INSERM UMR738, University Diderot Paris 7, Paris, France.
Stat Med. 2011 Sep 20;30(21):2582-600. doi: 10.1002/sim.4286. Epub 2011 Jul 26.
In this work, we develop a bioequivalence analysis using nonlinear mixed effects models (NLMEM) that mimics the standard noncompartmental analysis (NCA). We estimate NLMEM parameters, including between-subject and within-subject variability and treatment, period and sequence effects. We explain how to perform a Wald test on a secondary parameter, and we propose an extension of the likelihood ratio test for bioequivalence. We compare these NLMEM-based bioequivalence tests with standard NCA-based tests. We evaluate by simulation the NCA and NLMEM estimates and the type I error of the bioequivalence tests. For NLMEM, we use the stochastic approximation expectation maximisation (SAEM) algorithm implemented in monolix. We simulate crossover trials under H(0) using different numbers of subjects and of samples per subject. We simulate with different settings for between-subject and within-subject variability and for the residual error variance. The simulation study illustrates the accuracy of NLMEM-based geometric means estimated with the SAEM algorithm, whereas the NCA estimates are biased for sparse design. NCA-based bioequivalence tests show good type I error except for high variability. For a rich design, type I errors of NLMEM-based bioequivalence tests (Wald test and likelihood ratio test) do not differ from the nominal level of 5%. Type I errors are inflated for sparse design. We apply the bioequivalence Wald test based on NCA and NLMEM estimates to a three-way crossover trial, showing that Omnitrope®; (Sandoz GmbH, Kundl, Austria) powder and solution are bioequivalent to Genotropin®; (Pfizer Pharma GmbH, Karlsruhe, Germany). NLMEM-based bioequivalence tests are an alternative to standard NCA-based tests. However, caution is needed for small sample size and highly variable drug.
在这项工作中，我们开发了一种使用非线性混合效应模型（NLMEM）的生物等效性分析，该模型模拟了标准的非房室分析（NCA）。我们估计 NLMEM 参数，包括个体间和个体内变异性以及处理、周期和序列效应。我们解释了如何对次要参数进行 Wald 检验，并提出了用于生物等效性的似然比检验的扩展。我们将这些基于 NLMEM 的生物等效性检验与基于标准 NCA 的检验进行比较。我们通过模拟评估 NCA 和 NLMEM 估计值以及生物等效性检验的Ⅰ类错误。对于 NLMEM，我们使用 monolix 中实现的随机逼近期望最大化（SAEM）算法。我们使用不同数量的受试者和每个受试者的样本在 H(0)下模拟交叉试验。我们模拟了不同的个体间和个体内变异性以及残差方差的设置。模拟研究说明了使用 SAEM 算法估计的 NLMEM 基于几何平均值的准确性，而 NCA 估计值对于稀疏设计存在偏差。NCA 基于的生物等效性检验显示出良好的Ⅰ类错误，除非变异性很高。对于丰富的设计，NLMEM 基于的生物等效性检验（Wald 检验和似然比检验）的Ⅰ类错误与 5%的名义水平没有差异。稀疏设计会导致Ⅰ类错误增加。我们将基于 NCA 和 NLMEM 估计的生物等效性 Wald 检验应用于三向交叉试验，表明 Omnitrope®（Sandoz GmbH，奥地利 Kundl）粉末和溶液与 Genotropin®（辉瑞制药有限公司，德国卡尔斯鲁厄）生物等效。基于 NLMEM 的生物等效性检验是标准 NCA 基于检验的替代方法。然而，对于小样本量和高度可变的药物，需要谨慎。
