Specification of prior distributions in Bayesian methods for clinical research_Chinese Journal of Evidence-Based Medicine

Authors：

LI Wenwen ¹ , MU Rongji ² , LIN Cong ³ , SONG Chengyuan ⁴ , SHAO Peng ⁵ , DAI Luyan ⁶ , YAN Fangrong ⁷ ,  HUANG Lihong ¹ , ZHAO Yang ⁸ , CHEN Feng ⁸

1. Department of Biostatistics, Zhongshan Hospital, Fudan University, Shanghai 200032, P. R. China;
2. Clinical Research Institute, Shanghai Jiao Tong University School of Medicine, Shanghai 200025, P. R. China;
3. Novartis Institutes for Biomedical Research Co., Shanghai 201203, P. R. China;
4. Boehringer Ingelheim (China) Investment Co., Ltd., Shanghai 200040, P. R. China;
5. Clinical Research and Department Center, Qilu Pharmaceutical Co., Ltd., Jinan 250100, P. R. China;
6. Graceful Plume Consulting, Shanghai 202150, P. R. China;
7. Research Center of Biostatistics and Computational Pharmacy, China Pharmaceutical University, Nanjing 210009, P. R. China;
8. Department of Biostatistics, School of Public Health, Nanjing Medical University, Nanjing 211166, P. R. China;

Corresponding?author：

HUANG Lihong, Email: huang.lihong@zs-hospital.sh.cn

Keywords：

Bayesian; Prior distribution; Clinical research; Standardized reporting

DOI：

10.7507/1672-2531.202512205

Video：

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Bayesian methods have inherent advantages in flexibility and uncertainty quantification, which is increasingly used in clinical research. Proper specification of prior distributions is essential to their valid application. This paper analyzes the properties and practical contexts of various priors, summarizes common selection issues, proposes a standardized specification process, and illustrates its application through simulations and case studies. To enhance research transparency and rigor, we propose standardized reporting of prior distributions.

Citation： LI Wenwen, MU Rongji, LIN Cong, SONG Chengyuan, SHAO Peng, DAI Luyan, YAN Fangrong, HUANG Lihong, ZHAO Yang, CHEN Feng. Specification of prior distributions in Bayesian methods for clinical research. Chinese Journal of Evidence-Based Medicine, 2026, 26(8): 958-965. doi: 10.7507/1672-2531.202512205 Copy

