Abstract
ObjectiveTo provide a practical guidance for the analysis of N-of-1 trials by comparing four commonly used models.MethodsThe 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.ResultsThe 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.ConclusionWe 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.
Highlights
N-of-1 trials are multicycle, double-blinded controlled cross-over trials based on individuals [1,2,3,4]
Since N-of-1 trials were first introduced in an experimental paradigm in 1945 [5], they have been increasingly utilized in social, educational sciences, biomedical, clinical areas [6], and notably in medical area including rheumatism [7], pediatric rheumatism [8], arthritis pain [9], chronic neuropathic pain [10], insomnia [11], heart disease [12], chronic obstructive pulmonary disease [13], and pediatric oncology [14]
Type I error of Model 2 was less than 5%, while that of Model 4 was far from 5% under three compound symmetry (CS) structures
Summary
The four methods are introduced below in 3cycles design. Paired t-test (Model 1) In N-of-1 trials, each cycle with two periods which are assigned to Group A or Group B is considered as a pair. LA and lB represent carryover effect left over by Group A and Group B in the previous period respectively. LA and lB represent carryover effect of Group A and Group B respectively. ZA = 1 (ZB = 1) represents that there is carryover effect in Group A (Group B); ZA = 0 and ZB = 0 mean no carryover effect in both Group A and Group B. ci indicates random effects of the i-th subject. Note: M1, M2, M3 and M4 denoted paired t-test (Model 1), mixed effects model of difference (Model 2), mixed effects model (Model 3) and meta-analysis (Model 4) respectively. 4-cycles) normal distribution data were generated by a multivariate normal random number generator (a SAS Macro) [26,27] based on mixed effect model. 0.100 0.100 0.042 N/A 0.160 0.160 0.067 N/A 0.322 0.322 0.156 N/A 0.080 0.080 0.039 N/A 0.126 0.126 0.061 N/A 0.239 0.239 0.138 N/A
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