Principles of network meta-analysis and applications of mainstream software packages_Chinese Journal of Evidence-Based Medicine

Authors：

ZHENG Qingyong ^1,2 , LI Tengfei ³ , XU Jianguo ^1,2 , ZHOU Yongjia ³ , Gao Ya ^1,2 , LIU Ming ^1,2 , XU Caihua ^1,2 , CUI Yating ^1,2 , MA Zhichao ⁴ , YUAN Kaisen ¹ ,  SHANG Yi ^5,6 ,  TIAN Jinhui ^1,2

1. Evidence-Based Medicine Center, School of Basic Medical Sciences, Lanzhou University, Lanzhou 730000, P. R. China;
2. Key Laboratory of Evidence-based Medicine of Gansu Province, Lanzhou 730000, P. R. China;
3. School of Nursing, Gansu University of Chinese Medicine, Lanzhou 730000, P. R. China;
4. The Second Clinical Medical College of Lanzhou University, Lanzhou 730000, P. R. China;
5. Department of Nursing, the Second Hospital of Lanzhou University, Lanzhou 730030;
6. School of Nursing, Lanzhou University, Lanzhou 730000, P. R. China;

Corresponding author：

SHANG Yi, Email: 1208299573@qq.com; TIAN Jinhui, Email: tjh996@163.com

Keywords：

Network meta-analysis; Principles; Frequentist approach; Bayesian method; Software packages

DOI：

10.7507/1672-2531.202407073

Video：

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Abstract Full text Figures/Tables Video References Cited by

Systematic reviews and meta-analyses have become the cornerstone methodologies for integrating multi-source research data and enhancing the quality of evidence. Traditional meta-analyses often demonstrate limitations when handling multiple treatment options. Network meta-analysis (NMA) overcomes these limitations by constructing a network of evidence that encompasses various treatment options, allowing for the simultaneous comparison of both direct and indirect evidence across multiple treatment plans. This provides more comprehensive and precise support for clinical decision-making. This article comprehensively reviews the statistical principles of NMA, its three fundamental assumptions, and the statistical inference framework. It also critically analyzes the mainstream NMA software and packages currently available, such as R (including gemtc, netmeta, rjags, pcnetmeta), Stata (mvmeta, network), WinBUGS, SAS, ADDIS, and various online applications, highlighting their strengths, weaknesses, and suitable scenarios. This analysis provides researchers with a scientific and unified framework for conducting clinical studies and policy-making.

