Nonlinear mixed effects model NONMEM

NONMEM (commercial) WWW.globomax.com General purpose toolkit for parameter estimation for nonlinear mixed effects models (NONMEM). 

Estimation of nonlinear mixed effects models has been implemented in a number of software packages and includes different estimation methods [12]. As NONMEM is the most commonly used software to estimate population parameters this program is base for the following description. 

The NONMEM (nonlinear mixed-effects modeling) software (Beal et al. 1992), mostly used in population pharmacokinetics, was developed at the University of California and is presently distributed by Globomax. For data management, post processing and diagnostic plots, the software S-plus (Mathsoft) is frequently used. 

The non-linear mixed effects model is the most widely used method and has proven to be very useful for continuous measures of drug effect, categorical response data, and survival-type data. The nonlinear mixed-effects modeling software (NONMEM) introduced by Sheiner and Beal is one of the most commonly used programs for population analysis. A detailed review of software for performing population PK/PD analysis is available. ... 

First-Order (NONMEM) Method. The first nonlinear mixed-effects modeling program introduced for the analysis of large pharmacokinetic data was NONMEM, developed by Beal and Sheiner. In the NONMEM program, linearization of the model in the random effects is effected by using the first-order Taylor series expansion with respect to the random effect variables r], and Cy. This software is the only program in which this type of linearization is used. The jth measurement in the ith subject of the population can be obtained from a variant of Eq. (5) as follows ... 

NONMEM, nonlinear mixed effects modeling RSC, reciprocal of serum creatinine HIV, human immunodeficiency virus. 

The theory and techniques described in this chapter focus on the application of logistic regression to binary outcome data and the development of models to describe the relationship between binary endpoints and one or more explanatory variables (covariates). While many software options are available for fitting fixed or mixed effects logistic regression models, this chapter endeavors to illustrate the use of nonlinear mixed effects modeling to analyze binary endpoint data as implemented in the NONMEM software. 

The Laplacian estimation method as implemented in the NONMEM program (a program the authors use for nonlinear mixed effects modeling) is used to provide... 

The aim of this chapter is to equip the pharmacometrician with sufficient theory and application to confidently approach the PK/PD-based analysis of count data and thus derive the maximum return on investment from clinical study data. Section 27.2 provides a motivating example and Section 27.3 presents relevant definitions and theory. Section 27.4 applies the theory to the example and introduces diagnostics methods. Throughout the chapter, the focus is on population approaches using nonlinear mixed effects models. Code segments of NONMEM control files are presented in the appendix. Mixed effects analysis methodology is described in detail in Chapter 4 of this text. 

Data were analyzed using the nonlinear mixed effects model software program NONMEM (Version 5 level 1.1 double precision (32)). Nelfinavir and M8 were fitted simultaneously. The molecular weight of nelfinavir and M8 is comparable with a ratio of M8 to nelhnavir of 1.028. Therefore, the concentrations were not corrected and are expressed in nanogram per milliliter. 

Suppose Y = f(x, 0, t ) + g(z, e) where nr] — (0, il), (0, ), x is the set of subject-specific covariates x, z, O is the variance-covariance matrix for the random effects in the model (t ), and X is the residual variance matrix. NONMEM (version 5 and higher) offers two general approaches towards parameter estimation with nonlinear mixed effects models first-order approximation (FO) and first-order conditional estimation (FOCE), with FOCE being more accurate and computationally difficult than FO. First-order (FO) approximation, which was the first algorithm derived to estimate parameters in a nonlinear mixed effects models, was originally developed by Sheiner and Beal (1980 1981 1983). FO-approximation expands the nonlinear mixed effects model as a first-order Taylor series approximation about t) = 0 and then estimates the model parameters based on the linear approximation to the nonlinear model. Consider the model... 

The NLME function in S-Plus offers three different estimation algorithms a FOCE algorithm similar to NONMEM, adaptive Gaussian quadrature, and Laplacian approximation. The FOCE algorithm in S-Plus, similar to the one in NONMEM, was developed by Lindstrom and Bates (1990). The algorithm is predicated on normally distributed random effects and normally distributed random errors and makes a first-order Taylor series approximation of the nonlinear mixed effects model around both the current parameter estimates 0 and the random effects t). The adaptive Gaussian quadrature and Laplacian options are similar to the options offered by SAS. 

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