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.

Citation： XU Yingjian, SHUAI Yuxing, ZHAI Jiaxiang, CHEN Zhuoqun, GU Jing, DU Liang, TAN Bo, MA Qing, FENG Taichuan, HAN Xue, CHEN Xinlin. Covariate-adjusted response-adaptive designs: principles, applications and R code implementation. Chinese Journal of Evidence-Based Medicine, 2025, 25(9): 1078-1082. doi: 10.7507/1672-2531.202503039 Copy

1.	楊凱璇, 周齊, 姜英玉, 等. 適應性設計隨機對照臨床試驗. 中國卒中雜志, 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.	錢真真, 周莎, 于亞南, 等. 適應性隨機化及其在臨床試驗中的應用操作要點. 中國循證醫學雜志, 2022, 22(8): 971-977.
11.	衡明莉, 王北琪, 王駿. 對美國FDA適應性設計指導原則的介紹. 中國臨床藥理學雜志, 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.	王雨寧, 徐暢, 鄒康, 等. 臨床試驗中適應性隨機化的應用. 中國循證醫學雜志, 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.	韋紅霞, 康佩, 劉穎欣, 等. 基于Adaptive Elastic Net與加速失效時間模型的亞組識別方法的應用拓展. 南方醫科大學學報, 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, 馬維, 張紹洪, 等. 自適應臨床試驗設計的近期進展及展望. 數理統計與管理, 2020, 39(4): 595-610.
25.	金秋百, 張穎, 姜楓, 等. 反應適應性隨機的實施要點及其在中醫藥臨床研究中的應用前景. 中醫雜志, 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. 楊凱璇, 周齊, 姜英玉, 等. 適應性設計隨機對照臨床試驗. 中國卒中雜志, 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. 錢真真, 周莎, 于亞南, 等. 適應性隨機化及其在臨床試驗中的應用操作要點. 中國循證醫學雜志, 2022, 22(8): 971-977.
11. 衡明莉, 王北琪, 王駿. 對美國FDA適應性設計指導原則的介紹. 中國臨床藥理學雜志, 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. 王雨寧, 徐暢, 鄒康, 等. 臨床試驗中適應性隨機化的應用. 中國循證醫學雜志, 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. 韋紅霞, 康佩, 劉穎欣, 等. 基于Adaptive Elastic Net與加速失效時間模型的亞組識別方法的應用拓展. 南方醫科大學學報, 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, 馬維, 張紹洪, 等. 自適應臨床試驗設計的近期進展及展望. 數理統計與管理, 2020, 39(4): 595-610.
25. 金秋百, 張穎, 姜楓, 等. 反應適應性隨機的實施要點及其在中醫藥臨床研究中的應用前景. 中醫雜志, 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.

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Covariate-adjusted response-adaptive designs: principles, applications and R code implementation

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