1.	田金徽, 李伦, 赵晔, 等. 网状Meta分析的撰写与报告. 中国药物评价, 2013, 30(6): 321-323,333.
2.	田金徽, 李伦. 网状Meta分析方法与实践. 北京: 中国医药科技出版社, 2017.
3.	Rouse B, Chaimani A, Li T. Network meta-analysis: an introduction for clinicians. Intern Emerg Med, 2017, 12(1): 103-111.
4.	李伦, 田金徽, 姚亮, 等. 网状Meta分析的统计学基础、假设和证据质量评估. 循证医学, 2015, 15(3): 180-183.
5.	刘国伟, 于莉莉, 贾洪霞, 等. 系统评价中的间接比较与网状Meta分析方法研究进展. 中国循证医学杂志, 2014, 14(10): 1276-1280.
6.	Turri G, Ostuzzi G, Vita G, et al. Treatment of locally advanced rectal cancer in the era of total neoadjuvant therapy: a systematic review and network meta-analysis. JAMA Netw Open, 2024, 7(6): e2414702.
7.	许倩倩, 韩松洁, 尤良震, 等. 中药干预肿瘤患者化疗后并发心律失常的系统评价和网状Meta分析. 中草药, 2023, 54(24): 8180-8190.
8.	Higgins JP, Welton NJ. Network meta-analysis: a norm for comparative effectiveness. Lancet, 2015, 386(9994): 628-630.
9.	Izcovich A, Chu DK, Mustafa RA, et al. A guide and pragmatic considerations for applying GRADE to network meta-analysis. BMJ, 2023, 381: e074495.
10.	Xu W, Qiu L, Li F, et al. Induction chemotherapy regimes in first-line treatment for locoregionally advanced nasopharyngeal carcinoma: a network meta-analysis and cost-effectiveness analysis. Oral Oncol, 2024, 154: 106865.
11.	Owen RK, Cooper NJ, Quinn TJ, et al. Network meta-analysis of diagnostic test accuracy studies identifies and ranks the optimal diagnostic tests and thresholds for health care policy and decision-making. J Clin Epidemiol, 2018, 99: 64-74.
12.	张天嵩, 孙凤, 董圣杰, 等. 网络Meta分析研究进展系列(二): 网络Meta分析统计模型及模型拟合软件选择. 中国循证心血管医学杂志, 2020, 12(7): 769-774,793.
13.	Efthimiou O, Debray TP, van Valkenhoef G, et al. GetReal in network meta-analysis: a review of the methodology. Res Synth Methods, 2016, 7(3): 236-263.
14.	Song F, Loke YK, Walsh T, et al. Methodological problems in the use of indirect comparisons for evaluating healthcare interventions: survey of published systematic reviews. BMJ, 2009, 338: b1147.
15.	Sadeghirad B, Foroutan F, Zoratti MJ, et al. Theory and practice of Bayesian and frequentist frameworks for network meta-analysis. BMJ Evid Based Med, 2023, 28(3): 204-209.
16.	Greco T, Edefonti V, Biondi-Zoccai G, et al. A multilevel approach to network meta-analysis within a frequentist framework. Contemp Clin Trials, 2015, 42: 51-59.
17.	曾宪涛, 曹世义, 孙凤, 等. Meta分析系列之六: 间接比较及网状分析. 中国循证心血管医学杂志, 2012, 4(5): 399-402.
18.	张超, 鄢金柱, 孙凤, 等. 网状Meta分析一致性的鉴别与处理方法. 中国循证医学杂志, 2014, 14(7): 884-888.
19.	Lu G, Ades AE. Combination of direct and indirect evidence in mixed treatment comparisons. Stat Med, 2004, 23(20): 3105-3124.
20.	van Valkenhoef G, Dias S, Ades AE, et al. Automated generation of node-splitting models for assessment of inconsistency in network meta-analysis. Res Synth Methods, 2016, 7(1): 80-93.
21.	Balduzzi S, Ruecker G, Nikolakopoulou A, et al. Netmeta: an r package for network meta-analysis using frequentist methods. J Stat Softw, 2023, 106(2): 1-40.
22.	张超, 孙凤, 曾宪涛. R软件调用JAGS软件实现网状Meta分析. 中国循证医学杂志, 2014, 14(2): 241-248.
23.	Lin L, Zhang J, Hodges JS, et al. Performing arm-based network meta-analysis in R with the pcnetmeta package. J Stat Softw, 2017, 80: 5.
24.	Lim D, Chen MH, Ibrahim JG, et al. metapack: an R package for bayesian meta-analysis and network meta-analysis with a unified formula interface. R J, 2022, 14(3): 142-161.
25.	Röver C, Friede T. Using the bayesmeta R package for Bayesian random-effects meta-regression. Comput Methods Programs Biomed, 2023, 229: 107303.
26.	Sturtz S, Ligges U, Gelman A. R2WinBUGS: a package for running WinBUGS from R. J Stat Softw, 2005, 12(3): 1-16.
27.	Plummer M, Best N, Cowles K, et al. CODA: convergence diagnosis and output analysis for MCMC. R news, 2006, 6(1): 7-11.
28.	Stan Development Team. RStan: the R interface to Stan. 2024.
29.	Sturtz S, Ligges U, Gelman A. R2OpenBUGS: a package for running OpenBUGS from R. R Package Version, 2019, 3(2): 1.
30.	Viechtbauer W. Conducting meta-analyses in R with the metafor package. J Stat Softw, 2010, 36(3): 1-48.
31.	Phillippo DM. Multinma: an R package for Bayesian network meta-analysis of individual and aggregate data. Evidence Synthesis and Meta-Analysis in R Conference, 2021.