1.	Goligher EC, Heath A, Harhay MO. Bayesian statistics for clinical research[J]. Lancet, 2024, 404(10457): 1067-1076.
2.	言方榮, 王駿, 袁鷹. 腫瘤臨床試驗貝葉斯設計方法[M]. 北京: 人民衛生出版社, 2021.
3.	國家藥品監督管理局藥品審評中心. 藥物臨床試驗中應用貝葉斯外部信息借用方法的指導原則(試行)[Z]. 2026.
4.	U. S. Food and Drug Administration. Use of Bayesian methodology in clinical trials of drug and biological products: draft guidance for industry[Z]. 2026.
5.	茆詩松, 湯銀才. 貝葉斯統計(第二版)[M]. 北京: 中國統計出版社, 2012.
6.	Press SJ. Subjective and objective Bayesian statistics: principles, models, and applications[Z]. John Wiley & Sons, 2009.
7.	Jeffreys H. An invariant form for the prior probability in estimation problems[J]. Proc R Soc Lond A Math Phys Sci, 1946, 186(1007): 453-461.
8.	Berger JO, Bernardo JM. On the development of the reference prior method[J]. Bayesian Anal, 1992, 4(4): 35-60.
9.	Neuenschwander B, Capkun-Niggli G, Branson M, et al. Summarizing historical information on controls in clinical trials[J]. Clin Trials, 2010, 7(1): 5-18.
10.	Muehlemann N, Zhou T, Mukherjee R, et al. A tutorial on modern Bayesian methods in clinical trials[J]. Ther Innov Regul Sci, 2023, 57(3): 402-416.
11.	Ibrahi m JG, Chen MH, Gwon Y, et al. The power prior: theory and applications[J]. Stat Med, 2015, 34(28): 3724-3749.
12.	Schmidli H, Gsteiger S, Roychoudhury S, et al. Robust meta-analytic-predictive priors in clinical trials with historical control information[J]. Biometrics, 2014, 70(4): 1023-1032.
13.	Gelman A. Prior distributions for variance parameters in hierarchical models[J]. Bayesian Anal, 2006, 1(3): 515-534.
14.	Malec D. A closer look at combining data among a small number of binomial experiments[J]. Stat Med, 2001, 20(12): 1811-1824.
15.	Morita S, Thall PF, Müller P. Determining the effective sample size of a parametric prior[J]. Biometrics, 2008, 64(2): 595-602.
16.	Sarma A, Kay M. Prior setting in practice: strategies and rationales used in choosing prior distributions for Bayesian analysis[C]// In Conference on Human Factors in Computing Systems, 2020.
17.	Lee SY. Using Bayesian statistics in confirmatory clinical trials in the regulatory setting: a tutorial review[J]. BMC Med Res Methodol, 2024, 24(1): 110.
18.	Jiang L, Nie L, Yuan Y. Elastic priors to dynamically borrow information from historical data in clinical trials[J]. Biometrics, 2023, 79(1): 49-60.
19.	Gosho M, Ishii R, Nagashima K, et al. Determining the prior mean in Bayesian logistic regression with sparse data: a nonarbitrary approach[J]. J R Stat Soc Ser C Appl Stat, 2025, 74(1): 126-141.
20.	Demartino RM, Egidi L, Torelli N, et al. Eliciting prior information from clinical trials via calibrated Bayes factor[J]. Comput Stat Data An, 2025, 209: 108180.
21.	Seliem MM, Kamel AR, Taha IM, et al. A note on prior selection in Bayesian estimation[J]. Stat Optim Inf Comput, 2025, 13(2): 795-806.
22.	Wang Y, Tu W, Koh W, et al. Bayesian hierarchical models for subgroup analysis[J]. Pharm Stat, 2024, 23(6): 1065-1083.
23.	US Food and Drug Administration. Guidance for the use of Bayesian statistics in medical device clinical trials[Z]. 2010.
24.	Lee JJ, Yin G. Principles and reporting of Bayesian trials[J]. J Thorac Oncol, 2021, 16(1): 30-36.
25.	Kruschke JK. Bayesian analysis reporting guidelines[J]. Nat Hum Behav, 2021, 5(10): 1282-1291.
26.	Brunner HI, Abud-Mendoza C, Viola DO, et al. Safety and efficacy of intravenous belimumab in children with systemic lupus erythematosus: results from a randomised, placebo-controlled trial[J]. Ann Rheum Dis, 2020, 79(10): 1340-1348.
27.	Muehlemann N, Mukherjee R, Taher AT, et al. Innovative adaptive study design in transfusion-dependent beta-thalassemia: Bayesian design with concurrent randomization and borrowing from historical data[J]. Blood, 2021, 138: 4160.
28.	Polack FP, Thomas SJ, Kitchin N, et al. Safety and efficacy of the BNT162b2 mRNA COVID-19 vaccine[J]. N Engl J Med, 2020, 383(27): 2603-2615.
29.	Sharretts J, Higginbotham L, Ketterman A, et al. Drugs at FDA: FDA-approved drugs, application number: 211616Orig1s000 integrated review, executive summary, inter disciplinary assessment, appendices[Z]. 2019.
30.	Bertolet M, Brooks MM, Ragni MV. The design of a Bayesian platform trial to prevent and eradicate inhibitors in patients with hemophilia[J]. Blood Adv, 2020, 4(21): 5433-5441.
31.	Morris BH, Oh W, Tyson JE, et al. Aggressive vs conservative phototherapy for infants with extremely low birth weight[J]. N Engl J Med, 2008, 359(18): 1885-1896.
32.	Laptook AR, Shankaran S, Tyson JE, et al. Effect of therapeutic hypothermia initiated after 6 hours of age on death or disability among newborns with hypoxic-ischemic encephalopathy: a randomized clinical trial[J]. JAMA, 2017, 318(16): 1550-1560.
33.	U. S. Food and Drug Administration. Complex innovative trial design meeting program. CID pilot program trial design Case Studies[Z]. 2022.
34.	Price D, Scott J. The U. S. Food and Drug Administration's complex innovative trial design pilot meeting program: progress to date[J]. Clin Trials, 2021, 18(6): 706-710.
35.	U. S. Department of Health and Human Services. Food and Drug Administration. Non-inferiority clinical trials. Guidance for industry[Z]. 2016.
36.	U. S. Food and Drug Administration. Interacting with the FDA on complex innovative trial designs for drugs and biological products: guidance for industry[Z]. 2020.
37.	International Council for Harmonization of Technical Requirements for Pharmaceuticals for Human Use[Z]. Pediatric extrapolation E11A, 2022.

