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

Author

Listed:
  • 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)

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.

Suggested Citation

  • James Stamey & Will Stamey, 2024. "A Bayesian Hierarchical Model for 2-by-2 Tables with Structural Zeros," Stats, MDPI, vol. 7(4), pages 1-13, October.
    • Handle: RePEc:gam:jstats:v:7:y:2024:i:4:p:68-1171:d:1499509
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    References listed on IDEAS

    as
    1. Guang Yang & Dungang Liu & Junyuan Wang & Min‐ge Xie, 2016. "Meta‐analysis framework for exact inferences with application to the analysis of rare events," Biometrics, The International Biometric Society, vol. 72(4), pages 1378-1386, December.
    2. Tang, Nian-Sheng & Jiang, Shao-Ping, 2011. "Testing equality of risk ratios in multiple 2x2 tables with structural zero," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1273-1284, March.
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