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中国循证儿科杂志

中国循证儿科杂志 ›› 2019, Vol. 14 ›› Issue (2): 123-128.DOI: 10.3969/j.issn.1673-5501.2019.02.009

• 论著 • 上一篇    下一篇

基于二项式-正态层次模型框架下比例的贝叶斯Meta分析方法及实现

张天嵩   

  1. 复旦大学附属静安区中心医院 上海,200040
  • 收稿日期:2019-03-26 出版日期:2019-04-25
  • 通讯作者: 张天嵩, E-mail: zhangtiansong@fudan.edu.cn

Bayesian methods for meta-analysis of proportions and its application in the framework of binomial-normal hierarchical model

ZHANG Tian-song   

  1. Jing'an District Central Hospital,Fudan university ,Shanghai 200040, China
  • Received:2019-03-26 Online:2019-04-25
  • Contact: ZHANG Tian-song, E-mail: zhangtiansong@fudan.edu.cn

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摘要： 目的 介绍适用于比例Meta分析的二项式-正态层次模型及其贝叶斯方法实现。方法 阐述二项式-正态层次模型和正态-正态层次模型,分别在此两模型框架下,选择随机效应模型对两个文献数据重新分析。采用贝叶斯和频率学方法拟合二项式-正态层次模型;对数据未经或经logit转换后,采用倒方差法等经典频率学方法拟合正态-正态层次模型。结果 在二项式-正态层次模型框架下,采用贝叶斯方法获得合并比例的点估计及95%可信区间分别为0.057(0.039,0.077)和0.799(0.693,0.897),研究间方差分别为0.488和0.919;采用频率学方法获得合并比例的点估计及95%置信区间分别为0.056(0.041,0.078)和0.798(0.692,0.875),研究间方差分别为0.400和0.589。在正态-正态层次模型框架下,经logit转换后获得合并比例的点估计及95%置信区间分别为0.073(0.057,0.094)和0.754(0.661,0.827),研究间方差分别为0.170和0.301;直接合并原始数据获得合并比例的点估计及95%置信区间分别为0.049(0.032,0.065)和0.804(0.719,0.888),研究间方差分别为0.001和0.018。结论 不同模型可以获得不同的结果,NNHM可能低估研究间方差。基于二项式-正态层次模型框架下贝叶斯方法更适用于比例的Meta分析。

关键词: Meta分析, R软件, 贝叶斯方法, 比例, 二项式-正态层次模型

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