1. Goligher EC, Heath A, Harhay MO. Bayesian statistics for clinical research[J]. Lancet, 2024, 404(10457): 1067-1076.
2. 言方榮, 王駿, 袁鷹. 腫瘤臨床試驗貝葉斯設計方法[M]. 北京: 人民衛生出版社, 2021.
3. 國家藥品監督管理局藥品審評中心. 藥物臨床試驗中應用貝葉斯外部信息借用方法的指導原則(試行)[Z]. 2026.
4. U. S. Food and Drug Administration. Use of Bayesian methodology in clinical trials of drug and biological products: draft guidance for industry[Z]. 2026.
5. 茆詩松, 湯銀才. 貝葉斯統計(第二版)[M]. 北京: 中國統計出版社, 2012.
6. Press SJ. Subjective and objective Bayesian statistics: principles, models, and applications[Z]. John Wiley & Sons, 2009.
7. Jeffreys H. An invariant form for the prior probability in estimation problems[J]. Proc R Soc Lond A Math Phys Sci, 1946, 186(1007): 453-461.
8. Berger JO, Bernardo JM. On the development of the reference prior method[J]. Bayesian Anal, 1992, 4(4): 35-60.
9. Neuenschwander B, Capkun-Niggli G, Branson M, et al. Summarizing historical information on controls in clinical trials[J]. Clin Trials, 2010, 7(1): 5-18.
10. Muehlemann N, Zhou T, Mukherjee R, et al. A tutorial on modern Bayesian methods in clinical trials[J]. Ther Innov Regul Sci, 2023, 57(3): 402-416.
11. Ibrahi m JG, Chen MH, Gwon Y, et al. The power prior: theory and applications[J]. Stat Med, 2015, 34(28): 3724-3749.
12. Schmidli H, Gsteiger S, Roychoudhury S, et al. Robust meta-analytic-predictive priors in clinical trials with historical control information[J]. Biometrics, 2014, 70(4): 1023-1032.
13. Gelman A. Prior distributions for variance parameters in hierarchical models[J]. Bayesian Anal, 2006, 1(3): 515-534.
14. Malec D. A closer look at combining data among a small number of binomial experiments[J]. Stat Med, 2001, 20(12): 1811-1824.
15. Morita S, Thall PF, Müller P. Determining the effective sample size of a parametric prior[J]. Biometrics, 2008, 64(2): 595-602.
16. Sarma A, Kay M. Prior setting in practice: strategies and rationales used in choosing prior distributions for Bayesian analysis[C]// In Conference on Human Factors in Computing Systems, 2020.
17. Lee SY. Using Bayesian statistics in confirmatory clinical trials in the regulatory setting: a tutorial review[J]. BMC Med Res Methodol, 2024, 24(1): 110.
18. Jiang L, Nie L, Yuan Y. Elastic priors to dynamically borrow information from historical data in clinical trials[J]. Biometrics, 2023, 79(1): 49-60.
19. Gosho M, Ishii R, Nagashima K, et al. Determining the prior mean in Bayesian logistic regression with sparse data: a nonarbitrary approach[J]. J R Stat Soc Ser C Appl Stat, 2025, 74(1): 126-141.
20. Demartino RM, Egidi L, Torelli N, et al. Eliciting prior information from clinical trials via calibrated Bayes factor[J]. Comput Stat Data An, 2025, 209: 108180.
21. Seliem MM, Kamel AR, Taha IM, et al. A note on prior selection in Bayesian estimation[J]. Stat Optim Inf Comput, 2025, 13(2): 795-806.
