Covariate-adjusted response-adaptive designs: principles, applications and R code implementation_Chinese Journal of Evidence-Based Medicine

Authors：

XU Yingjian ¹ , SHUAI Yuxing ¹ , ZHAI Jiaxiang ¹ , CHEN Zhuoqun ¹ , GU Jing ² , DU Liang ³ , TAN Bo ¹ , MA Qing ¹ , FENG Taichuan ¹ ,  HAN Xue ¹ ,  CHEN Xinlin ¹

1. School of Basic Medical Sciences, Guangzhou University of Chinese Medicine, Guangzhou 510006, P. R. China;
2. School of Public Health, Sun Yat-sen University, Guangzhou 510080, P. R. China;
3. West China Hospital, Sichuan University, Chengdu 610041, P. R. China;

Corresponding author：

HAN Xue, Email: hanxue@gzucm.edu.cn; CHEN Xinlin, Email: chenxlsums@126.com

Keywords：

Covariate-adjusted response-adaptive randomisation; Adaptive design; Code implementation; Urn model; Atkinson model

DOI：

10.7507/1672-2531.202503039

Video：

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Abstract Full text Figures/Tables Video References Cited by

The covariate-adjusted response-adaptive randomisation (CARA) design combines the advantages of response-adaptive randomisation and covariate-adaptive randomisation, and improves the efficiency and reliability of clinical trials by combining analytical results and covariates and dynamically adjusting the allocation of subsequent patients. This paper describes in detail several methods of CARA design and their example applications of various methods, including the dominant confidence method, the urn model, the generalized linear model, and the Atkinson model, and provides the corresponding R codes in anticipation of a wider application of the provided R codes in clinical trials.

1.	杨凯璇, 周齐, 姜英玉, 等. 适应性设计随机对照临床试验. 中国卒中杂志, 2022, 17(10): 1152-1158.
2.	Bhatt DL, Mehta C. Adaptive designs for clinical trials. N Engl J Med, 2016, 375(1): 65-74.
3.	Moher D, Hopewell S, Schulz KF, et al. CONSORT 2010 explanation and elaboration: updated guidelines for reporting parallel group randomised trials. BMJ, 2010, 340: c869.
4.	Chamberlain JM, Kapur J, Shinnar S, et al. Efficacy of levetiracetam, fosphenytoin, and valproate for established status epilepticus by age group (ESETT): a double-blind, responsive-adaptive, randomised controlled trial. Lancet, 2020, 395(10231): 1217-1224.
5.	Guglielmetti L, Khan U, Velásquez GE, et al. Oral regimens for rifampin-resistant, fluoroquinolone-susceptible tuberculosis. N Engl J Med, 2025, 392(5): 468-482.
6.	Proschan M, Evans S. Resist the temptation of response-adaptive randomization. Clin Infect Dis, 2020, 71(11): 3002-3004.
7.	Hu F, Ye X, Zhang LX. Multi-arm covariate-adaptive randomization. Sci China Math, 2023, 66(1): 163-190.
8.	Bugni FA, Canay IA, Shaikh AM. Inference under covariate-adaptive randomization. J Am Stat Assoc, 2018, 113(524): 1784-1796.
9.	Jin H, Kim MO, Scheffler A, et al. Bayesian adaptive design for covariate-adaptive historical control information borrowing. Stat Med, 2023, 42(29): 5338-5352.
10.	钱真真, 周莎, 于亚南, 等. 适应性随机化及其在临床试验中的应用操作要点. 中国循证医学杂志, 2022, 22(8): 971-977.
11.	衡明莉, 王北琪, 王骏. 对美国FDA适应性设计指导原则的介绍. 中国临床药理学杂志, 2019, 35(12): 1316-1320.
12.	Baldi Antognini A, Cecconi S, Frieri R, et al. Biomarker-driven optimal designs for patient enrollment restriction. Stat Methods Med Res, 2025, 2025: 9622802251327690.
13.	Mei H, Xie J, Qin Y, et al. Network and covariate adjusted response-adaptive design for binary response. Stat Med, 2023, 42(29): 5369-5388.
14.	王雨宁, 徐畅, 邹康, 等. 临床试验中适应性随机化的应用. 中国循证医学杂志, 2020, 20(5): 616-620.
15.	Xiong W, Roy J, Liu H, et al. Leveraging machine learning: covariate-adjusted Bayesian adaptive randomization and subgroup discovery in multi-arm survival trials. Contemp Clin Trials, 2024, 142: 107547.
16.	Villar SS, Rosenberger WF. Covariate-adjusted response-adaptive randomization for multi-arm clinical trials using a modified forward looking Gittins index rule. Biometrics, 2018, 74(1): 49-57.
17.	Qiao W, Ning J, Huang X. A clinical trial design with covariate-adjusted response-adaptive randomization using superiority confidence of treatments. Stat Biopharm Res, 2019, 11(4): 336-347.
18.	Bandyopadhyay U, Bhattacharya R. An urn based covariate adjusted response adaptive allocation design. Stat Methods Med Res, 2012, 21(2): 135-148.
19.	Selvaratnam S, Yi Y, Oyet A. Maximum likelihood estimation of generalized linear models for adaptive designs: Applications and asymptotics. Biom J, 2019, 61(3): 630-651.
20.	Hu J, Zhu H, Hu F. A Unified Family of Covariate-Adjusted Response-Adaptive Designs Based on Efficiency and Ethics. J Am Stat Assoc, 2015, 110(509): 357-367.
21.	Barbáchano Y, Coad DS. Inference following designs which adjust for imbalances in prognostic factors. Clin Trials, 2013, 10(4): 540-551.
22.	韦红霞, 康佩, 刘颖欣, 等. 基于Adaptive Elastic Net与加速失效时间模型的亚组识别方法的应用拓展. 南方医科大学学报, 2021, 41(3): 391-398.
23.	Guo Z, Liu Y, Xia L. Covariate selection for optimizing balance with an innovative adaptive randomization approach. Stat Methods Med Res, 2025, 2025: 9622802241313283.
24.	高敬雅, 马维, 张绍洪, 等. 自适应临床试验设计的近期进展及展望. 数理统计与管理, 2020, 39(4): 595-610.
25.	金秋百, 张颖, 姜枫, 等. 反应适应性随机的实施要点及其在中医药临床研究中的应用前景. 中医杂志, 2021, 62(17): 1478-1483.
26.	Bandyopadhyay U, Bhattacharya R. A covariate-adjusted response-adaptive allocation in clinical trials for a general class of responses. Stat Med, 2013, 32(29): 5053-5061.

