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目的针对多阶段交叉设计中的不完整数据,分别采用多水平模型RIGLS算法、MOM以及REML算法分析,并与完整数据的结果进行比较。方法针对BE研究中4×4交叉设计,分别运用FDA指导原则中推荐的矩法(Method of Moments,MOM)、限制性极大似然法(Restricted Maximum Likelihood Method,REML)以及基于限制性迭代广义最小二乘法(Restricted Iterative Generalized Least Squares,RIGLS)估计的多水平模型,采用实例与模拟结合的方式进行分析,探讨不同方法在有随机缺失的不完整数据中的结果比较。结果 (1)多水平模型的首要优势在于考虑了数据误差的层次性,将传统模型中的误差随机项分解到与数据层次结构对应的各个水平上。(2)多水平模型可通过在个体水平拟合随机效应,直接估计个体-药物交互作用的方差σ2D,克服传统方法因间接估计而引起的偏倚。(3)多水平模型其算法不要求所有的观测个体有相同的观测次数,可充分利用含有缺失值的信息,对于缺失数据和非均衡设计具有较好普适性。结论本研究将生物等效性与多水平建模有机结合,为非均衡、高变异、小样本、有缺失的生物等效性评价开拓了新的思路,提供了新的方法。
Aim To analyze the incomplete data in the multi-stage cross-over design, the multi-level model RIGLS algorithm, the MOM algorithm and the REML algorithm are respectively used and compared with the results of the complete data. Methods Based on the 4 × 4 crossover design in BE study, the proposed Method of Moments (MOM), Restricted Maximum Likelihood Method (REML) and the generalized restriction-based iterative method The multi-level model of Restricted Iterative Generalized Least Squares (RIGLS) estimation is analyzed by means of a combination of examples and simulations to explore the comparison of different methods in incomplete data with random missing. Results (1) The primary advantage of the multi-level model is that it considers the hierarchy of data errors and decomposes the random items in the traditional model to all levels corresponding to the data hierarchy. (2) The multi-level model can directly estimate the variance σ2D of individual-drug interactions by fitting the random effects at the individual level to overcome the bias caused by the indirect estimation due to the traditional method. (3) Multi-level model The algorithm does not require all observed individuals to have the same number of observations and can make full use of the information containing the missing values, and has good universality for missing data and unbalanced design. Conclusion This study combines bioequivalence with multilevel modeling and opens up new ideas and provides new methods for bioequivalence evaluation of non-equilibrium, high variation, small sample and deletion.