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

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.	陳新林, 李海文, 劉鳳斌, 等. 單病例隨機對照試驗的設計和評價方法. 中國循證醫學雜志, 2016, 16(2): 242-245.
4.	陳新林, 黃海茵, 張長榮, 等. 2015 版 CENT 聲明簡介: 單病例隨機對照試驗報告指南. 中國循證醫學雜志, 2016, 16(7): 860-863.
5.	陳新林, 趙菲, 胡月, 等. 探索適合中醫藥 N-of-1 試驗的設計方案及模型. 廣州中醫藥大學學報, 2018, 35(1): 172-175.
6.	劉玉, 黃彬, 陳生, 等. 六味地黃膠囊治療肝腎陰虛證療效評價的例隨機對照雙盲試驗. 中醫雜志, 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. 涼血化瘀方加減治療原發性血小板增多癥單病例隨機對照研究. 中醫雜志, 2019, 60(8): 680-683.
9.	胡嘉元, 李江, 翟靜波, 等. 中醫藥單病例隨機對照試驗報告規范(中醫藥 CENT): CENT 聲明的擴展、說明與詳述. 中國循證醫學雜志, 2021, 21(3): 338-346.
10.	劉雪瑩, 司雨琦, 潘治森, 等. 中醫藥臨床應用 N-of-1 試驗報告質量評價的研究. 廣州中醫藥大學學報, 2020, 37(12): 2466-2471.
11.	劉沛, 陳啟光. 貝葉斯統計及其在診斷和篩檢試驗評價中的應用. 中國衛生統計, 2006, 23(4): 361-363.
12.	張繼巍, 高文龍, 李學朝, 等. Cox 比例風險回歸模型的貝葉斯估計方法研究. 中國衛生統計, 2017, 34(6): 999-1001.
13.	翟靜波, 商洪才, 王輝, 等. 貝葉斯單病例隨機對照試驗簡介. 中國循證醫學雜志, 2017, 17(7): 848-851.
14.	王婧, 鮑貴. 貝葉斯統計與傳統統計方法的比較. 統計與決策, 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.	陳新林, 陳平雁. N-of-1 無殘留效應定量數據混合效應模型的模擬研究. 中國衛生統計, 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.	陳長生, 徐勇勇, 王彤. 交叉設計資料的混合效應模型分析. 中國衛生統計, 2005, 22(4): 214-217.
22.	陳新林. 單病例隨機對照(N-of-1)試驗的樣本量估計方法. 中國循證醫學雜志, 2019, 19(7): 871-874.
23.	黃福強, 曾新, 王玉珠, 等. 2×2 交叉設計生物等效性研究受試者脫落的分析策略研究. 中國臨床藥理學雜志, 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. 陳新林, 李海文, 劉鳳斌, 等. 單病例隨機對照試驗的設計和評價方法. 中國循證醫學雜志, 2016, 16(2): 242-245.
4. 陳新林, 黃海茵, 張長榮, 等. 2015 版 CENT 聲明簡介: 單病例隨機對照試驗報告指南. 中國循證醫學雜志, 2016, 16(7): 860-863.
5. 陳新林, 趙菲, 胡月, 等. 探索適合中醫藥 N-of-1 試驗的設計方案及模型. 廣州中醫藥大學學報, 2018, 35(1): 172-175.
6. 劉玉, 黃彬, 陳生, 等. 六味地黃膠囊治療肝腎陰虛證療效評價的例隨機對照雙盲試驗. 中醫雜志, 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. 涼血化瘀方加減治療原發性血小板增多癥單病例隨機對照研究. 中醫雜志, 2019, 60(8): 680-683.
9. 胡嘉元, 李江, 翟靜波, 等. 中醫藥單病例隨機對照試驗報告規范(中醫藥 CENT): CENT 聲明的擴展、說明與詳述. 中國循證醫學雜志, 2021, 21(3): 338-346.
10. 劉雪瑩, 司雨琦, 潘治森, 等. 中醫藥臨床應用 N-of-1 試驗報告質量評價的研究. 廣州中醫藥大學學報, 2020, 37(12): 2466-2471.
11. 劉沛, 陳啟光. 貝葉斯統計及其在診斷和篩檢試驗評價中的應用. 中國衛生統計, 2006, 23(4): 361-363.
12. 張繼巍, 高文龍, 李學朝, 等. Cox 比例風險回歸模型的貝葉斯估計方法研究. 中國衛生統計, 2017, 34(6): 999-1001.
13. 翟靜波, 商洪才, 王輝, 等. 貝葉斯單病例隨機對照試驗簡介. 中國循證醫學雜志, 2017, 17(7): 848-851.
14. 王婧, 鮑貴. 貝葉斯統計與傳統統計方法的比較. 統計與決策, 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. 陳新林, 陳平雁. N-of-1 無殘留效應定量數據混合效應模型的模擬研究. 中國衛生統計, 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. 陳長生, 徐勇勇, 王彤. 交叉設計資料的混合效應模型分析. 中國衛生統計, 2005, 22(4): 214-217.
22. 陳新林. 單病例隨機對照(N-of-1)試驗的樣本量估計方法. 中國循證醫學雜志, 2019, 19(7): 871-874.
23. 黃福強, 曾新, 王玉珠, 等. 2×2 交叉設計生物等效性研究受試者脫落的分析策略研究. 中國臨床藥理學雜志, 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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