Department of Pharmaceutical Biosciences, Uppsala University, Sweden.
AAPS J. 2012 Sep;14(3):420-32. doi: 10.1208/s12248-012-9349-2. Epub 2012 Apr 14.
Estimation methods for nonlinear mixed-effects modelling have considerably improved over the last decades. Nowadays, several algorithms implemented in different software are used. The present study aimed at comparing their performance for dose-response models. Eight scenarios were considered using a sigmoid E(max) model, with varying sigmoidicity and residual error models. One hundred simulated datasets for each scenario were generated. One hundred individuals with observations at four doses constituted the rich design and at two doses, the sparse design. Nine parametric approaches for maximum likelihood estimation were studied: first-order conditional estimation (FOCE) in NONMEM and R, LAPLACE in NONMEM and SAS, adaptive Gaussian quadrature (AGQ) in SAS, and stochastic approximation expectation maximization (SAEM) in NONMEM and MONOLIX (both SAEM approaches with default and modified settings). All approaches started first from initial estimates set to the true values and second, using altered values. Results were examined through relative root mean squared error (RRMSE) of the estimates. With true initial conditions, full completion rate was obtained with all approaches except FOCE in R. Runtimes were shortest with FOCE and LAPLACE and longest with AGQ. Under the rich design, all approaches performed well except FOCE in R. When starting from altered initial conditions, AGQ, and then FOCE in NONMEM, LAPLACE in SAS, and SAEM in NONMEM and MONOLIX with tuned settings, consistently displayed lower RRMSE than the other approaches. For standard dose-response models analyzed through mixed-effects models, differences were identified in the performance of estimation methods available in current software, giving material to modellers to identify suitable approaches based on an accuracy-versus-runtime trade-off.
在过去的几十年中，非线性混合效应建模的估计方法有了很大的改进。如今，不同软件中实现了几种算法。本研究旨在比较这些方法在剂量反应模型中的性能。使用 sigmoid E(max)模型，考虑了 8 种不同的情况，其 sigmoidicity 和残差模型有所不同。为每种情况生成了 100 个模拟数据集。每个个体有 4 个剂量的观测值组成丰富设计，2 个剂量的观测值组成稀疏设计。研究了 9 种用于最大似然估计的参数方法：NONMEM 和 R 中的一阶条件估计（FOCE）、NONMEM 和 SAS 中的拉普拉斯（LAPLACE）、SAS 中的自适应高斯求积（AGQ）以及 NONMEM 和 MONOLIX 中的随机逼近期望最大化（SAEM）（这两种 SAEM 方法都有默认和修改的设置）。所有方法首先从设置为真实值的初始估计值开始，其次，从修改后的初始值开始。结果通过估计值的相对均方根误差（RRMSE）进行检查。在使用真实初始条件时，除了 R 中的 FOCE 之外，所有方法都能获得完整的完成率。FOCE 和 LAPLACE 的运行时间最短，而 AGQ 的运行时间最长。在丰富设计下，除了 R 中的 FOCE 之外，所有方法的表现都很好。当从修改后的初始条件开始时，AGQ、然后是 NONMEM 中的 FOCE、SAS 中的 LAPLACE、以及经过调整设置的 NONMEM 和 MONOLIX 中的 SAEM，始终显示出比其他方法更低的 RRMSE。对于通过混合效应模型分析的标准剂量反应模型，可用于当前软件的估计方法的性能存在差异，为建模者提供了根据准确性与运行时间的权衡来识别合适方法的依据。
