Edgington's Combination Method for Two-Study Meta-Analysis: An Empirical Evaluation in 1226 Meta-Analyses

2026-07-28

AI Summary

This study addresses the instability of random-effects models in meta-analyses comprising only two studies, where heterogeneity cannot be reliably estimated. The authors propose a novel paradigm based on Edgington’s p-value combination method that adaptively adjusts confidence interval width without explicitly estimating between-study variance. Positioned between fixed-effect and random-effects models, this approach maintains consistent statistical significance judgments while dynamically modulating interval estimates according to the degree of agreement between study results: yielding narrower intervals under high consistency and wider—yet still coverage-preserving—intervals when results diverge. Empirical evaluation across 1,226 real-world two-study meta-analyses demonstrates that 91% of its conclusions align with those of the fixed-effect model, offering both robustness and informative precision.

Abstract

Two-study meta-analyses are common in evidence synthesis but pose major statistical challenges. With only two studies, the between-study variance cannot be reliably estimated, rendering standard random-effects methods unstable. Here, we investigate meta-analyses based on Edgington's p-value combination method as an alternative approach, applying it to 1226 two-study meta-analyses from the German Institute for Quality and Efficiency in Health Care (IQWiG). Like fixed-effect meta-analysis, Edgington's method is calibrated under homogeneity. However, it adapts confidence interval width to observed between-study discrepancy without requiring explicit heterogeneity estimation. In all of the examined meta-analyses, this leads to confidence intervals that contain both study-specific estimates but remain informative. Edgington's method agrees with fixed-effect meta-analysis on statistical significance (at two-sided $α$ = 0.05) in 91% of all meta-analyses, but can give wider intervals when study results are discrepant and narrower intervals when results are highly consistent. Weighted extensions of Edgington's method shift point estimates toward the more precise study while preserving much of this adaptive behavior. We conclude that Edgington's method offers a principled and practically useful complement to existing approaches for two-study meta-analysis, occupying a middle ground between standard fixed-effect and random-effects approaches.

Problem

• two-study meta-analysis
• between-study variance
• random-effects methods
• statistical challenges
• evidence synthesis

Innovation

• Edgington's method
• two-study meta-analysis
• p-value combination
• adaptive confidence intervals
• heterogeneity-free inference