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Meta-Analysis with Few Studies and Binary Data: A Bayesian Model Averaging Approach

Author

Listed:
  • Francisco-José Vázquez-Polo

    (Department of Quantitative Methods & TiDES Institute, University of Las Palmas de Gran Canaria, 35017 Las Palmas, Spain)

  • Miguel-Ángel Negrín-Hernández

    (Department of Quantitative Methods & TiDES Institute, University of Las Palmas de Gran Canaria, 35017 Las Palmas, Spain)

  • María Martel-Escobar

    (Department of Quantitative Methods & TiDES Institute, University of Las Palmas de Gran Canaria, 35017 Las Palmas, Spain)

Abstract

In meta-analysis, the existence of between-sample heterogeneity introduces model uncertainty, which must be incorporated into the inference. We argue that an alternative way to measure this heterogeneity is by clustering the samples and then determining the posterior probability of the cluster models. The meta-inference is obtained as a mixture of all the meta-inferences for the cluster models, where the mixing distribution is the posterior model probabilities. When there are few studies, the number of cluster configurations is manageable, and the meta-inferences can be drawn with BMA techniques. Although this topic has been relatively neglected in the meta-analysis literature, the inference thus obtained accurately reflects the cluster structure of the samples used. In this paper, illustrative examples are given and analysed, using real binary data.

Suggested Citation

  • Francisco-José Vázquez-Polo & Miguel-Ángel Negrín-Hernández & María Martel-Escobar, 2020. "Meta-Analysis with Few Studies and Binary Data: A Bayesian Model Averaging Approach," Mathematics, MDPI, vol. 8(12), pages 1-13, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2159-:d:456651
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    References listed on IDEAS

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    1. Dulal K. Bhaumik & Anup Amatya & Sharon-Lise T. Normand & Joel Greenhouse & Eloise Kaizar & Brian Neelon & Robert D. Gibbons, 2012. "Meta-Analysis of Rare Binary Adverse Event Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 555-567, June.
    2. Tuyl, Frank & Gerlach, Richard & Mengersen, Kerrie, 2008. "A Comparison of BayesLaplace, Jeffreys, and Other Priors: The Case of Zero Events," The American Statistician, American Statistical Association, vol. 62, pages 40-44, February.
    3. Larose, Daniel T. & Dey, Dipak K., 1998. "Modeling publication bias using weighted distributions in a Bayesian framework," Computational Statistics & Data Analysis, Elsevier, vol. 26(3), pages 279-302, January.
    4. Weber, Frank & Knapp, Guido & Ickstadt, Katja & Kundt, Günther & Glass, Anne, 2020. "Zero-cell corrections in random-effects meta-analyses," OSF Preprints qjh5f, Center for Open Science.
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