Population Pharmacokinetic Models: Parametric and Nonparametric Approaches

Population modeling seeks to evaluate the contributions of interindividual and intraindividual variability, based on the raw subject data and the assay error, and to describe the findings in terms that are useful both for research and for optimal patient care. With parametric models, the probability distributions of each PK/PD parameter are described in terms of other parameters such as means and covariances which define the assumed shape of these distributions. Commonly used distributions are the normal or lognormal ones. The parameter values found are the single best estimates such as mean, median, or mode, which are felt to be the best estimators of the central tendency for each such distribution. Nonparametric models have a different flavor. No such parametric assumptions are made about the assumed shape of a parameter distribution, nor is a single parameter value what is really sought. The approach proceeds rather from the point of view that the very best population model possible would be the correct structural model, plus the entire collection of each subject's exactly known parameter values, if it were somehow possible to know them. Nonparametric methods estimate essentially one set of parameter values for each subject, along with an estimated probability for each such set. The richness of the method is in the ability to obtain not simply a single estimate for the central tendency and one for the dispersion, but rather to estimate the entire population parameter joint density. Optimal population modeling currently begins by determining the assay error pattern explicitly over its working range. One then uses a parametric population modeling approach to separate intrafrom inter-individual variability. Having this information, one can then use a nonparametric approach to obtain the entire estimated population parameter joint density.