Journal of Pharmacokinetics and Pharmacodynamics

, Volume 34, Issue 5, pp 575–593 | Cite as

Derivation of various NONMEM estimation methods

  • Yaning WangEmail author


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.


Nonlinear mixed-effects Likelihood approximation Laplacian First-order conditional method (FOCE) First-order method (FO) 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Food and Drug AdministrationOffice of Clinical Pharmacology, CDERSilver SpringUSA

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