1. 杨凯璇, 周齐, 姜英玉, 等. 适应性设计随机对照临床试验. 中国卒中杂志, 2022, 17(10): 1152-1158.
2. Bhatt DL, Mehta C. Adaptive designs for clinical trials. N Engl J Med, 2016, 375(1): 65-74.
3. Moher D, Hopewell S, Schulz KF, et al. CONSORT 2010 explanation and elaboration: updated guidelines for reporting parallel group randomised trials. BMJ, 2010, 340: c869.
4. Chamberlain JM, Kapur J, Shinnar S, et al. Efficacy of levetiracetam, fosphenytoin, and valproate for established status epilepticus by age group (ESETT): a double-blind, responsive-adaptive, randomised controlled trial. Lancet, 2020, 395(10231): 1217-1224.
5. Guglielmetti L, Khan U, Velásquez GE, et al. Oral regimens for rifampin-resistant, fluoroquinolone-susceptible tuberculosis. N Engl J Med, 2025, 392(5): 468-482.
6. Proschan M, Evans S. Resist the temptation of response-adaptive randomization. Clin Infect Dis, 2020, 71(11): 3002-3004.
7. Hu F, Ye X, Zhang LX. Multi-arm covariate-adaptive randomization. Sci China Math, 2023, 66(1): 163-190.
8. Bugni FA, Canay IA, Shaikh AM. Inference under covariate-adaptive randomization. J Am Stat Assoc, 2018, 113(524): 1784-1796.
9. Jin H, Kim MO, Scheffler A, et al. Bayesian adaptive design for covariate-adaptive historical control information borrowing. Stat Med, 2023, 42(29): 5338-5352.
10. 钱真真, 周莎, 于亚南, 等. 适应性随机化及其在临床试验中的应用操作要点. 中国循证医学杂志, 2022, 22(8): 971-977.
11. 衡明莉, 王北琪, 王骏. 对美国FDA适应性设计指导原则的介绍. 中国临床药理学杂志, 2019, 35(12): 1316-1320.
12. Baldi Antognini A, Cecconi S, Frieri R, et al. Biomarker-driven optimal designs for patient enrollment restriction. Stat Methods Med Res, 2025, 2025: 9622802251327690.
13. Mei H, Xie J, Qin Y, et al. Network and covariate adjusted response-adaptive design for binary response. Stat Med, 2023, 42(29): 5369-5388.
14. 王雨宁, 徐畅, 邹康, 等. 临床试验中适应性随机化的应用. 中国循证医学杂志, 2020, 20(5): 616-620.
15. Xiong W, Roy J, Liu H, et al. Leveraging machine learning: covariate-adjusted Bayesian adaptive randomization and subgroup discovery in multi-arm survival trials. Contemp Clin Trials, 2024, 142: 107547.
16. Villar SS, Rosenberger WF. Covariate-adjusted response-adaptive randomization for multi-arm clinical trials using a modified forward looking Gittins index rule. Biometrics, 2018, 74(1): 49-57.
17. Qiao W, Ning J, Huang X. A clinical trial design with covariate-adjusted response-adaptive randomization using superiority confidence of treatments. Stat Biopharm Res, 2019, 11(4): 336-347.
18. Bandyopadhyay U, Bhattacharya R. An urn based covariate adjusted response adaptive allocation design. Stat Methods Med Res, 2012, 21(2): 135-148.
19. Selvaratnam S, Yi Y, Oyet A. Maximum likelihood estimation of generalized linear models for adaptive designs: Applications and asymptotics. Biom J, 2019, 61(3): 630-651.
20. Hu J, Zhu H, Hu F. A Unified Family of Covariate-Adjusted Response-Adaptive Designs Based on Efficiency and Ethics. J Am Stat Assoc, 2015, 110(509): 357-367.
21. Barbáchano Y, Coad DS. Inference following designs which adjust for imbalances in prognostic factors. Clin Trials, 2013, 10(4): 540-551.
22. 韦红霞, 康佩, 刘颖欣, 等. 基于Adaptive Elastic Net与加速失效时间模型的亚组识别方法的应用拓展. 南方医科大学学报, 2021, 41(3): 391-398.
23. Guo Z, Liu Y, Xia L. Covariate selection for optimizing balance with an innovative adaptive randomization approach. Stat Methods Med Res, 2025, 2025: 9622802241313283.
24. 高敬雅, 马维, 张绍洪, 等. 自适应临床试验设计的近期进展及展望. 数理统计与管理, 2020, 39(4): 595-610.
25. 金秋百, 张颖, 姜枫, 等. 反应适应性随机的实施要点及其在中医药临床研究中的应用前景. 中医杂志, 2021, 62(17): 1478-1483.
26. Bandyopadhyay U, Bhattacharya R. A covariate-adjusted response-adaptive allocation in clinical trials for a general class of responses. Stat Med, 2013, 32(29): 5053-5061.

Chinese Journal of Evidence-Based Medicine

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