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A Hierarchical Bayesian Model for Combining Multiple 2 × 2 Tables Using Conditional Likelihoods
Author(s) -
Liao J. G.
Publication year - 1999
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.1999.00268.x
Subject(s) - gibbs sampling , bayesian probability , computer science , bayesian inference , mathematics , statistics , hypergeometric distribution , variance (accounting) , bayesian hierarchical modeling , algorithm , accounting , business
Summary. This paper introduces a hierarchical Bayesian model for combining multiple 2×2 tables that allows the flexibility of different odds ratio estimates for different tables and at the same time allows the tables to borrow information from each other. The proposed model, however, is different from a full Bayesian model in that the nuisance parameters are eliminated by conditioning instead of integration. The motivation is a more robust model and a faster and more stable Gibbs algorithm. We work out a Gibbs scheme using the adaptive rejection sampling for log concave density and an algorithm for the mean and variance of the noncentral hypergeometric distribution. The model is applied to a multicenter ulcer clinical trial.