32.	Béliveau A, Boyne DJ, Slater J, et al. BUGSnet: an R package to facilitate the conduct and reporting of Bayesian network meta-analyses. BMC Med Res Methodol, 2019, 19(1): 196.
33.	Gonzalez-Diaz JM, Radua J, Sanchez-Dalmau B, et al. Mapping retinal abnormalities in psychosis: meta-analytical evidence for focal peripapillary and macular reductions. Schizophr Bull, 2022, 48(6): 1194-1205.
34.	张超, 陶华, 李胜, 等. 应用Stata软件mvmeta程序包实现网状Meta分析. 中国循证医学杂志, 2014, 14(9): 1150-1159.
35.	Shim S, Yoon BH, Shin IS, et al. Network meta-analysis: application and practice using Stata. Epidemiol Health, 2017, 39: e2017047.
36.	Baek E, Ferron JM. Bayesian analysis for multiple-baseline studies where the variance differs across cases in OpenBUGS. Dev Neurorehabil, 2021, 24(2): 130-143.
37.	Greco T, Landoni G, Biondi-Zoccai G, et al. A Bayesian network meta-analysis for binary outcome: how to do it. Stat Methods Med Res, 2016, 25(5): 1757-1773.
38.	Brown S, Hutton B, Clifford T, et al. A Microsoft-Excel-based tool for running and critically appraising network meta-analyses--an overview and application of NetMetaXL. Syst Rev, 2014, 3: 110.
39.	Piepho HP, Madden LV. How to observe the principle of concurrent control in an arm-based meta-analysis using SAS procedures GLIMMIX and BGLIMM. Res Synth Methods, 2022, 13(6): 821-828.
40.	Rott KW, Lin L, Hodges JS, et al. Bayesian meta-analysis using SAS PROC BGLIMM. Res Synth Methods, 2021, 12(6): 692-700.
41.	Van Valkenhoef G, Tervonen T, Zwinkels T, et al. ADDIS: a decision support system for evidence-based medicine. Dec Sup Sys, 2013, 55(2): 459-475.
42.	Depaoli S, Clifton JP, Cobb PR. Just another Gibbs sampler (JAGS) flexible software for MCMC implementation. J Educ Behav Stat, 2016, 41(6): 628-649.
43.	Metelli S, Chaimani A. NMAstudio: a fully interactive web-application for producing and visualising network meta-analyses. SRSM Annual Meeting, 2021.
44.	Owen RK, Bradbury N, Xin Y, et al. MetaInsight: an interactive web-based tool for analyzing, interrogating, and visualizing network meta-analyses using R-shiny and netmeta. Res Synth Methods, 2019, 10(4): 569-581.
45.	曾宪涛, 张超, 邝心颖, 等. 基于使用的网状Meta分析软件的比较研究与选择. 中国循证医学杂志, 2014, 14(10): 1270-1275.
46.	张超, 耿培亮, 郭毅, 等. 应用R语言netmeta程序包实现网状Meta分析. 中国循证医学杂志, 2014, 14(5): 625-630.
47.	Wiksten A, Hawkins N, Piepho HP, et al. Nonproportional hazards in network meta-analysis: efficient strategies for model building and analysis. Value Health, 2020, 23(7): 918-927.
48.	Madden LV, Piepho HP, Paul PA. Statistical models and methods for network meta-analysis. Phytopathology, 2016, 106(8): 792-806.
49.	Watt J, Hofmeister M, Del Giovane C, et al. Implementing hierarchical network meta-analysis incorporating exchangeable dose effects compared to standard hierarchical network meta-analysis. BMJ Evid Based Med, 2023, 28(5): 332-336.
50.	Kessels A, ter Riet G, Puhan MA, et al. A simple regression model for network meta-analysis. OA Epidemiol, 2013, 1(1): 7.
51.	Riley RD, Jackson D, Salanti G, et al. Multivariate and network meta-analysis of multiple outcomes and multiple treatments: rationale, concepts, and examples. BMJ, 2017, 358: j3932.
52.	Cooper NJ, Sutton AJ, Morris D, et al. Addressing between-study heterogeneity and inconsistency in mixed treatment comparisons: application to stroke prevention treatments in individuals with non-rheumatic atrial fibrillation. Stat Med, 2009, 28(14): 1861-1881.
53.	Dias S, Welton NJ, Sutton AJ, et al. Evidence synthesis for decision making 4: inconsistency in networks of evidence based on randomized controlled trials. Med Decis Making, 2013, 33(5): 641-656.
54.	Veroniki AA, Mavridis D, Higgins JP, et al. Characteristics of a loop of evidence that affect detection and estimation of inconsistency: a simulation study. BMC Med Res Methodol, 2014, 14: 106.
55.	White IR, Barrett JK, Jackson D, et al. Consistency and inconsistency in network meta-analysis: model estimation using multivariate meta-regression. Res Synth Methods, 2012, 3(2): 111-125.

