Modeling nonlinear mixed effects

Nonlinear mixed effects models consist of two components the structural model (which may or may not contain covariates) and the statistical or variance model. The structural model describes the mean response for the population. Similar to a linear mixed effects model, nonlinear mixed effects models can be developed using a hierarchical approach. Data consist of an independent sample of n-subjects with the ith subject having -observations measured at time points t i, t 2, . t n . Let Y be the vector of observations, Y = Y1 1, Yi,2,. ..Ynjl,Yn,2,. ..Yn,ni)T and let s... 

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. 

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... 

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. 

The population pharmacokinetic aproach assesses the impact of various covariates on the pharmacokinetic of a drug. Nonlinear mixed effects modeling may be used to model the relationship between various covariates and pharmacokinetic parameters. Age or age group may be one of the covariates. This type of approach has its advantages as it involves assessment of the effect of age on the pharmacokinetics in the target population. 

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. 

R., Hauck, W.W. et al., An individual bioequivalence criterion regnlatory considerations, Stat. Med. 19, 2821-2842, 2000 Meyer, M.C., United States Food and Drug Administration requirements for approval of generic drug products, J. Clin. Psychiatry 62 (Suppl. 5), 4-9, 2001 Temple, R., Policy developments in regulatory approval, Stat. Med. 21, 2939-3048, 2002 Gould, A.L, Substantial evidence of effect, J. Biopharm. Stat. 12, 53-77, 2002 Chen, M.L., Panhard, X., and Mentre, F, Evaluation by simulation of tests based on nonlinear mixed-effects models in pharmacokinetic interaction and bioequivalence cross-over clinical trials, Stat. Med. 24,1509-1524,2005 Bolton, S., Bioequivalence studies for levothy-roxine, AAPS J. 7, E47-E53, 2005. 

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. ... 

Steimer, J.L. Mallet, A. Golmard, J.L. Boisvieux, J.F. Alternative approaches to estimation of population pharmacokinetic parameters comparison with nonlinear mixed-effect model. Drug Metab. Rev. 1984,15 (1-2), 265-292. 

Mentre, F. Gomeni, R. A two-step iterative algorithm for estimation in nonlinear mixed-effect models with an evaluation on population pharmacokinetics. J. Biopharm. Stat. 1995, 5 (2), 141-158. 

The number of samples per subject used for this approach is typically small, ranging from one to six. As does the pooled analysis technique, nonlinear mixed-effects modeling approaches analyze the data of all individuals at once, but take the interindividual random effects structure into account. This ensures that confounding correlations and imbalance that may occur in observational data are properly accounted for. 

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 ... 

Hossain, M. Wright, E. Baweja, R. Ludden, T.M. Miller, R. Nonlinear mixed effects modeling of single dose and multiple dose data for an immediate release (IR) and controlled release (CR) dosage form of alpazolam. Pharm. Res. 1997, 14, 309-315. 

Padoin C, Tod M, Perret G, Petitjean O. Analysis of the pharmacokinetic interaction between cephalexin and quinapril by a nonlinear mixed-effect model. Antimicrob Agents Chemother 1998 42(6) 1463-9. 

Bonate PL. Nonlinear Mixed Effects Models. In Bonate PL, Pharmacokinetic-Pharmacodynamic Modeling and Simulation Springer New York, 2006. 

M. Davidian and D. M. Giltinan, Some general estimation methods for nonlinear mixed effects models. / Biopharm Slat 3 23-55 (1993). 

Linear, Generalized Linear, and Nonlinear Mixed Effects Models... 

LINEAR, GENERALIZED LINEAR, AND NONLINEAR MIXED EFFECTS MODELS... 

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