Background: Although Cochrane intervention reviews focus on randomized trials, the interest may lie in non-comparative binary outcomes. In treatment evaluation, pooling absolute risks from several single-arm studies may be required. In diagnostic accuracy assessment, separate meta-analyses of sensitivity/specificity estimates may be necessary when bivariate models do not converge. Appropriate statistical methods must be applied to combine binomial data from several trials. Objectives: We aimed to review available methods and to compare their statistical performance. Methods: Methods must handle overdispersion, where the observed variation exceeds that predicted from the binomial distribution, which might result from unmodelled heterogeneity. First, we considered the use of variance-stabilizing transformations followed by standard fixed-effect or random-effects meta-analysis of transformed proportions and back-transformation of the combined estimate. Second, we considered two hierarchical models, the beta-binomial and logistic-normal models, using both the frequentist and Bayesian approaches. We programmed all methods using R software. To compare methods, we carried out an empirical study. Monte Carlo simulation studies are underway. Scenario parameters included the number of individual studies, the study sample size, the true proportion and an overdispersion/heterogeneity parameter. The comparison criteria were bias, mean squared error, and coverage probability. Results: The empirical study was based on a meta-analysis of the perioperative risk of stroke or death after carotid angioplasty and stenting of carotid stenosis. In 42 studies totalling 4910 symptomatic patients, 366 patients experienced stroke or death within 30 days. There was evidence of large heterogeneity and overdispersion. The estimates of absolute risks of 30-day stroke or death ranged from 6.94%, 95%CI 5.68 8.44 to 7.65, 95%CI 6.31 9.10. Conclusion: A range of methods is available for the meta-analysis of proportions. Our results should provide general guidance to choose a relevant method, in particular when there are few studies or when the underlying true proportion is near 0 or 1.