1. 田金徽, 李伦, 赵晔, 等. 网状Meta分析的撰写与报告. 中国药物评价, 2013, 30(6): 321-323,333.
2. 田金徽, 李伦. 网状Meta分析方法与实践. 北京: 中国医药科技出版社, 2017.
3. Rouse B, Chaimani A, Li T. Network meta-analysis: an introduction for clinicians. Intern Emerg Med, 2017, 12(1): 103-111.
4. 李伦, 田金徽, 姚亮, 等. 网状Meta分析的统计学基础、假设和证据质量评估. 循证医学, 2015, 15(3): 180-183.
5. 刘国伟, 于莉莉, 贾洪霞, 等. 系统评价中的间接比较与网状Meta分析方法研究进展. 中国循证医学杂志, 2014, 14(10): 1276-1280.
6. Turri G, Ostuzzi G, Vita G, et al. Treatment of locally advanced rectal cancer in the era of total neoadjuvant therapy: a systematic review and network meta-analysis. JAMA Netw Open, 2024, 7(6): e2414702.
7. 许倩倩, 韩松洁, 尤良震, 等. 中药干预肿瘤患者化疗后并发心律失常的系统评价和网状Meta分析. 中草药, 2023, 54(24): 8180-8190.
8. Higgins JP, Welton NJ. Network meta-analysis: a norm for comparative effectiveness. Lancet, 2015, 386(9994): 628-630.
9. Izcovich A, Chu DK, Mustafa RA, et al. A guide and pragmatic considerations for applying GRADE to network meta-analysis. BMJ, 2023, 381: e074495.
10. Xu W, Qiu L, Li F, et al. Induction chemotherapy regimes in first-line treatment for locoregionally advanced nasopharyngeal carcinoma: a network meta-analysis and cost-effectiveness analysis. Oral Oncol, 2024, 154: 106865.
11. Owen RK, Cooper NJ, Quinn TJ, et al. Network meta-analysis of diagnostic test accuracy studies identifies and ranks the optimal diagnostic tests and thresholds for health care policy and decision-making. J Clin Epidemiol, 2018, 99: 64-74.
12. 张天嵩, 孙凤, 董圣杰, 等. 网络Meta分析研究进展系列(二): 网络Meta分析统计模型及模型拟合软件选择. 中国循证心血管医学杂志, 2020, 12(7): 769-774,793.
13. Efthimiou O, Debray TP, van Valkenhoef G, et al. GetReal in network meta-analysis: a review of the methodology. Res Synth Methods, 2016, 7(3): 236-263.
14. Song F, Loke YK, Walsh T, et al. Methodological problems in the use of indirect comparisons for evaluating healthcare interventions: survey of published systematic reviews. BMJ, 2009, 338: b1147.
15. Sadeghirad B, Foroutan F, Zoratti MJ, et al. Theory and practice of Bayesian and frequentist frameworks for network meta-analysis. BMJ Evid Based Med, 2023, 28(3): 204-209.
16. Greco T, Edefonti V, Biondi-Zoccai G, et al. A multilevel approach to network meta-analysis within a frequentist framework. Contemp Clin Trials, 2015, 42: 51-59.
17. 曾宪涛, 曹世义, 孙凤, 等. Meta分析系列之六: 间接比较及网状分析. 中国循证心血管医学杂志, 2012, 4(5): 399-402.
18. 张超, 鄢金柱, 孙凤, 等. 网状Meta分析一致性的鉴别与处理方法. 中国循证医学杂志, 2014, 14(7): 884-888.
19. Lu G, Ades AE. Combination of direct and indirect evidence in mixed treatment comparisons. Stat Med, 2004, 23(20): 3105-3124.
20. van Valkenhoef G, Dias S, Ades AE, et al. Automated generation of node-splitting models for assessment of inconsistency in network meta-analysis. Res Synth Methods, 2016, 7(1): 80-93.
