Population pharmacokinetics model validation

There are many approaches used for PPK model development in the literature. These range from modeling population pharmacokinetic data without exploratory data analysis to approaches that incorporate the latter. Excellent examples of population pharmacokinetic model development, which incorporate exploratory data analysis into population pharmacokinetic model development, can be found in the articles by Ette and Ludden and Mandema, Verotta, and Sheiner Excellent reviews on the validation of PPK models are available in the literature. Thus, validation will not be discussed. 

Bruno, R., Vivier, N., Vergniol, J.C., De Phillips, S.L., Mon-tay, G., and Shiener, L.B. A population pharmacokinetic model for docetaxel (Taxotere) Model building and validation. Journal of Pharmacokinetics and Biopharmaceutics 1996 24 153-172. 

Gibiansky, L., Gibiansky, E., Yu, R.Z., and Geary, R.S. ISIS 2302 Validation of the population pharmacokinetic model and PK/PD analysis. Presented at American Association of Pharmaceutical Scientists Annual Meeting, Boston MA, 2001. 

Population pharmacokinetics usually consists of three steps exploratory data analysis, population pharmacokinetic model development, and model validation. 

Validation Determine predictive performance of the population pharmacokinetic model. 

In an external validation, data from a study other than that used to build the model are used as the validation or test data. The FDA guidance states that this is the most stringent means of validating a population pharmacokinetic model. Indeed, the performance of the hnal model developed on a given data set when projected onto data from a separate study goes a long way toward the establishment of a credible model and the conhdence in the recommendations based on such models. 

Bruno, R. N., et al., A population pharmacokinetic model for Docetaxel (Taxotere) model building and validation, J. Pharmacokinet. Biopharm., 24 153-172, 1996. 

Vermes A et al. Population pharmacokinetics of flucytosine comparison and validation of three models using STS, NPEM, and NONMEM. Therapeutic Drug Monitoring, 2000, 22 676-687. 

Bootstrapping is the resampling with replacement method that has the advantage of using the entire data set. It has been demonstrated to be useful in PMM validation (1,3, 22) and has the same advantages as do other internal validation methods in that it obviates the need for collecting data from a test population. Bootstrapping has been applied to population pharmacokinetic (PPK) model development, stability check and evaluation, and bias estimation (1-3, 25). 

Phillips, L., Grasela, T.H., Agnew, J.R., Ludwig, E.A., and Thompson, G.A. A population pharmacokinetic-pharma-codynamic analysis and model validation of azimilide. Clinical Pharmacology and Therapeutics 2001 70 370-383. 

Olsson Gisleskog, P. et al., Validation of a population pharmacokinetic/pharmacody-namic model for 5a-reductase inhibitors, Ear. J. Pharm. Set, 8 291-299, 1999. 

Cross-validation is a leave-one-out or leave-some-out validation technique in which part of the data set is reserved for validation. Essentially, it is a data-splitting technique. The distinction lies within the manner of the split and the number of data sets evaluated. In the strict sense a -fold cross-validation involves the division of available data into k subsets of approximately equal size. Models are built k times, each time leaving out one of the subsets from the build. The k models are evaluated and compared as described previously, and a hnal model is dehned based on the complete data set. Again, this technique as well as all validation strategies offers flexibility in its application. Mandema et al. successfully utilized a cross-validation strategy for a population pharmacokinetic analysis with oxycodone in which a portion of the data was reserved for an evaluation of predictive performance. Although not strictly a cross-validation, it does illustrate the spirit of the approach. 

Phase I studies evaluate the pharmacokinetics and safety of the drug in a small number (tens) of healthy volunteers. Phase I studies are sometimes conducted in a small patient population (Proof of Concept studies) with a specific objective such as the validation of the relevance of preclinical models in man. The purpose of these studies may be the rapid elimination of potential failures from the pipeline, definition of biological markers for efficacy or toxicity, or demonstration of early evidence of efficacy. These studies have a potential go/no-go decision criteria such as safety, tolerability, bioavailability/PK, pharmacodynamics, and efficacy. Dosage forms used in Phase I or Proof of Concept studies must be developed with the objectives of the clinical study in mind. 

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]. 

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. 

The bootstrap has been used in pharmacokinetics sporadically on a largely theoretical basis and has not really been implemented on a routine basis, except in the case of validating population models. Bonate (1993), which was later improved upon by Jones et al. (1996), showed how the bootstrap can be applied to obtain CIs for individual drug concentrations, which could be of importance in therapeutic drug monitoring. Bonate later... 

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