22. Wang Y, Tu W, Koh W, et al. Bayesian hierarchical models for subgroup analysis[J]. Pharm Stat, 2024, 23(6): 1065-1083.
23. US Food and Drug Administration. Guidance for the use of Bayesian statistics in medical device clinical trials[Z]. 2010.
24. Lee JJ, Yin G. Principles and reporting of Bayesian trials[J]. J Thorac Oncol, 2021, 16(1): 30-36.
25. Kruschke JK. Bayesian analysis reporting guidelines[J]. Nat Hum Behav, 2021, 5(10): 1282-1291.
26. Brunner HI, Abud-Mendoza C, Viola DO, et al. Safety and efficacy of intravenous belimumab in children with systemic lupus erythematosus: results from a randomised, placebo-controlled trial[J]. Ann Rheum Dis, 2020, 79(10): 1340-1348.
27. Muehlemann N, Mukherjee R, Taher AT, et al. Innovative adaptive study design in transfusion-dependent beta-thalassemia: Bayesian design with concurrent randomization and borrowing from historical data[J]. Blood, 2021, 138: 4160.
28. Polack FP, Thomas SJ, Kitchin N, et al. Safety and efficacy of the BNT162b2 mRNA COVID-19 vaccine[J]. N Engl J Med, 2020, 383(27): 2603-2615.
29. Sharretts J, Higginbotham L, Ketterman A, et al. Drugs at FDA: FDA-approved drugs, application number: 211616Orig1s000 integrated review, executive summary, inter disciplinary assessment, appendices[Z]. 2019.
30. Bertolet M, Brooks MM, Ragni MV. The design of a Bayesian platform trial to prevent and eradicate inhibitors in patients with hemophilia[J]. Blood Adv, 2020, 4(21): 5433-5441.
31. Morris BH, Oh W, Tyson JE, et al. Aggressive vs conservative phototherapy for infants with extremely low birth weight[J]. N Engl J Med, 2008, 359(18): 1885-1896.
32. Laptook AR, Shankaran S, Tyson JE, et al. Effect of therapeutic hypothermia initiated after 6 hours of age on death or disability among newborns with hypoxic-ischemic encephalopathy: a randomized clinical trial[J]. JAMA, 2017, 318(16): 1550-1560.
33. U. S. Food and Drug Administration. Complex innovative trial design meeting program. CID pilot program trial design Case Studies[Z]. 2022.
34. Price D, Scott J. The U. S. Food and Drug Administration's complex innovative trial design pilot meeting program: progress to date[J]. Clin Trials, 2021, 18(6): 706-710.
35. U. S. Department of Health and Human Services. Food and Drug Administration. Non-inferiority clinical trials. Guidance for industry[Z]. 2016.
36. U. S. Food and Drug Administration. Interacting with the FDA on complex innovative trial designs for drugs and biological products: guidance for industry[Z]. 2020.
37. International Council for Harmonization of Technical Requirements for Pharmaceuticals for Human Use[Z]. Pediatric extrapolation E11A, 2022.

Chinese Journal of Evidence-Based Medicine

Specification of prior distributions in Bayesian methods for clinical research

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