary across publications and conversion tools, and it is unclear which one is most appropriate for use in MASEM. The aim of this article is to describe and evaluate several conversions of standardized mean differences to point-biserial correlations in the context of RCTs. We investigate the impact of the usage of various conversions on MASEM parameter estimation using the R package metaSEM in a simulation study, varying the ratio of group sample sizes, number of primary studies, sample sizes, and missingness. The results show that a relatively unknown d-to-r_pb conversion generally performs best. However, this conversion formula is not implemented in the mainstream conversion tools. We developed a user-friendly web application entitled Effect Size Calculator and Converter (https://hdejonge.shinyapps.io/ESCACO) that converts the user's primary study statistics into an effect size suitable for use in MASEM. (PsycInfo Database Record (c) 2025 APA, all rights reserved).