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A hierarchical Bayesian model for combining multiple 2 x 2 tables using conditional likelihoods.

¹Department of Epidemiology and Biostatistics, University of South Florida, Tampa 33612, USA. jliao@com1.med.usf.edu

|April 25, 2001

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This study presents a novel hierarchical Bayesian model for analyzing multiple 2x2 tables, improving odds ratio estimation and data sharing across studies. The method offers a robust and efficient approach for complex data analysis.

Area of Science:

Biostatistics
Statistical Modeling
Clinical Trial Analysis

Background:

Combining data from multiple 2x2 tables is crucial for robust statistical inference.
Existing methods may lack flexibility in estimating varying odds ratios or efficient information sharing.

Purpose of the Study:

Introduce a hierarchical Bayesian model for flexible combination of multiple 2x2 tables.
Develop a robust and computationally efficient statistical framework for analyzing such data.

Main Methods:

A hierarchical Bayesian model is proposed, conditioning on nuisance parameters instead of full integration.
A Gibbs sampling scheme is developed, incorporating adaptive rejection sampling and algorithms for the noncentral hypergeometric distribution.

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Main Results:

The model allows for different odds ratio estimates across tables while enabling information borrowing.
The proposed Gibbs algorithm demonstrates improved speed and stability compared to traditional methods.

Conclusions:

The hierarchical Bayesian model provides a flexible and robust approach for meta-analysis of 2x2 tables.
The method is successfully applied to a multicenter ulcer clinical trial, demonstrating its practical utility.