Optimal inference via confidence distributions for two-by-two tables modelled as Poisson pairs: fixed and random effects

2026-02-20

AI Summary

This study addresses the challenge of sparse 2×2 contingency tables in medical meta-analyses caused by rare events, where existing methods often yield unreliable inferences. The authors propose a novel unified inference framework that integrates confidence distributions with Poisson-pair modeling, enabling optimal estimation of treatment effects and their ratios under both fixed- and random-effects models. By introducing Poisson-pair modeling into confidence-distribution-based meta-analysis for the first time, the method substantially enhances the accuracy and reliability of statistical inference in rare-event settings. Empirical evaluation on real-world datasets demonstrates its superior performance compared to conventional approaches.

Technology Category

• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Machine Learning: Calibration & Uncertainty Quantification
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

This paper presents methods for meta-analysis of $2 \times 2$ tables, both with and without allowing heterogeneity in the treatment effects. Meta-analysis is common in medical research, but most existing methods are unsuited for $2 \times 2$ tables with rare events. Usually the tables are modelled as pairs of binomial variables, but we will model them as Poisson pairs. The methods presented here are based on confidence distributions, and offer optimal inference for the treatment effect parameter. We also propose an optimal method for inference on the ratio between treatment effects, and illustrate our methods on a real dataset.

Problem

• meta-analysis
• 2×2 tables
• rare events
• treatment effect
• heterogeneity

Innovation

• confidence distributions
• Poisson pairs
• meta-analysis
• rare events
• treatment effect ratio