A Bayesian Hierarchical Model for 2-by-2 Tables with Structural Zeros

James Stamey () and Will Stamey
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James Stamey: Department of Statistical Science, Baylor University, Waco, TX 76798, USA
Will Stamey: Mendoza College of Business, University of Notre Dame, South Bend, IN 46556, USA

Stats, 2024, vol. 7, issue 4, 1-13

Abstract: Correlated binary data in 2 × 2 tables have been analyzed from both the frequentist and Bayesian perspectives, but a fully Bayesian hierarchical model has not yet been proposed. This is a commonly used model for correlated proportions when considering, for example, a diagnostic test performance where subjects with negative results are tested a second time. We consider a new hierarchical Bayesian model for the parameters resulting from a 2 × 2 table with a structural zero. We investigate the performance of the hierarchical model via simulation. We then illustrate the usefulness of the model by showing how a set of historical studies can be used to build a predictive distribution for a new study that can be used as a prior distribution for both the risk ratio and marginal probability of a positive test. We then show how the prior based on historical 2 × 2 tables can be used to power a future study that accounts for pre-experimental uncertainty. High-quality prior information can lead to better decision-making by improving precision in estimation and by providing realistic numbers to power studies.

Keywords: meta-analytic prior; structural-zero; Bayesian (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2024
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