Population pharmacokinetics nonlinear mixed-effects

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. 

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]. 

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. 

The nonlinear mixed-effects method is depicted in Figure 10.4 and is described here using the conventions of the NONMEM software (2, 3) and the description by Vozeh ef a/. (3). It is based on the principle that the individual pharmacokinetic parameters of a patient population arise from a distribution that can be described by the population mean and the interindividual variance. Each individual pharmacokinetic parameter can be expressed as a population mean and a deviation, typical for an individual. The deviation is the difference between the population mean and the individual parameter and is assumed to be... 

Although population pharmacokinetic parameters have been estimated either by fitting all individuals data together as if there were no kinetic differences, or by fitting each individual s data separately and then combining the individual parameter estimates, these methods have certain theoretical problems that can only be aggravated when the deficiencies of typical clinical data are present. The nonlinear mixed-effect analysis avoids many of these deficiencies and... 

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. 

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 ... 

S. Retout and E. Mentre, Eurther developments of the Fisher information matrix in nonlinear mixed effects models with evaluation in population pharmacokinetics. J Biop harm Stat 13 209-227 (2003). 

The approach involves a semimechanistic or mechanistic model that describes the joint probability of the time of remedication and the pain relief score (which is related to plasma drug concentrations). This joint probability can be written as the product of the conditional probability of the time of remedication, given the level of pain relief and the probability of the pain relief score. First, a population pharmacokinetic (PK) model is developed using the nonlinear mixed effects modeling approach (16-19) (see also Chapters 10 and 14 of this book). With this approach both population (average) and random (inter- and intraindividual) effects parameters are estimated. When the PK model is linked to an effect (pharmacodynamic (PD) model), the effect site concentration (C ) as defined by Sheiner et al. (20) can be obtained. The effect site concentration is useful in linking dose to pain relief and subsequently to the decision to remedicate. 

Nonlinear mixed effects models are similar to linear mixed effects models with the difference being that the function under consideration f(x, 0) is nonlinear in the model parameters 0. Population pharmacokinetics (PopPK) is the study of pharmacokinetics in the population of interest and instead of modeling data from each individual separately, data from all individuals are modeled simultaneously. To account for the different levels of variability (between-subject, within-subject, interoccasion, residual, etc.), nonlinear mixed effects models are used. For the remainder of the chapter, the term PopPK will be used synonymously with nonlinear mixed effects models, even though the latter covers a richer class of models and data types. Along with PopPK is population pharmacodynamics (PopPD), which is the study of a drug s effect in the population of interest. Often PopPK and PopPD are combined into a singular PopPK-PD analysis. 

In the last chapter, the theory behind nonlinear mixed effects models was introduced. In this chapter, practical issues related to nonlinear mixed effects modeling will be introduced. Due to space considerations not all topics will be given the coverage they deserve, e.g., handling missing data. What is intended is a broad coverage of problems and issues routinely encountered in actual population pharmacokinetics (PopPK) analyses. The reader is referred to the original source material and references for further details. 

Retout, S., Mentre, F., and Bruno, R. Fisher information matrix for nonlinear mixed-effects models Evaluation and application for optimal design of enoxaparin population pharmacokinetics. Statistics in Medicine 2002 30 2623-2629. 

All the objective functions shown in Table 15.1 are derived from a least-squares regression approach as previously described, whereas the estimation method more commonly used in population pharmacokinetics and nonlinear mixed effect modeling in general is based on a maximum likelihood (ML) approach. ML is an alternative to the least-squares objective function it seeks to maximize the likelihood or log-likelihood function (or to minimize the negative log-likelihood function). In general terms, the likelihood function is defined as... 

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