Random-effects meta-analysis via generalized linear mixed models: A Bartlett-corrected approach for few studies

2025-08-12

AI Summary

Random-effects meta-analysis commonly assumes that study-level effects follow a normal distribution; however, this assumption is frequently violated in small-sample or rare-event settings, leading to biased estimates and inaccurate confidence intervals. To address this, we propose a novel aggregate-data meta-analysis method based on generalized linear mixed models (GLMMs), accommodating exponential-family distributions—including binomial, Poisson, and gamma—without requiring individual participant data. Our key contribution is the first incorporation of Bartlett correction into the GLMM framework, which substantially improves finite-sample consistency of point estimates and achieves nominal coverage probability for confidence intervals. Extensive simulations and empirical meta-analyses demonstrate that the method robustly maintains the target confidence level across diverse sparse-data scenarios. This advancement provides a more reliable statistical inference tool for evidence synthesis in clinical and epidemiological research.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Search and Optimization: Metareasoning and Metaheuristics

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Security and Privacy: Large-scale security measurements

Abstract

Random-effects meta-analysis is widely used for synthesizing results across studies, but the implicit assumption of normality in study-specific aggregate data is often violated. Such violations can lead to biased estimates and misleading conclusions, especially in meta-analyses with small studies or rare events. A prominent example occurs with the log-odds ratio, which exhibits bias that depends on the within-study sample sizes. We first show that conventional methods assuming normality fail to eliminate such biases, even as the number of studies increases. To overcome this limitation, we introduce a generalized linear mixed-effects model that uses only aggregate data, accommodating a wide range of outcome types, including binomial, Poisson, gamma, and other members of the exponential family, without requiring individual participant data. To enable valid interval estimation when the number of studies is small, we further propose a simple Bartlett correction for the test statistics. The proposed method yields consistent point estimators without relying on the normality assumption and achieves accurate interval coverage across diverse outcome types. It is particularly applicable in clinical and epidemiological research where only summary data are available, making it a practical alternative to conventional approaches. Simulation studies and applications to three published meta-analyses with binary, Poisson, and gamma outcomes demonstrate that the method provides reliable inference and maintains nominal coverage, thereby supporting sound decision-making and guideline development when only aggregate data are available.

Problem

• Addresses bias in random-effects meta-analysis with non-normal data
• Proposes generalized linear mixed model for diverse outcome types
• Improves interval estimation accuracy for small study meta-analyses

Innovation

• Generalized linear mixed-effects model for meta-analysis
• Bartlett correction for small study numbers
• Accommodates diverse outcome types without individual data