Bayesian meta-analysis methods for integrating randomised and non-randomised intervention studies and R language implementation_Chinese Journal of Evidence-Based Medicine

Authors：

JIAYIDAER Huan ^1,2 ,  YAO Minghong ² , MEI Fan ² , MA Yu ² , LI Ling ² ,  SUN Xin ^1,2

1. Department of Epidemiology and Biostatistics, West China School of Public Health and West China Fourth Hospital, Sichuan University, Chengdu 610041, P. R. China;
2. Chinese Evidence-based Medicine Center, West China Hospital, Sichuan University, Chengdu 610041, P. R. China;

Corresponding author：

YAO Minghong, Email: ymhldjxa@sina.com; SUN Xin, Email: sunxin@wchscu.cn

Keywords：

Randomized controlled trial; Non-randomized study of interventions (NRSI); Bayesian meta-analysis; R language

DOI：

10.7507/1672-2531.202506107

Video：

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Objective To introduce a Bayesian meta-analysis method for quantitatively integrating evidence from both randomized controlled trials (RCTs) and non-randomized studies of interventions (NRSIs), using concrete examples and R code, thereby supporting the combined utilization of both study types in empirical research. Methods Using a meta-analysis on the association between low-dose methotrexate exposure and melanoma as an example, we employed the jarbes package in R to conduct both a traditional Bayesian meta-analysis and a Bayesian nonparametric bias-correction meta-analysis model for quantitative integration. The differences between the two pooled results were then compared. Results The traditional Bayesian meta-analysis indicated a posterior probability of 99% that low-dose methotrexate exposure increases melanoma risk. The Bayesian nonparametric bias-correction meta-analysis model showed a posterior probability of 92% that low-dose methotrexate exposure increases melanoma risk. Conclusion Compared to the traditional Bayesian meta-analysis model, the nonparametric bias-correction meta-analysis model is more suitable for quantitatively integrating evidence from RCTs and NRSIs, demonstrating potential for broader application. However, the comparability between the two evidence bodies should be carefully assessed prior to quantitative integration.

