Nonlinear Mixed Model

R. D. WoUinger, Laplace s approximation for nonlinear mixed models. Biometrika 80 791-795 (1993). 

Data were analyzed using a nonlinear Mixed model in SAS (2001). 

The best way to approach the retrofit synthesis of the heat-exchanger network is to model all five tasks simultaneously. A mixed-integer nonlinear programming model is usually formulated to accomplish this goal. 

Pinheiro JC, Bates DM. Approximations to the loglikelihood function in the nonlinear mixed effects model. / Comput Graphical Stat, 1995 4 12-35. 

Lindstrom MJ, Bates DM. Nonlinear mixed effects models for repeated measures data. Biometrics, 1990 46 673-87. 

By comparison, estimation of land of by nonlinear regression (file exl9- 1. msp) leads to the following values t = 9.9 mm, and 072 = 97.7 min2 The only way to determine which parameter set is more correct is to predict the experimental concentrations using these parameters in an appropriate mixing model. This procedure is explained in Section 19.4. 

Munoz MJ, Merino-Sanjuan M, Lledo-Garcia R, Casabo VG, Manez-Castillejo F and Nacher A (2005) Use of Nonlinear Mixed Effect Modeling for the Intestinal Absorption Data Application to Ritonavir in the Rat. Eur J Pharm Biopharm 61 ... 

There are two common methods for obtaining estimates of the fixed effects (the mean) and the variability the two-stage approach and the nonlinear, mixed-effects modeling approach. The two-stage approach involves multiple measurements on each subject. The nonlinear, mixed-effects model can be used in situations where extensive measurements cannot or will not be made on all or any of the subjects. 

Pharmacokinetic/pharmacodynamic model using nonlinear, mixed-effects model in two compartment, best described time course of concentration strong correlation with creatinine clearance predicted concentration at the efi ect site and in reduction of heart rate during atrial fibrillation using population kinetic approach... 

Dealing with mixed-integer nonlinear optimization models of the form (6.1) or (6.2) present two major challenges/difficulties. These difficulties are associated with the nature of the problem, namely, the combinatorial domain (y-domain) and the continuous domain ( -domain). 

Section 9.2 presents key issues that arise in the synthesis of heat-integrated sharp distillation columns and presents a mixed-integer nonlinear optimization model which allows for treating the pressure of each column explicitly as a variable while at the same time heat integration alternatives are incorporated. For further reading in this subject the reader is referred to Floudas and Paules (1988) and the other suggested references. 

A. R. Ciric and C. A. Floudas. A mixed-integer nonlinear programming model for retrofitting heat exchanger networks. I EC Res., 29 239,1990. 

H. H. Hoang. Topological optimization of networks A nonlinear mixed integer model employing generalized Benders decomposition. IEEE Trans. Automatic Control, AC-27 164, 1982. 

Various methods are available to estimate population parameters, but today the nonlinear mixed effects modeling approach is the most common one employed. Population analyses have been performed for mAbs such as basiliximab, daclizu-mab and trastuzumab, as well as several others in development, including clenolixi-mab and sibrotuzumab. Population pharmacokinetic models comprise three submodels the structural the statistical and covariate submodels (Fig. 3.13). Their development and impact for mAbs will be discussed in the following section. 

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 models are built similar to the descriptive mechanism-based PD models. Most of them are also estimated by the nonlinear mixed effects modeling approach considering interindividual and residual variability. In addition, covariates influencing the disease progression can also be investigated. 

Mentre, F. History and new developments in estimation methods in nonlinear mixed-effects models. PAGE 2005, 2005 14. 

Nonlinear mixed-effects modeling methods as applied to pharmacokinetic-dynamic data are operational tools able to perform population analyses [461]. In the basic formulation of the model, it is recognized that the overall variability in the measured response in a sample of individuals, which cannot be explained by the pharmacokinetic-dynamic model, reflects both interindividual dispersion in kinetics and residual variation, the latter including intraindividual variability and measurement error. The observed response of an individual within the framework of a population nonlinear mixed-effects regression model can be described as... 

Beyond pharmacokinetics and pharmacodynamics, population modeling and parameter estimation are applications of a statistical model that has general validity, the nonlinear mixed effects model. The model has wide applicability in all areas, in the biomedical science and elsewhere, where a parametric functional relationship between some input and some response is studied and where random variability across individuals is of concern [458]. 

Davidian, M. and Gallant, R., The nonlinear mixed effect model with a smooth random effects density, Biometrika, Vol. 80, 1993, pp. 475-488. 

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