Distributional regression models for meta-analysis

TL;DR

This paper introduces a flexible distributional regression framework for meta-analysis that models all distribution parameters as functions of explanatory variables, enabling more comprehensive analysis of effect size distributions.

Contribution

It generalizes existing meta-analysis models by allowing location, scale, and shape parameters to vary with covariates, unifying various approaches and enabling new hypothesis testing.

Findings

Applied to 67,393 Cochrane meta-analyses using location-scale models.

Investigated small-study effects and heterogeneity systematically.

Discussed implementation, model selection, and future methodological developments.

Abstract

Meta-analyses are regarded as the highest level in the hierarchy of evidence, yet standard models traditionally concentrated on estimating the mean effect size, often under restrictive assumptions about the underlying distribution, such as homogeneous variance, symmetric shapes. We introduce a distributional regression framework for meta-analysis that generalizes these conventional models by allowing all parameters of the effect size distribution, such as location, scale, and shape, to be modelled as functions of explanatory variables. This unified framework accommodates a wide range of existing models, including random-effects, multilevel, multivariate, location-scale, and outlier-robust meta-analyses, as special cases. We provide an illustrative example, using 67,393 meta-analyses from the Cochrane Database of Systematic Reviews, employing location-scale models to investigate whether smaller studies tend to report larger effect sizes (i.e., small-study effects) and exhibit greater heterogeneity. We discuss implementation strategies using existing software, considerations for model selection and pre-registration, and the need for further methodological development. By moving beyond the mean effect size, distributional regression enables researchers to explore systematic variation in distributional structure, facilitating the joint test of new hypotheses corresponding to multiple distributional parameters.