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2.	孙鑫, 谭婧, 唐立, 等. 重新认识真实世界研究. 中国循证医学杂志, 2017, 17(2): 126-130.
3.	Yan MK, Wolfe R, Orchard SG, et al. Effect of methotrexate on melanoma risk in older adults: secondary analysis of a randomised controlled trial. Australas J Dermatol, 2022, 63(1): 114-115.
4.	Cheurfa C, Tsokani S, Kontouli KM, et al. Empirical evaluation of the methods used in systematic reviews including observational studies and randomized trials. J Clin Epidemiol, 2023, 158: 44-52.
5.	Bun RS, Scheer J, Guillo S, et al. Meta-analyses frequently pooled different study types together: a meta-epidemiological study. J Clin Epidemiol, 2020, 118: 18-28.
6.	Saldanha IJ, Adam GP, Bañez LL, et al. Inclusion of nonrandomized studies of interventions in systematic reviews of interventions: updated guidance from the agency for health care research and quality effective health care program. J Clin Epidemiol, 2022, 152: 300-306.
7.	Zhou Y, Yao M, Mei F, et al. Integrating randomized controlled trials and non-randomized studies of interventions to assess the effect of rare events: a Bayesian re-analysis of two meta-analyses. BMC Med Res Methodol, 2024, 24(1): 219.
8.	Yan MK, Wang C, Wolfe R, et al. Association between low-dose methotrexate exposure and melanoma: a systematic review and meta-analysis. JAMA Dermatol, 2022, 158(10): 1157-1166.
9.	Breedveld FC, Weisman MH, Kavanaugh AF, et al. The PREMIER study: a multicenter, randomized, double-blind clinical trial of combination therapy with adalimumab plus methotrexate versus methotrexate alone or adalimumab alone in patients with early, aggressive rheumatoid arthritis who had not had previous methotrexate treatment. Arthritis Rheum, 2006, 54(1): 26-37.
10.	Klareskog L, van der Heijde D, de Jager JP, et al. Therapeutic effect of the combination of etanercept and methotrexate compared with each treatment alone in patients with rheumatoid arthritis: double-blind randomised controlled trial. Lancet, 2004, 363(9410): 675-681.
11.	Puéchal X, Pagnoux C, Perrodeau É, et al. Long-term outcomes among participants in the wegent trial of remission-maintenance therapy for granulomatosis with polyangiitis (wegener's) or microscopic polyangiitis. Arthritis Rheumatol, 2016, 68(3): 690-701.
12.	Vanni KMM, Berliner N, Paynter NP, et al. Adverse effects of low-dose methotrexate in a randomized double-blind placebo-controlled trial: adjudicated hematologic and skin cancer outcomes in the cardiovascular inflammation reduction trial. ACR Open Rheumatol, 2020, 2(12): 697-704.
13.	van Vollenhoven R, Takeuchi T, Pangan AL, et al. Efficacy and safety of upadacitinib monotherapy in methotrexate-naive patients with moderately-to-severely active rheumatoid arthritis (SELECT-EARLY): a multicenter, multi-country, randomized, double-blind, active comparator-controlled trial. Arthritis Rheumatol, 2020, 72(10): 1607-1620.
14.	Westhovens R, Rigby WFC, van der Heijde D, et al. Filgotinib in combination with methotrexate or as monotherapy versus methotrexate monotherapy in patients with active rheumatoid arthritis and limited or no prior exposure to methotrexate: the phase 3, randomised controlled FINCH 3 trial. Ann Rheum Dis, 2021, 80(6): 727-738.
15.	Berge LAM, Andreassen BK, Stenehjem JS, et al. Use of immunomodulating drugs and risk of cutaneous melanoma: a nationwide nested case-control study. Clin Epidemiol, 2020, 12: 1389-1401.
16.	Polesie S, Gillstedt M, Paoli J, et al. Methotrexate treatment for patients with psoriasis and risk of cutaneous melanoma: a nested case-control study. Br J Dermatol, 2020, 183(4): 684-691.
17.	Chaparro M, Ramas M, Benítez JM, et al. Extracolonic cancer in inflammatory bowel disease: data from the GETECCU eneida registry. Am J Gastroenterol, 2017, 112(7): 1135-1143.
18.	Polesie S, Gillstedt M, Sönnergren HH, et al. Methotrexate treatment and risk for cutaneous malignant melanoma: a retrospective comparative registry-based cohort study. Br J Dermatol, 2017, 176(6): 1492-1499.
19.	Polesie S, Gillstedt M, Paoli J, et al. Methotrexate treatment in patients with a history of cutaneous melanoma and the risk of a consecutive primary melanoma: a national retrospective registry-based cohort study. J Am Acad Dermatol, 2017, 77(1): 161-163.
20.	Verde PE, Ohmann C. Combining randomized and non-randomized evidence in clinical research: a review of methods and applications. Res Synth Methods, 2015, 6(1): 45-62.
21.	Yao M, Wang Y, Ren Y, et al. Comparison of statistical methods for integrating real-world evidence in a rare events meta-analysis of randomized controlled trials. Res Synth Methods, 2023, 14(5): 689-706.
22.	Verde PE, Rosner GL. A bias-corrected Bayesian nonparametric model for combining studies with varying quality in meta-analysis. Biom J, 2025, 67(1): e70034.
23.	Sarri G, Patorno E, Yuan H, et al. Framework for the synthesis of non-randomised studies and randomised controlled trials: a guidance on conducting a systematic review and meta-analysis for healthcare decision making. BMJ Evid Based Med, 2022, 27(2): 109-119.
24.	赖鸿皓, 田晨, 朱鸿飞, 等. 如何整合随机与非随机干预研究. 中国循证医学杂志, 2022, 22(7): 836-841.
25.	赖鸿皓, 王浙, 李滢, 等. 中医药多元证据整合方法学MERGE框架. 协和医学杂志, 2024, 15(1): 172-182.
26.	Yao M, Mei F, Ma Y, et al. Including non-randomized studies of interventions in meta-analyses of randomized controlled trials changed the estimates in more than a third of the studies: evidence from an empirical analysis. J Clin Epidemiol, 2025, 183: 111815.
27.	Turner RM, Spiegelhalter DJ, Smith GC, et al. Bias modelling in evidence synthesis. J R Stat Soc Ser A Stat Soc, 2009, 172(1): 21-47.
28.	Efthimiou O, Mavridis D, Cipriani A, et al. An approach for modelling multiple correlated outcomes in a network of interventions using odds ratios. Stat Med, 2014, 33(13): 2275-2287.
29.	Yao M, Mei F, Zou K, et al. A Bayesian bias-adjusted random-effects model for synthesizing evidence from randomized controlled trials and nonrandomized studies of interventions. J Evid Based Med, 2024, 17(3): 550-558.
30.	Cuello CA, Morgan RL, Brozek J, et al. Case studies to explore the optimal use of randomized and nonrandomized studies in evidence syntheses that use GRADE. J Clin Epidemiol, 2022, 152: 56-69.
31.	Stadelmaier J, Beyerbach J, Roux I, et al. Evaluating agreement between evidence from randomised controlled trials and cohort studies in nutrition: a meta-research replication study. Eur J Epidemiol, 2024, 39(4): 363-378.

