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

TL;DR

This paper develops confidence distribution-based methods for optimal meta-analysis of 2x2 tables modeled as Poisson pairs, accommodating heterogeneity and rare events, with applications to real medical data.

Contribution

It introduces novel confidence distribution methods for Poisson pair models in meta-analysis, handling fixed and random effects, especially for rare event data.

Findings

Methods provide optimal inference for treatment effects.

Proposed approach handles heterogeneity effectively.

Illustrated with real dataset application.

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.