Pharmacokinetic-pharmacodynamic model validation data

There are several approaches to population model development that have been discussed in the literature (7, 9, 15-17). The traditional approach has been to make scatterplots of weighted residuals versus covariates and look at trends in the plot to infer some sort of relationship. The covariates identified with the scatterplots are then tested against each of the parameters in a population model, one covariate at a time. Covariates identified are used to create a full model and the final irreducible, given the data, is obtained by backward elimination. The drawback of this approach is that it is only valid for covariates that act independently on the pharmacokinetic (PK) or pharmacokinetic/pharmacodynamic (PK/PD) parameters, and the understanding of the dimensionality of the covariate diata is not taken into account. 

Pharmacokinetic/pharmacodynamic (PK/PD) knowledge creation is the process of building on current understanding of data that is already acquired by generating more data (information) that can be translated into knowledge. It entails the use of (valid) models to synthesize data, estimate inestimable uncertainty, or supplement data for further knowledge acquisition (1, 2). 

Consideration should be given to the selection of relevant animal models or other test systems so that scientifically valid information can be derived. Selection factors can include the pharmacodynamic responsiveness of the model, pharmacokinetic profile, species, strain, gender, and age of the experimental animals, the susceptibility, sensitivity, and reproducibility of the test system and available background data on the substance. Data from humans (e.g., in vitro metabolism), when available, should also be considered in the test system selection. 

Biopharmaceutical research often involves the collection of repeated measures on experimental units (such as patients or healthy volunteers) in the form of longitudinal data and/or multilevel hierarchical data. Responses collected on the same experimental unit are typically correlated and, as a result, classical modeling methods that assume independent observations do not lead to valid inferences. Mixed effects models, which allow some or all of the parameters to vary with experimental unit through the inclusion of random effects, can flexibly account for the within-unit correlation often observed with repeated measures and provide proper inference. This chapter discusses the use of mixed effects models to analyze biopharmaceutical data, more specihcally pharmacokinetic (PK) and pharmacodynamic (PD) data. Different types of PK and PD data are considered to illustrate the use of the three most important classes of mixed effects models linear, nonlinear, and generalized linear. 

Model refinement and validation for both the chltnpyrifos and the diazinon PBPK/PD models wa.s accomplished by conducting a scries of in vivo pharmacokinetic and pharmacodynamic studies in the rat and by evaluating the capability of the model to accurately simulate in vivo data published in the literature. The experimental details are fully described in Timchalk et ai (2002b) and Poet et at. (2004). In brief, these studies involved an acute oral exposure to chlorpyrifos or diazinon and the blood time course of the parent compounds and metabolites was determined, as well as the time course for the cholinesterase inhibition in several tissues. Representative results and model simulations are presented in Fig. 12 and 13 for the pharmacokinetic and pharmacodynamic response in rats following comparable oral doses (50 and 100 mg/kg) of chlorpyrifos and diazinon, respectively, The overall response was fairly comparable for these two insecticides, and the models reasonably simulated both dosimetry and the dose-dependent cholinesterase inhibition. These results arc very consistent with a fairly rapid oral absorption for both insecticides and subsequent metabolism and distribution of the active oxon metabolites. Figure 14 illustrates the capability of the diazinon PBPK/PD model to simulate rodent dosimetry data from the open literature and the capability of the model to accommodate alternative exposure routes (Poet et ai, 2004). In these examples, the time course of diazinon in plasma and cholinesterase inhibition in tissues (i.e.. blood,... 

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