Distributional regression models for meta-analysis

2026-03-31

AI Summary

Traditional meta-analytic models typically estimate only the mean effect size and assume homoscedasticity and symmetric distributions, thereby failing to fully characterize the distribution of effect sizes and their heterogeneity. This work proposes a distributional regression framework that jointly models the location, scale, and shape parameters of the effect size distribution as functions of covariates, moving beyond the conventional focus on the mean to enable flexible modeling of the entire effect size distribution and simultaneous inference on multiple parameters. The approach naturally accommodates random-effects, multilevel, multivariate, and robust meta-analytic structures and can be implemented using existing statistical software. An empirical analysis of 67,393 meta-analyses from the Cochrane Database reveals that smaller studies not only exhibit larger effect sizes but also greater heterogeneity, providing strong evidence for the presence of the “small-study effect.”

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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.

Problem

• meta-analysis
• effect size distribution
• distributional regression
• heterogeneity
• small-study effects

Innovation

• distributional regression
• meta-analysis
• location-scale models
• heterogeneity
• small-study effects