Wang Yaning
Food and Drug Administration, Office of Clinical Pharmacology, CDER, WO21 RM3662 HFD-880, 10903 New Hampshire Avenue, Silver Spring, MD 20993, USA.
J Pharmacokinet Pharmacodyn. 2007 Oct;34(5):575-93. doi: 10.1007/s10928-007-9060-6. Epub 2007 Jul 10.
Various estimation methods and the lack of a systematic derivation of the core objective function implemented in NONMEM for nonlinear mixed effect modeling has caused consistent confusion and inquiry among scientists who routinely use NONMEM for data analysis. This paper provides a detailed derivation of the objective functions for the most commonly used estimation methods in NONMEM, such as the Laplacian method, the first-order conditional estimation method (FOCE) with or without interaction, and the first-order method (FO). In addition, models with homogenous or heterogeneous residual error were used to demonstrate the relationship between the objective functions derived from two different types of approximation, namely Laplacian approximation of log-likelihood and linearized model approximation. The relationship between these estimation methods and those implemented in SAS and Splus is discussed.
用于非线性混合效应建模的各种估计方法以及NONMEM中实现的核心目标函数缺乏系统推导，这在经常使用NONMEM进行数据分析的科学家中引发了持续的困惑和疑问。本文详细推导了NONMEM中最常用估计方法的目标函数，如拉普拉斯方法、带或不带交互作用的一阶条件估计方法（FOCE）以及一阶方法（FO）。此外，使用具有同质或异质残差误差的模型来证明从两种不同类型近似推导的目标函数之间的关系，即对数似然的拉普拉斯近似和线性化模型近似。还讨论了这些估计方法与SAS和Splus中实现的方法之间的关系。
