Sample size estimation methods for continuous outcomes in two-stage asymmetric SMART designs and applications in traditional Chinese medicine_Chinese Journal of Evidence-Based Medicine

Authors：

MA Qing ¹ , FENG Taichuan ¹ , CAI Jingyi ¹ , ZHANG Yingying ¹ , ZHANG Junguo ¹ , HOU Zhengkun ² , LU Xuejing ³ ,  CHEN Xinlin ¹

1. Basic Medical College, Guangzhou University of Chinese Medicine, Guangzhou 510006, P. R. China;
2. The First Affiliated Hospital of Guangzhou University of Chinese Medicine, Guangzhou 510405, P. R. China;
3. Eye School of Chengdu University of Traditional Chinese Medicine, Chengdu 610103, P. R. China;

Corresponding?author：

CHEN Xinlin, Email: chenxlsums@126.com

Keywords：

Sequential multiple assignment randomized trial; Dynamic treatment regimens; Sample size estimation; Continuous outcome; Traditional Chinese medicine

DOI：

10.7507/1672-2531.202603180

Video：

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The sequential multiple assignment randomized trial (SMART) is an individualized medical model that adjusts intervention strategies in real time based on individual characteristics and stage-specific efficacy, applying to dynamic treatment regimens (DTRs) of "treatment based on syndrome differentiation" in traditional Chinese medicine (TCM). Focusing on two-stage asymmetric SMART designs with continuous outcomes, this paper reviews sample size estimation methods for four research objectives (comparing first-stage main effects, comparing second-stage main effects, comparing two DTRs, and selecting the optimal DTR), and details calculation formulas and parameters. Integrating the characteristics of TCM clinical research, this paper analyzes methodological considerations regarding parameter setting, dynamic decision logic, and tailoring variable selection within the context of syndrome differentiation. Finally, a TCM insomnia treatment example demonstrates the application. This study aims to provide a methodological reference for conducting SMART designs in TCM research, guiding researchers to estimate sample sizes accurately.

Citation： MA Qing, FENG Taichuan, CAI Jingyi, ZHANG Yingying, ZHANG Junguo, HOU Zhengkun, LU Xuejing, CHEN Xinlin. Sample size estimation methods for continuous outcomes in two-stage asymmetric SMART designs and applications in traditional Chinese medicine. Chinese Journal of Evidence-Based Medicine, 2026, 26(9): 1068-1073. doi: 10.7507/1672-2531.202603180 Copy