1. Cuello-Garcia CA, Santesso N, Morgan RL, et al. GRADE guidance 24 optimizing the integration of randomized and non-randomized studies of interventions in evidence syntheses and health guidelines. J Clin Epidemiol, 2022, 200-208.
2. 孙鑫, 谭婧, 唐立, 等. 重新认识真实世界研究. 中国循证医学杂志, 2017, 17(2): 126-130.
3. Yan MK, Wolfe R, Orchard SG, et al. Effect of methotrexate on melanoma risk in older adults: secondary analysis of a randomised controlled trial. Australas J Dermatol, 2022, 63(1): 114-115.
4. Cheurfa C, Tsokani S, Kontouli KM, et al. Empirical evaluation of the methods used in systematic reviews including observational studies and randomized trials. J Clin Epidemiol, 2023, 158: 44-52.
5. Bun RS, Scheer J, Guillo S, et al. Meta-analyses frequently pooled different study types together: a meta-epidemiological study. J Clin Epidemiol, 2020, 118: 18-28.
6. Saldanha IJ, Adam GP, Bañez LL, et al. Inclusion of nonrandomized studies of interventions in systematic reviews of interventions: updated guidance from the agency for health care research and quality effective health care program. J Clin Epidemiol, 2022, 152: 300-306.
7. Zhou Y, Yao M, Mei F, et al. Integrating randomized controlled trials and non-randomized studies of interventions to assess the effect of rare events: a Bayesian re-analysis of two meta-analyses. BMC Med Res Methodol, 2024, 24(1): 219.
8. Yan MK, Wang C, Wolfe R, et al. Association between low-dose methotrexate exposure and melanoma: a systematic review and meta-analysis. JAMA Dermatol, 2022, 158(10): 1157-1166.
9. Breedveld FC, Weisman MH, Kavanaugh AF, et al. The PREMIER study: a multicenter, randomized, double-blind clinical trial of combination therapy with adalimumab plus methotrexate versus methotrexate alone or adalimumab alone in patients with early, aggressive rheumatoid arthritis who had not had previous methotrexate treatment. Arthritis Rheum, 2006, 54(1): 26-37.
10. Klareskog L, van der Heijde D, de Jager JP, et al. Therapeutic effect of the combination of etanercept and methotrexate compared with each treatment alone in patients with rheumatoid arthritis: double-blind randomised controlled trial. Lancet, 2004, 363(9410): 675-681.
11. Puéchal X, Pagnoux C, Perrodeau É, et al. Long-term outcomes among participants in the wegent trial of remission-maintenance therapy for granulomatosis with polyangiitis (wegener's) or microscopic polyangiitis. Arthritis Rheumatol, 2016, 68(3): 690-701.
12. Vanni KMM, Berliner N, Paynter NP, et al. Adverse effects of low-dose methotrexate in a randomized double-blind placebo-controlled trial: adjudicated hematologic and skin cancer outcomes in the cardiovascular inflammation reduction trial. ACR Open Rheumatol, 2020, 2(12): 697-704.
13. van Vollenhoven R, Takeuchi T, Pangan AL, et al. Efficacy and safety of upadacitinib monotherapy in methotrexate-naive patients with moderately-to-severely active rheumatoid arthritis (SELECT-EARLY): a multicenter, multi-country, randomized, double-blind, active comparator-controlled trial. Arthritis Rheumatol, 2020, 72(10): 1607-1620.
14. Westhovens R, Rigby WFC, van der Heijde D, et al. Filgotinib in combination with methotrexate or as monotherapy versus methotrexate monotherapy in patients with active rheumatoid arthritis and limited or no prior exposure to methotrexate: the phase 3, randomised controlled FINCH 3 trial. Ann Rheum Dis, 2021, 80(6): 727-738.
