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A Bayesian Hierarchical Model for 2-by-2 Tables with Structural Zeros
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Version 1
: Received: 22 August 2024 / Approved: 23 August 2024 / Online: 23 August 2024 (11:44:40 CEST)
How to cite: Stamey, W.; Stamey, J. D. A Bayesian Hierarchical Model for 2-by-2 Tables with Structural Zeros. Preprints 2024, 2024081726. https://doi.org/10.20944/preprints202408.1726.v1 Stamey, W.; Stamey, J. D. A Bayesian Hierarchical Model for 2-by-2 Tables with Structural Zeros. Preprints 2024, 2024081726. https://doi.org/10.20944/preprints202408.1726.v1
Abstract
Correlated binary data in a 2x2 table has been analyzed from both the frequentist and Bayesian perspectives, but a fully Bayesian hierarchical model has not been proposed. This is a commonly used model for correlated proportions when considering, for example, a diagnostic test performance where negative subjects are tested a second time. We consider a new hierarchical Bayesian model for the parameters resulting from a 2x2 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 rate ratio and marginal probability of a positive test. We then show how the prior based on historical 2x2 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
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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