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2.	Frommeyer TC, Gilbert MM, Fursmidt RM, et al. Reinforcement learning and its clinical applications within healthcare: a systematic review of precision medicine and dynamic treatment regimes[J]. Healthcare (Basel), 2025, 13(14): 1752.
3.	Murphy SA. An experimental design for the development of adaptive treatment strategies[J]. Stat Med, 2005, 24(10): 1455-1481.
4.	Murphy SA, Lynch KG, Oslin D, et al. Developing adaptive treatment strategies in substance abuse research[J]. Drug Alcohol Depend, 2007, 88(Suppl 2): S24-S30.
5.	Kidwell KM, Hyde LW. Adaptive interventions and SMART designs: application to child behavior research in a community setting[J]. Am J Eval, 2016, 37(3): 344-363.
6.	Kidwell KM. SMART designs in cancer research: past, present, and future[J]. Clin Trials, 2014, 11(4): 445-456.
7.	Almirall D, Nahum-Shani I, Sherwood NE, et al. Introduction to SMART designs for the development of adaptive interventions: with application to weight loss research[J]. Transl Behav Med, 2014, 4(3): 260-274.
8.	周莎, 帥雨杏, 吉萌萌, 等. 基于適應性干預與順序多重分配隨機試驗設計探討中醫“辨證論治”治療策略的評價方法[J]. 中國循證醫學雜志, 2024, 24(12): 1476-1481.
9.	馬文欣, 王雪惠, 王禹毅, 等. 序列多重分配隨機試驗方法學進展及其在中醫學領域應用的思考[J]. 世界科學技術-中醫藥現代化, 2025, 27(6): 1530-1539.
10.	曹卉娟, 魯春麗, 劉建平. 序列多重分配隨機試驗設計方法及其在中醫藥領域的應用探討[J]. 中國中西醫結合雜志, 2022, 42(4): 482-486.
11.	潘知玉, 武紅莉, 張道培, 等. 序貫多重分配隨機試驗慢性病中醫藥臨床研究應用[J]. 中國中西醫結合雜志, 2025, 45(10): 1173-1180.
12.	姜燕華. 澤瀉湯辨治痰濕型良性陣發性位置性眩暈的SMART設計與治療策略研究[D]. 北京: 中國中醫科學院, 2024.
13.	卜志軍, 張雨歡, 孫源, 等. 序貫多分配隨機試驗設計樣本量估算方法及應用[J]. 現代中醫臨床, 2024, 31(4): 39-43.
14.	梁雪晴, 余世杰, 朱思宇, 等. SMART設計及其統計分析方法介紹[J]. 中國衛生統計, 2025, 42(2): 286-292.
15.	孫源, 鞠傳蘭, 鄭薇, 等. 中醫藥序列多重分配隨機試驗設計分析思路及統計方法應用[J]. 現代中醫臨床, 2024, 31(5): 86-91.
16.	Lei H, Nahum-Shani I, Lynch K, et al. A "SMART" design for building individualized treatment sequences[J]. Annu Rev Clin Psychol, 2012, 8: 21-48.
17.	Wallace MP, Moodie EM, Stephens DA. SMART thinking: a review of recent developments in sequential multiple assignment randomized trials[J]. Curr Epidemiol Rep, 2016, 3(3): 225-232.
18.	Nahum-Shani I, Qian M, Almirall D, et al. Experimental design and primary data analysis methods for comparing adaptive interventions[J]. Psychol Methods, 2012, 17(4): 457-477.
19.	Seewald NJ, Kidwell KM, Nahum-Shani I, et al. Sample size considerations for comparing dynamic treatment regimens in a sequential multiple-assignment randomized trial with a continuous longitudinal outcome[J]. Stat Methods Med Res, 2020, 29(7): 1891-1912.
20.	Pelham WE Jr, Fabiano GA, Waxmonsky JG, et al. Treatment sequencing for childhood ADHD: a multiple-randomization study of adaptive medication and behavioral interventions[J]. J Clin Child Adolesc Psychol, 2016, 45(4): 396-415.
21.	Oetting AI, Levy JA, Weiss RD, et al. Statistical methodology for a SMART design in the development of adaptive treatment strategies//Shrout PE, Keyes KM, Ornstein K. Causality and psychopathology: finding the determinants of disorders and their cures[M]. New York: Oxford University Press, 2011: 171-205.
22.	Cohen J. Statistical power analysis for the behavioral sciences (2nd ed)[M]. Hillsdale, NJ: Lawrence Erlbaum Associates, 1988.
23.	Lu X, Nahum-ShaniI, Kasari C, et al. Comparing dynamic treatment regimens using repeated‐measures outcomes: modeling considerations in SMART studies[J]. Stat Med, 2016, 35(10): 1595-1615.
24.	Artman WJ, Nahum-Shani I, Wu T, et al. Power analysis in a SMART design: sample size estimation for determining the best embedded dynamic treatment regime[J]. Biostatistics, 2020, 21(3): 432-448.
25.	Almirall D, Compton SN, Gunlicks-Stoessel M, et al. Designing a pilot sequential multiple assignment randomized trial for developing an adaptive treatment strategy[J]. Stat Med, 2012, 31(17): 1887-1902.
26.	Shortreed SM, Laber E, Scott Stroup T, et al. A multiple imputation strategy for sequential multiple assignment randomized trials[J]. Stat Med, 2014, 33(24): 4202-4214.
27.	Liu Y, Wang Y, Zeng D. Sequential multiple assignment randomization trials with enrichment design[J]. Biometrics, 2017, 73(2): 378-390.
28.	Turchetta A, Moodie EEM, Stephens DA, et al. Bayesian sample size calculations for comparing two strategies in SMART studies[J]. Biometrics, 2023, 79(3): 2489-2502.
29.	Nahum-Shani I, Dziak JJ, Venera H, et al. Design of experiments with sequential randomizations on multiple timescales: the hybrid experimental design[J]. Behav Res Methods, 2024, 56(3): 1770-1792.
30.	Tamura RN, Krischer JP, Pagnoux C, et al. A small n sequential multiple assignment randomized trial design for use in rare disease research[J]. Contemp Clin Trials, 2016, 46: 48-51.
31.	Wei B, Braun TM, Tamura RN, et al. Sample size determination for Bayesian analysis of small n sequential, multiple assignment, randomized trials (snSMARTs) with three agents[J]. J Biopharm Stat, 2020, 30(6): 1109-1120.
32.	Wei B, Braun TM, Tamura RN, et al. A Bayesian analysis of small n sequential multiple assignment randomized trials (snSMARTs)[J]. Stat Med, 2018, 37(26): 3723-3732.
33.	Fang F, Tamura RN, Braun TM, et al. Bayesian sample size calculation in small n, sequential multiple assignment randomized trials (snSMART)[J]. Pharm Stat, 2025, 24(1): e2465.
34.	Fang FT, Roy NB, Thomas M, et al. Comparing dose levels to placebo using a continuous outcome in a small n, sequential, multiple assignment, randomized trial (snSMART)[J]. Stat Bioph Res, 2023, 15(3): 502-509.
35.	Fang F, Hochstedler KA, Tamura RN, et al. Bayesian methods to compare dose levels with placebo in a small n, sequential, multiple assignment, randomized trial[J]. Stat Med, 2021, 40(4): 963-977.

