Simulation study on quantitative data in series of N-of-1 trials based on mixed-effect model_Chinese Journal of Evidence-Based Medicine

Authors：

 CHEN XinLin ¹ , CHEN Lixia ¹ , HUANG Haiyin ² , CHEN Yiming ¹ , ZHANG Shijing ¹ , PENG Bin ³ , DENG Jiemin ¹ , HU Yue ¹ , HOU Jiangtao ³ , LIN Wenjia ¹

1. Basic Medical College, Guangzhou University of Chinese Medicine, Guangzhou 510006, P.R.China;
2. Yueyang Hospital of Integrative Chinese and Western Medicine, Shanghai University of Chinese Medicine, Shanghai 200437, P.R.China;
3. The First Affiliated Hospital, Guangzhou University of Chinese Medicine, Guangzhou 510405, P.R.China;

Corresponding author：

CHEN XinLin, Email: chenxlsums@126.com

Keywords：

Series of N-of-1 trials; Bayesian; Mixed-effects model; Simulation study

DOI：

10.7507/1672-2531.202012037

Video：

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Objective A simulation study was used to generate the multivariate normal distribution data with a residual effect based on series of N-of-1 trials. The statistical performance of paired t-test, mixed effect model and Bayesian mixed effect model were compared.Methods Three-cycles N-of-1 trials were set, and the participants were randomly assigned to 2 different treatments in each cycle. The simulation study included the following procedures: producing six-dimensional normal distribution data, randomly allocating intervention methods and patients, adding residual effects, constructing and evaluating 3 models, and setting the parameters. The sample sizes were set as 3, 5, 8 and 10, and the correlation coefficients among different times were set as 0.0, 0.5 and 0.8. Different proportions of residual effects for the 2 groups were set. Type I error, power, mean error (ME), and mean square error (MSE) were used to compare the 3 models.Results When there was no residual effect in the 2 groups, type I errors of 3 models were approximately 0.05, and their MEs were approximately 0. Paired t-test had the highest power and the lowest MSE. When the residual effect existed in the 2 groups, the type I error of paired t-test increased, and its estimated value deviated from the true value (ME≠0). Type I errors of the mixed effect model and Bayesian mixed-effect model were approximately 0.05, and they had the same power. The estimated values of the two models were close to the true value (ME was approximately 0).Conclusions When there is no residual effect (0% vs. 0%), paired t-test is suitable for data analysis of N-of-1 trials. When there is a residual effect, the mixed effect model and Bayesian mixed-effect model are suitable for data analysis of N-of-1 trials.

Citation： CHEN XinLin, CHEN Lixia, HUANG Haiyin, CHEN Yiming, ZHANG Shijing, PENG Bin, DENG Jiemin, HU Yue, HOU Jiangtao, LIN Wenjia. Simulation study on quantitative data in series of N-of-1 trials based on mixed-effect model. Chinese Journal of Evidence-Based Medicine, 2021, 21(6): 689-695. doi: 10.7507/1672-2531.202012037 Copy

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19.	陈新林, 陈平雁. N-of-1 无残留效应定量数据混合效应模型的模拟研究. 中国卫生统计, 2013, 30(3): 347-350.
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21.	陈长生, 徐勇勇, 王彤. 交叉设计资料的混合效应模型分析. 中国卫生统计, 2005, 22(4): 214-217.
22.	陈新林. 单病例随机对照(N-of-1)试验的样本量估计方法. 中国循证医学杂志, 2019, 19(7): 871-874.
23.	黄福强, 曾新, 王玉珠, 等. 2×2 交叉设计生物等效性研究受试者脱落的分析策略研究. 中国临床药理学杂志, 2019, 35(9): 849-853.

