Abstract: Objective To introduce a binomial-normal hierarchical model (BNHM) that is appropriate for meta-analysis of proportions, and explain how to fit the model with bayesian methods.Methods The BNHM and a normal-normal hierarchical model(NNHM)were explained. Random effects model was used to reanalyze two worked examples from literature in the framework of the BNHM and NNHM respectively. Bayesian and frequentist methods were used to fit the BNHM. The frequentist methods were used to fit the NNHM with standard inverse variance method for the two untransformed or logit transformed data of proportions.Results In the framework of BNHM, the point estimates and 95% credit interval(CI) of pooled proportions using the bayesian method were 0.057(0.039,0.077) and 0.799(0.693,0.897) respectively, and the between-study variances were 0.488 and 0.919 respectively. The point estimates and 95% confidence interval(CI) of pooled proportions using the frequentist method were 0.056(0.041,0.078) and 0.798(0.692,0.875) respectively, and the between-study variances were 0.400 and 0.589 respectively. In the framework of NNHM, for the logit transformed data, the point estimates and 95%CI of pooled proportions were 0.073(0.057,0.094) and 0.754(0.661,0.827) respectively, and the between-study variances were 0.170 and 0.301 respectively. For the untransformed data,the point estimates and 95%CI of pooled proportions were 0.049(0.032,0.065) and 0.804(0.719,0.888) respectively,and the between-study variances were 0.001 and 0.018 respectively.Conclusion Different models might give different results,and the NNHM might underestimate the between-study variances. Bayesian methods were preferable for the meta-analysis of proportions in the framework of BNHM.

Key words: Bayesian methods, Binomial-normal hierarchical model, Meta-analysis, Proportions, R software