1. Chakraborty B, Murphy SA. Dynamic treatment regimes[J]. Annu Rev Stat Appl, 2014, 1: 447-464.
2. Frommeyer TC, Gilbert MM, Fursmidt RM, et al. Reinforcement learning and its clinical applications within healthcare: a systematic review of precision medicine and dynamic treatment regimes[J]. Healthcare (Basel), 2025, 13(14): 1752.
3. Murphy SA. An experimental design for the development of adaptive treatment strategies[J]. Stat Med, 2005, 24(10): 1455-1481.
4. Murphy SA, Lynch KG, Oslin D, et al. Developing adaptive treatment strategies in substance abuse research[J]. Drug Alcohol Depend, 2007, 88(Suppl 2): S24-S30.
5. Kidwell KM, Hyde LW. Adaptive interventions and SMART designs: application to child behavior research in a community setting[J]. Am J Eval, 2016, 37(3): 344-363.
6. Kidwell KM. SMART designs in cancer research: past, present, and future[J]. Clin Trials, 2014, 11(4): 445-456.
7. Almirall D, Nahum-Shani I, Sherwood NE, et al. Introduction to SMART designs for the development of adaptive interventions: with application to weight loss research[J]. Transl Behav Med, 2014, 4(3): 260-274.
8. 周莎, 帥雨杏, 吉萌萌, 等. 基于適應性干預與順序多重分配隨機試驗設計探討中醫“辨證論治”治療策略的評價方法[J]. 中國循證醫學雜志, 2024, 24(12): 1476-1481.
9. 馬文欣, 王雪惠, 王禹毅, 等. 序列多重分配隨機試驗方法學進展及其在中醫學領域應用的思考[J]. 世界科學技術-中醫藥現代化, 2025, 27(6): 1530-1539.
10. 曹卉娟, 魯春麗, 劉建平. 序列多重分配隨機試驗設計方法及其在中醫藥領域的應用探討[J]. 中國中西醫結合雜志, 2022, 42(4): 482-486.
11. 潘知玉, 武紅莉, 張道培, 等. 序貫多重分配隨機試驗慢性病中醫藥臨床研究應用[J]. 中國中西醫結合雜志, 2025, 45(10): 1173-1180.
12. 姜燕華. 澤瀉湯辨治痰濕型良性陣發性位置性眩暈的SMART設計與治療策略研究[D]. 北京: 中國中醫科學院, 2024.
13. 卜志軍, 張雨歡, 孫源, 等. 序貫多分配隨機試驗設計樣本量估算方法及應用[J]. 現代中醫臨床, 2024, 31(4): 39-43.
14. 梁雪晴, 余世杰, 朱思宇, 等. SMART設計及其統計分析方法介紹[J]. 中國衛生統計, 2025, 42(2): 286-292.
15. 孫源, 鞠傳蘭, 鄭薇, 等. 中醫藥序列多重分配隨機試驗設計分析思路及統計方法應用[J]. 現代中醫臨床, 2024, 31(5): 86-91.
16. Lei H, Nahum-Shani I, Lynch K, et al. A "SMART" design for building individualized treatment sequences[J]. Annu Rev Clin Psychol, 2012, 8: 21-48.
17. Wallace MP, Moodie EM, Stephens DA. SMART thinking: a review of recent developments in sequential multiple assignment randomized trials[J]. Curr Epidemiol Rep, 2016, 3(3): 225-232.
18. Nahum-Shani I, Qian M, Almirall D, et al. Experimental design and primary data analysis methods for comparing adaptive interventions[J]. Psychol Methods, 2012, 17(4): 457-477.
19. Seewald NJ, Kidwell KM, Nahum-Shani I, et al. Sample size considerations for comparing dynamic treatment regimens in a sequential multiple-assignment randomized trial with a continuous longitudinal outcome[J]. Stat Methods Med Res, 2020, 29(7): 1891-1912.
20. Pelham WE Jr, Fabiano GA, Waxmonsky JG, et al. Treatment sequencing for childhood ADHD: a multiple-randomization study of adaptive medication and behavioral interventions[J]. J Clin Child Adolesc Psychol, 2016, 45(4): 396-415.
21. Oetting AI, Levy JA, Weiss RD, et al. Statistical methodology for a SMART design in the development of adaptive treatment strategies//Shrout PE, Keyes KM, Ornstein K. Causality and psychopathology: finding the determinants of disorders and their cures[M]. New York: Oxford University Press, 2011: 171-205.
