Population pharmacokinetic and dynamic models: Parametric (P) and nonparametric (NP)approaches

With P models, the probability distributions of each PK/PD model parameter are described as means and covariances, as estimators of the central tendency and the dispersion. With NP models, however, no assumptions at all are made about the shape of the parameter distributions. This robust approach has the point of view, that the very best (the ideal) population model 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. NP methods resolve the results into tip to one set of parameter values for each subject, along with an estimated probability for each parameter set. The strength of the method is its ability to estimate the entire population parameter joint density with maximum likelihood. Optimal population modeling currently begins by determining the assay error pattern explicitly over its working range. Next, one currently uses a P population modeling method to separate intra- from inter-individual variability. One can then use this information in an NP approach to estimate the entire population parameter discrete joint density. NP models lend themselves naturally to "multiple model" (MM) dosage design for maximally precise regimens for optimal patient care.