{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,18]],"date-time":"2026-05-18T15:52:35Z","timestamp":1779119555308,"version":"3.51.4"},"reference-count":53,"publisher":"Wiley","issue":"11","license":[{"start":{"date-parts":[[2017,1,25]],"date-time":"2017-01-25T00:00:00Z","timestamp":1485302400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2017,1,25]],"date-time":"2017-01-25T00:00:00Z","timestamp":1485302400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1"},{"start":{"date-parts":[[2017,1,25]],"date-time":"2017-01-25T00:00:00Z","timestamp":1485302400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2017,5,20]]},"abstract":"<jats:p>In meta\u2010analysis of odds ratios (OR<jats:italic>s<\/jats:italic>), heterogeneity between the studies is usually modelled via the additive random effects model (REM). An alternative, multiplicative REM for OR<jats:italic>s<\/jats:italic>uses overdispersion. The multiplicative factor in this overdispersion model (ODM) can be interpreted as an intra\u2010class correlation (ICC) parameter. This model naturally arises when the probabilities of an event in one or both arms of a comparative study are themselves beta\u2010distributed, resulting in beta\u2010binomial distributions. We propose two new estimators of the ICC for meta\u2010analysis in this setting. One is based on the inverted Breslow\u2010Day test, and the other on the improved gamma approximation by Kulinskaya and Dollinger (2015, p. 26) to the distribution of Cochran's<jats:italic>Q<\/jats:italic>. The performance of these and several other estimators of ICC on bias and coverage is studied by simulation. Additionally, the Mantel\u2010Haenszel approach to estimation of ORs is extended to the beta\u2010binomial model, and we study performance of various ICC estimators when used in the Mantel\u2010Haenszel or the inverse\u2010variance method to combine ORs in meta\u2010analysis. The results of the simulations show that the improved gamma\u2010based estimator of ICC is superior for small sample sizes, and the Breslow\u2010Day\u2010based estimator is the best for<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/sim7233-math-0001.png\" xlink:title=\"urn:x-wiley:sim:media:sim7233:sim7233-math-0001\"\/>. The Mantel\u2010Haenszel\u2010based estimator of OR is very biased and is not recommended. The inverse\u2010variance approach is also somewhat biased for OR<jats:italic>s<\/jats:italic>\u22601, but this bias is not very large in practical settings. Developed methods and R programs, provided in the Web Appendix, make the beta\u2010binomial model a feasible alternative to the standard REM for meta\u2010analysis of ORs. \u00a9\u00a02017 The Authors.<jats:italic>Statistics in Medicine<\/jats:italic>Published by John Wiley &amp; Sons Ltd.<\/jats:p>","DOI":"10.1002\/sim.7233","type":"journal-article","created":{"date-parts":[[2017,1,26]],"date-time":"2017-01-26T04:32:43Z","timestamp":1485405163000},"page":"1715-1734","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Beta\u2010binomial model for meta\u2010analysis of odds ratios"],"prefix":"10.1002","volume":"36","author":[{"given":"Ilyas","family":"Bakbergenuly","sequence":"first","affiliation":[{"name":"School of Computing Sciences University of East Anglia Norwich 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