22. Cohen J. Statistical power analysis for the behavioral sciences (2nd ed)[M]. Hillsdale, NJ: Lawrence Erlbaum Associates, 1988.
23. Lu X, Nahum-ShaniI, Kasari C, et al. Comparing dynamic treatment regimens using repeated‐measures outcomes: modeling considerations in SMART studies[J]. Stat Med, 2016, 35(10): 1595-1615.
24. Artman WJ, Nahum-Shani I, Wu T, et al. Power analysis in a SMART design: sample size estimation for determining the best embedded dynamic treatment regime[J]. Biostatistics, 2020, 21(3): 432-448.
25. Almirall D, Compton SN, Gunlicks-Stoessel M, et al. Designing a pilot sequential multiple assignment randomized trial for developing an adaptive treatment strategy[J]. Stat Med, 2012, 31(17): 1887-1902.
26. Shortreed SM, Laber E, Scott Stroup T, et al. A multiple imputation strategy for sequential multiple assignment randomized trials[J]. Stat Med, 2014, 33(24): 4202-4214.
27. Liu Y, Wang Y, Zeng D. Sequential multiple assignment randomization trials with enrichment design[J]. Biometrics, 2017, 73(2): 378-390.
28. Turchetta A, Moodie EEM, Stephens DA, et al. Bayesian sample size calculations for comparing two strategies in SMART studies[J]. Biometrics, 2023, 79(3): 2489-2502.
29. Nahum-Shani I, Dziak JJ, Venera H, et al. Design of experiments with sequential randomizations on multiple timescales: the hybrid experimental design[J]. Behav Res Methods, 2024, 56(3): 1770-1792.
30. Tamura RN, Krischer JP, Pagnoux C, et al. A small n sequential multiple assignment randomized trial design for use in rare disease research[J]. Contemp Clin Trials, 2016, 46: 48-51.
31. Wei B, Braun TM, Tamura RN, et al. Sample size determination for Bayesian analysis of small n sequential, multiple assignment, randomized trials (snSMARTs) with three agents[J]. J Biopharm Stat, 2020, 30(6): 1109-1120.
32. Wei B, Braun TM, Tamura RN, et al. A Bayesian analysis of small n sequential multiple assignment randomized trials (snSMARTs)[J]. Stat Med, 2018, 37(26): 3723-3732.
33. Fang F, Tamura RN, Braun TM, et al. Bayesian sample size calculation in small n, sequential multiple assignment randomized trials (snSMART)[J]. Pharm Stat, 2025, 24(1): e2465.
34. Fang FT, Roy NB, Thomas M, et al. Comparing dose levels to placebo using a continuous outcome in a small n, sequential, multiple assignment, randomized trial (snSMART)[J]. Stat Bioph Res, 2023, 15(3): 502-509.
35. Fang F, Hochstedler KA, Tamura RN, et al. Bayesian methods to compare dose levels with placebo in a small n, sequential, multiple assignment, randomized trial[J]. Stat Med, 2021, 40(4): 963-977.

Chinese Journal of Evidence-Based Medicine

Sample size estimation methods for continuous outcomes in two-stage asymmetric SMART designs and applications in traditional Chinese medicine

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