Mixed effects modeling

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. 

Shkedy, Z. et al., Modeling anti-KLH ELISA data using two-stage and mixed effects models in support of immunotoxicological studies, J. Biopharm. Stat., 15, 205, 2005. 

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... 

Gupta, S.K., et al. 1999. Quantitative characterisation of therapeutic index Application of mixed-effects modelling to evaluate oxybutynin dose-efficacy and dose-side effect relationships. Clin Pharmacol Ther 65 672. 

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. 

Jolling, K., Perez-Ruixo, J. J., Hemeryck, A., Vermeulen, A., Greway, T. Mixed-effects modelling of the interspecies pharmacokinetic scaling of pegylated human erythropoietin. Eur J Pharm Sci 2005, 24 465-475. 

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... 

Then, given a model for data from a specific drug in a sample from a population, mixed-effect modeling produces estimates for the complete statistical distribution of the pharmacokinetic-dynamic parameters in the population. Especially, the variance in the pharmacokinetic-dynamic parameter distributions is a measure of the extent of inherent interindividual variability for the particular drug in that population (adults, neonates, etc.). The distribution of residual errors in the observations, with respect to the mean pharmacokinetic or pharmacodynamic model, reflects measurement or assay error, model misspecification, and, more rarely, temporal dependence of the parameters. 

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. 

B., Peck, C., and Danhof, M., A pharmacodynamic Markov mixed-effects model for the effect of temazepam on sleep, Clinical Pharmacology and Therapeutics, Vol. 68, No. 2, 2000, pp. 175-188. 

A population PK evaluation of patients from the safety and efficacy trials can be used to assess the impact of renal function on the disposition of a drug. Special care must be taken that patients with severe renal impairment are adequately represented in the population. The population PK approach assess the impact of various covariates on the disposition of a drug. Non linear mixed effects modeling may be used to model the relationship between various covariates and pharmacokinetic parameters. CLcr as a measure of renal function may be one of the covariates. This type of approach has it advantageous as it involves assessment of the effect of renal impairment on the PK 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. 

MODIFICATION OF THE METHOD Data from individuals drawn from a target population are not completely independent. Concentration time curves (longitudinal data) of a subject are considered to be driven by a functionality depending on individual parameter values. But what is the connection between the same parameters in different persons Parts of it may be described by a functionality depending on demographic variables. In any case, unexplained intra and inter individual random effects remain. Mixed effect modeling clearly distinguishes between these two sources of randomness. 

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