Meta-analysis of studies with bivariate binary outcomes: a marginal beta-binomial model approach

Area of Science:

• Biostatistics
• Statistical Modeling
• Meta-Analysis

Background:

• Meta-analysis of bivariate binary outcomes presents challenges in accounting for within-study correlation and between-study heterogeneity.
• Existing models like bivariate generalized linear mixed models and Sarmanov beta-binomial models have limitations regarding probability transformations, link functions, and parameter constraints.

Purpose of the Study:

• To propose a novel marginal beta-binomial model for meta-analysis of bivariate binary outcomes.
• To address limitations of existing models, particularly concerning the accurate modeling of correlation and heterogeneity.
• To evaluate the performance and robustness of the proposed model compared to existing methods.

Main Methods:

• Development of a marginal beta-binomial model utilizing the composite likelihood approach.
• Comparison of the proposed model with bivariate generalized linear mixed models and Sarmanov beta-binomial models through simulation studies.
• Application of the models to meta-analyses of diagnostic accuracy and case-control studies.

Main Results:

• The proposed marginal beta-binomial model demonstrates superior performance compared to the Sarmanov beta-binomial model, irrespective of the true underlying model.
• The marginal beta-binomial model exhibits greater robustness than the bivariate generalized linear mixed model when facing model misspecifications.
• The model effectively handles marginal distributions without requiring complex transformations or link functions.

Conclusions:

• The marginal beta-binomial model offers an attractive and robust alternative for meta-analysis of bivariate binary outcomes.
• Its ability to avoid potential misspecification of joint distributions provides more reliable inference.
• The model's advantages include a closed-form likelihood and no constraints on the correlation parameter, enhancing its practical utility.