21. Balduzzi S, Ruecker G, Nikolakopoulou A, et al. Netmeta: an r package for network meta-analysis using frequentist methods. J Stat Softw, 2023, 106(2): 1-40.
22. 张超, 孙凤, 曾宪涛. R软件调用JAGS软件实现网状Meta分析. 中国循证医学杂志, 2014, 14(2): 241-248.
23. Lin L, Zhang J, Hodges JS, et al. Performing arm-based network meta-analysis in R with the pcnetmeta package. J Stat Softw, 2017, 80: 5.
24. Lim D, Chen MH, Ibrahim JG, et al. metapack: an R package for bayesian meta-analysis and network meta-analysis with a unified formula interface. R J, 2022, 14(3): 142-161.
25. Röver C, Friede T. Using the bayesmeta R package for Bayesian random-effects meta-regression. Comput Methods Programs Biomed, 2023, 229: 107303.
26. Sturtz S, Ligges U, Gelman A. R2WinBUGS: a package for running WinBUGS from R. J Stat Softw, 2005, 12(3): 1-16.
27. Plummer M, Best N, Cowles K, et al. CODA: convergence diagnosis and output analysis for MCMC. R news, 2006, 6(1): 7-11.
28. Stan Development Team. RStan: the R interface to Stan. 2024.
29. Sturtz S, Ligges U, Gelman A. R2OpenBUGS: a package for running OpenBUGS from R. R Package Version, 2019, 3(2): 1.
30. Viechtbauer W. Conducting meta-analyses in R with the metafor package. J Stat Softw, 2010, 36(3): 1-48.
31. Phillippo DM. Multinma: an R package for Bayesian network meta-analysis of individual and aggregate data. Evidence Synthesis and Meta-Analysis in R Conference, 2021.
32. Béliveau A, Boyne DJ, Slater J, et al. BUGSnet: an R package to facilitate the conduct and reporting of Bayesian network meta-analyses. BMC Med Res Methodol, 2019, 19(1): 196.
33. Gonzalez-Diaz JM, Radua J, Sanchez-Dalmau B, et al. Mapping retinal abnormalities in psychosis: meta-analytical evidence for focal peripapillary and macular reductions. Schizophr Bull, 2022, 48(6): 1194-1205.
34. 张超, 陶华, 李胜, 等. 应用Stata软件mvmeta程序包实现网状Meta分析. 中国循证医学杂志, 2014, 14(9): 1150-1159.
35. Shim S, Yoon BH, Shin IS, et al. Network meta-analysis: application and practice using Stata. Epidemiol Health, 2017, 39: e2017047.
36. Baek E, Ferron JM. Bayesian analysis for multiple-baseline studies where the variance differs across cases in OpenBUGS. Dev Neurorehabil, 2021, 24(2): 130-143.
37. Greco T, Landoni G, Biondi-Zoccai G, et al. A Bayesian network meta-analysis for binary outcome: how to do it. Stat Methods Med Res, 2016, 25(5): 1757-1773.
38. Brown S, Hutton B, Clifford T, et al. A Microsoft-Excel-based tool for running and critically appraising network meta-analyses--an overview and application of NetMetaXL. Syst Rev, 2014, 3: 110.
39. Piepho HP, Madden LV. How to observe the principle of concurrent control in an arm-based meta-analysis using SAS procedures GLIMMIX and BGLIMM. Res Synth Methods, 2022, 13(6): 821-828.
40. Rott KW, Lin L, Hodges JS, et al. Bayesian meta-analysis using SAS PROC BGLIMM. Res Synth Methods, 2021, 12(6): 692-700.
