Background: In meta-analysis, it is common to find heterogeneity among the effect estimates reported (or computed from) the primary studies, so that an additional analysis stage is to search for moderators that can account for at least part of such heterogeneity. A particularly popular and flexible type of moderator analysis is meta-regression, which can accommodate both continuous and categorical moderator variables. The meta-regression models available at present enable to test for moderators of the magnitude of the effects, but they assume a constant value of the heterogeneity variance across studies. However, this assumption might not hold in some situations, and hence it would be helpful to have models that relax this assumption and enable to incorporate moderators of the amount of heterogeneity. The idea of regression models with predictors of both the mean and the variance has already been explored in the context of multilevel analysis with the so-called “location-scale models” (Hedeker, Mermelstein, & Demirtas, 2012). Extending these models to the meta-analytic context has also been proposed (Bowater & Escarela, 2013), but to our knowledge there are no statistical methods fully developed and readily available in any meta-analytic software tool.

Objective: to develop mixed-effects meta-regression models fit to search for moderators of both the magnitude and the amount of heterogeneity of the effect estimates, and to make them available to meta-analysts through open-source software.

Method: we propose an extension of standard mixed-effects meta-regression models which relaxes the assumption of a constant heterogeneity variance across studies. We use the label “location-scale models”, with location referring to the magnitude of effect estimates and scale referring to their variance. Such models make use of likelihood-based techniques for parameter estimation and allow for the incorporation of (possibly different) moderators of the location and scale parts. The new models can now be fitted using the rma function of the metafor package in R (Viechtbauer, 2010). In this talk, we will demonstrate the implementation of location-scale models in the metafor package using an illustrative example.

Funding: Agencia Estatal de Investigación (Government of Spain) and FEDER Funds: grant no. PID2019-104033GA-I00/AEI/10.13039/501100011033

References

Bowater, R. J., & Escarela, G. (2013). Heterogeneity and study size in random-effects meta-analysis. Journal of Applied Statistics, 40(1), 2-16.

Hedeker, D., Mermelstein, R. J., & Demirtas, H. (2012). Modeling between‐subject and within-subject variances in ecological momentary assessment data using mixed-effects

location scale models. Statistics in Medicine, 31(27), 3328-3336.

Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3), 1-48.