15. Berge LAM, Andreassen BK, Stenehjem JS, et al. Use of immunomodulating drugs and risk of cutaneous melanoma: a nationwide nested case-control study. Clin Epidemiol, 2020, 12: 1389-1401.
16. Polesie S, Gillstedt M, Paoli J, et al. Methotrexate treatment for patients with psoriasis and risk of cutaneous melanoma: a nested case-control study. Br J Dermatol, 2020, 183(4): 684-691.
17. Chaparro M, Ramas M, Benítez JM, et al. Extracolonic cancer in inflammatory bowel disease: data from the GETECCU eneida registry. Am J Gastroenterol, 2017, 112(7): 1135-1143.
18. Polesie S, Gillstedt M, Sönnergren HH, et al. Methotrexate treatment and risk for cutaneous malignant melanoma: a retrospective comparative registry-based cohort study. Br J Dermatol, 2017, 176(6): 1492-1499.
19. Polesie S, Gillstedt M, Paoli J, et al. Methotrexate treatment in patients with a history of cutaneous melanoma and the risk of a consecutive primary melanoma: a national retrospective registry-based cohort study. J Am Acad Dermatol, 2017, 77(1): 161-163.
20. Verde PE, Ohmann C. Combining randomized and non-randomized evidence in clinical research: a review of methods and applications. Res Synth Methods, 2015, 6(1): 45-62.
21. Yao M, Wang Y, Ren Y, et al. Comparison of statistical methods for integrating real-world evidence in a rare events meta-analysis of randomized controlled trials. Res Synth Methods, 2023, 14(5): 689-706.
22. Verde PE, Rosner GL. A bias-corrected Bayesian nonparametric model for combining studies with varying quality in meta-analysis. Biom J, 2025, 67(1): e70034.
23. Sarri G, Patorno E, Yuan H, et al. Framework for the synthesis of non-randomised studies and randomised controlled trials: a guidance on conducting a systematic review and meta-analysis for healthcare decision making. BMJ Evid Based Med, 2022, 27(2): 109-119.
24. 赖鸿皓, 田晨, 朱鸿飞, 等. 如何整合随机与非随机干预研究. 中国循证医学杂志, 2022, 22(7): 836-841.
25. 赖鸿皓, 王浙, 李滢, 等. 中医药多元证据整合方法学MERGE框架. 协和医学杂志, 2024, 15(1): 172-182.
26. Yao M, Mei F, Ma Y, et al. Including non-randomized studies of interventions in meta-analyses of randomized controlled trials changed the estimates in more than a third of the studies: evidence from an empirical analysis. J Clin Epidemiol, 2025, 183: 111815.
27. Turner RM, Spiegelhalter DJ, Smith GC, et al. Bias modelling in evidence synthesis. J R Stat Soc Ser A Stat Soc, 2009, 172(1): 21-47.
28. Efthimiou O, Mavridis D, Cipriani A, et al. An approach for modelling multiple correlated outcomes in a network of interventions using odds ratios. Stat Med, 2014, 33(13): 2275-2287.
29. Yao M, Mei F, Zou K, et al. A Bayesian bias-adjusted random-effects model for synthesizing evidence from randomized controlled trials and nonrandomized studies of interventions. J Evid Based Med, 2024, 17(3): 550-558.
30. Cuello CA, Morgan RL, Brozek J, et al. Case studies to explore the optimal use of randomized and nonrandomized studies in evidence syntheses that use GRADE. J Clin Epidemiol, 2022, 152: 56-69.
31. Stadelmaier J, Beyerbach J, Roux I, et al. Evaluating agreement between evidence from randomised controlled trials and cohort studies in nutrition: a meta-research replication study. Eur J Epidemiol, 2024, 39(4): 363-378.

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Latest ArticlesBayesian meta-analysis methods for integrating randomised and non-randomised intervention studies and R language implementation

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