41. Van Valkenhoef G, Tervonen T, Zwinkels T, et al. ADDIS: a decision support system for evidence-based medicine. Dec Sup Sys, 2013, 55(2): 459-475.
42. Depaoli S, Clifton JP, Cobb PR. Just another Gibbs sampler (JAGS) flexible software for MCMC implementation. J Educ Behav Stat, 2016, 41(6): 628-649.
43. Metelli S, Chaimani A. NMAstudio: a fully interactive web-application for producing and visualising network meta-analyses. SRSM Annual Meeting, 2021.
44. Owen RK, Bradbury N, Xin Y, et al. MetaInsight: an interactive web-based tool for analyzing, interrogating, and visualizing network meta-analyses using R-shiny and netmeta. Res Synth Methods, 2019, 10(4): 569-581.
45. 曾宪涛, 张超, 邝心颖, 等. 基于使用的网状Meta分析软件的比较研究与选择. 中国循证医学杂志, 2014, 14(10): 1270-1275.
46. 张超, 耿培亮, 郭毅, 等. 应用R语言netmeta程序包实现网状Meta分析. 中国循证医学杂志, 2014, 14(5): 625-630.
47. Wiksten A, Hawkins N, Piepho HP, et al. Nonproportional hazards in network meta-analysis: efficient strategies for model building and analysis. Value Health, 2020, 23(7): 918-927.
48. Madden LV, Piepho HP, Paul PA. Statistical models and methods for network meta-analysis. Phytopathology, 2016, 106(8): 792-806.
49. Watt J, Hofmeister M, Del Giovane C, et al. Implementing hierarchical network meta-analysis incorporating exchangeable dose effects compared to standard hierarchical network meta-analysis. BMJ Evid Based Med, 2023, 28(5): 332-336.
50. Kessels A, ter Riet G, Puhan MA, et al. A simple regression model for network meta-analysis. OA Epidemiol, 2013, 1(1): 7.
51. Riley RD, Jackson D, Salanti G, et al. Multivariate and network meta-analysis of multiple outcomes and multiple treatments: rationale, concepts, and examples. BMJ, 2017, 358: j3932.
52. Cooper NJ, Sutton AJ, Morris D, et al. Addressing between-study heterogeneity and inconsistency in mixed treatment comparisons: application to stroke prevention treatments in individuals with non-rheumatic atrial fibrillation. Stat Med, 2009, 28(14): 1861-1881.
53. Dias S, Welton NJ, Sutton AJ, et al. Evidence synthesis for decision making 4: inconsistency in networks of evidence based on randomized controlled trials. Med Decis Making, 2013, 33(5): 641-656.
54. Veroniki AA, Mavridis D, Higgins JP, et al. Characteristics of a loop of evidence that affect detection and estimation of inconsistency: a simulation study. BMC Med Res Methodol, 2014, 14: 106.
55. White IR, Barrett JK, Jackson D, et al. Consistency and inconsistency in network meta-analysis: model estimation using multivariate meta-regression. Res Synth Methods, 2012, 3(2): 111-125.

Chinese Journal of Evidence-Based Medicine

Latest ArticlesPrinciples of network meta-analysis and applications of mainstream software packages

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