Chen Xinlin, Chen Pingyan
Department of Biostatistics, School of Public Health, Southern Medical University, Guangzhou, Guangdong province, China ; Department of Preventive Medicine and Biostatistics, College of fundamental Medicine, Guangzhou University of Chinese Medicine, Guangzhou, Guangdong province, China.
Department of Biostatistics, School of Public Health, Southern Medical University, Guangzhou, Guangdong province, China.
PLoS One. 2014 Feb 4;9(2):e87752. doi: 10.1371/journal.pone.0087752. eCollection 2014.
To provide a practical guidance for the analysis of N-of-1 trials by comparing four commonly used models.
The four models, paired t-test, mixed effects model of difference, mixed effects model and meta-analysis of summary data were compared using a simulation study. The assumed 3-cycles and 4-cycles N-of-1 trials were set with sample sizes of 1, 3, 5, 10, 20 and 30 respectively under normally distributed assumption. The data were generated based on variance-covariance matrix under the assumption of (i) compound symmetry structure or first-order autoregressive structure, and (ii) no carryover effect or 20% carryover effect. Type I error, power, bias (mean error), and mean square error (MSE) of effect differences between two groups were used to evaluate the performance of the four models.
The results from the 3-cycles and 4-cycles N-of-1 trials were comparable with respect to type I error, power, bias and MSE. Paired t-test yielded type I error near to the nominal level, higher power, comparable bias and small MSE, whether there was carryover effect or not. Compared with paired t-test, mixed effects model produced similar size of type I error, smaller bias, but lower power and bigger MSE. Mixed effects model of difference and meta-analysis of summary data yielded type I error far from the nominal level, low power, and large bias and MSE irrespective of the presence or absence of carryover effect.
We recommended paired t-test to be used for normally distributed data of N-of-1 trials because of its optimal statistical performance. In the presence of carryover effects, mixed effects model could be used as an alternative.
通过比较四种常用模型，为单病例试验（N-of-1试验）的分析提供实用指导。
采用模拟研究比较配对t检验、差异混合效应模型、混合效应模型和汇总数据的Meta分析这四种模型。在正态分布假设下，设定假设的3周期和4周期单病例试验，样本量分别为1、3、5、10、20和30。数据基于方差协方差矩阵生成，假设（i）复合对称结构或一阶自回归结构，以及（ii）无残留效应或20%的残留效应。使用两组间效应差异的I型错误、检验效能、偏差（平均误差）和均方误差（MSE）来评估这四种模型的性能。
3周期和4周期单病例试验在I型错误、检验效能、偏差和MSE方面的结果具有可比性。配对t检验产生的I型错误接近名义水平，检验效能较高，偏差相当，MSE较小，无论是否存在残留效应。与配对t检验相比，混合效应模型产生的I型错误大小相似，偏差较小，但检验效能较低，MSE较大。差异混合效应模型和汇总数据的Meta分析无论是否存在残留效应，产生的I型错误都远离名义水平，检验效能低，偏差和MSE大。
由于其最佳的统计性能，我们建议对单病例试验的正态分布数据使用配对t检验。在存在残留效应的情况下，混合效应模型可作为替代方法。
