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It has also been used to investigate surrogacy patterns between treatment effects on the surrogate endpoint and the final outcome. Surrogate endpoints play an important role in drug development when they can be used to measure treatment effect early compared to the final outcome and to predict clinical benefit or harm. The standard bivariate meta\u2010analytic approach models the observed treatment effects on the surrogate and the final outcome outcomes jointly, at both the within\u2010study and between\u2010studies levels, using a bivariate normal distribution. For binomial data, a normal approximation on log odds ratio scale can be used. However, this method may lead to biased results when the proportions of events are close to one or zero, affecting the validation of surrogate endpoints. In this article, we explore modeling the two outcomes on the original binomial scale. First, we present a method that uses independent binomial likelihoods to model the within\u2010study variability avoiding to approximate the observed treatment effects. However, the method ignores the within\u2010study association. To overcome this issue, we propose a method using a bivariate copula with binomial marginals, which allows the model to account for the within\u2010study association. We applied the methods to an illustrative example in chronic myeloid leukemia to investigate the surrogate relationship between complete cytogenetic response and event\u2010free\u2010survival.<\/jats:p>","DOI":"10.1002\/sim.9547","type":"journal-article","created":{"date-parts":[[2022,8,6]],"date-time":"2022-08-06T05:43:50Z","timestamp":1659764630000},"page":"4961-4981","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Use of copula to model within\u2010study association in bivariate meta\u2010analysis of binomial data at the aggregate level: A\u00a0Bayesian approach and application to surrogate endpoint evaluation"],"prefix":"10.1002","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8971-6221","authenticated-orcid":false,"given":"Tasos","family":"Papanikos","sequence":"first","affiliation":[{"name":"Biostatistics Research Group, Department of Health Sciences University of Leicester  Leicester UK"},{"name":"GlaxoSmithKline R&amp;D Centre GlaxoSmithKline  Stevenage UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4819-1611","authenticated-orcid":false,"given":"John R.","family":"Thompson","sequence":"additional","affiliation":[{"name":"Genetic Epidemiology Group, Department of Health Sciences University of Leicester  Leicester UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7557-1567","authenticated-orcid":false,"given":"Keith R.","family":"Abrams","sequence":"additional","affiliation":[{"name":"Biostatistics Research Group, Department of Health Sciences University of Leicester  Leicester UK"},{"name":"Department of Statistics University of Warwick  Coventry UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3003-9403","authenticated-orcid":false,"given":"Sylwia","family":"Bujkiewicz","sequence":"additional","affiliation":[{"name":"Biostatistics Research Group, Department of Health Sciences University of Leicester  Leicester UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2022,8,5]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1136\/bmj.j3932"},{"key":"e_1_2_9_3_1","first-page":"289","article-title":"Tutorial in biostatistics advanced methods in meta\u2010analysis: multivariate approach and meta\u2010regression","volume":"2","author":"Houwelingen HC","year":"2005","journal-title":"Tutor Biostat Tutor Biostat Stat Model Complex Med Data"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2524"},{"key":"e_1_2_9_5_1","unstructured":"BujkiewiczS AchanaF PapanikosT RileyR AbramsK.Multivariate meta\u2010analysis of summary data for combining treatment effects on correlated outcomes and evaluating surrogate endpoints. 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