1. Li J, Gao W, Punja S, et al. Reporting quality of N-of-1 trials published between 1985 and 2013: a systematic review. J Clin Epidemiol, 2016, 76: 57-64.
2. Alemayehu C, Nikles J, Mitchell G. N-of-1 trials in the clinical care of patients in developing countries: a systematic review. Trials, 2018, 19(1): 246.
3. 陈新林, 李海文, 刘凤斌, 等. 单病例随机对照试验的设计和评价方法. 中国循证医学杂志, 2016, 16(2): 242-245.
4. 陈新林, 黄海茵, 张长荣, 等. 2015 版 CENT 声明简介: 单病例随机对照试验报告指南. 中国循证医学杂志, 2016, 16(7): 860-863.
5. 陈新林, 赵菲, 胡月, 等. 探索适合中医药 N-of-1 试验的设计方案及模型. 广州中医药大学学报, 2018, 35(1): 172-175.
6. 刘玉, 黄彬, 陈生, 等. 六味地黄胶囊治疗肝肾阴虚证疗效评价的例随机对照双盲试验. 中医杂志, 2018, 59(11): 947-951.
7. Huang H, Yang P, Wang J, et al. Investigation into the individualized treatment of traditional Chinese medicine through a series of N-of-1 trials. Evid Based Complement Alternat Med, 2018, 2018: 5813767.
8. 郭立中. 凉血化瘀方加减治疗原发性血小板增多症单病例随机对照研究. 中医杂志, 2019, 60(8): 680-683.
9. 胡嘉元, 李江, 翟静波, 等. 中医药单病例随机对照试验报告规范(中医药 CENT): CENT 声明的扩展、说明与详述. 中国循证医学杂志, 2021, 21(3): 338-346.
10. 刘雪莹, 司雨琦, 潘治森, 等. 中医药临床应用 N-of-1 试验报告质量评价的研究. 广州中医药大学学报, 2020, 37(12): 2466-2471.
11. 刘沛, 陈启光. 贝叶斯统计及其在诊断和筛检试验评价中的应用. 中国卫生统计, 2006, 23(4): 361-363.
12. 张继巍, 高文龙, 李学朝, 等. Cox 比例风险回归模型的贝叶斯估计方法研究. 中国卫生统计, 2017, 34(6): 999-1001.
13. 翟静波, 商洪才, 王辉, 等. 贝叶斯单病例随机对照试验简介. 中国循证医学杂志, 2017, 17(7): 848-851.
14. 王婧, 鲍贵. 贝叶斯统计与传统统计方法的比较. 统计与决策, 2021, 37(1): 24-29.
15. Gelman A. Bayesian statistics then and now. Statistical Science, 2010, 25(2): 162-165.
16. Senarathne SGJ, Overstall AM, McGree JM. Bayesian adaptive N-of-1 trials for estimating population and individual treatment effects. Stat Med, 2020, 39(29): 4499-4518.
17. Shrestha S, Jain S. A Bayesian-bandit adaptive design for N-of-1 clinical trials. Stat Med, 2021, 40(7): 1825-1844.
18. van de Schoot R, Broere JJ, Perryck KH, et al. Analyzing small data sets using Bayesian estimation: the case of posttraumatic stress symptoms following mechanical ventilation in burn survivors. Eur J Psychotraumatol, 2015, 6: 25216.
19. 陈新林, 陈平雁. N-of-1 无残留效应定量数据混合效应模型的模拟研究. 中国卫生统计, 2013, 30(3): 347-350.
20. Chen X, Chen P. A comparison of four methods for the analysis of N-of-1 trials. PLoS One, 2014, 9(2): e87752.
21. 陈长生, 徐勇勇, 王彤. 交叉设计资料的混合效应模型分析. 中国卫生统计, 2005, 22(4): 214-217.
22. 陈新林. 单病例随机对照(N-of-1)试验的样本量估计方法. 中国循证医学杂志, 2019, 19(7): 871-874.
23. 黄福强, 曾新, 王玉珠, 等. 2×2 交叉设计生物等效性研究受试者脱落的分析策略研究. 中国临床药理学杂志, 2019, 35(9): 849-853.

Chinese Journal of Evidence-Based Medicine

Simulation study on quantitative data in series of N-of-1 trials based on mixed-effect model

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