Nonparametric density estimation applied to population pharmacokinetics

Kinetic parameters are estimated to assess absorption, distribution, metabolism, and elimination of a drug in a subject. In a group of subjects, pharmacokinetic population studies are developed to describe the variability and to detect particular subsets by establishing the relationships between kinetic parameters and easily measurable subject characteristics, the covariates (age, body weight, etc.). The usually proposed methods are based on linear regression equations relating kinetic parameters to the covariates. We propose to measure these dependencies and describe the interindividual variability through the joint probability density function. This function is estimated by a nonparametric method superposing potential functions or kernels over the sample. In this estimation, the Shannon information theory was applied to determine the number of individuals needed to describe the variability reliably and to screen informative covariates with respect to the kinetic parameters. This approach was used to obtain the nonparametric conditional probability density functions of the kinetic parameters, given the covariates. These functions supplied prior information for a Bayesian estimation. The feasibility of the global approach was illustrated by a simulation in which nonlinear relations link covariates and pharmacokinetic parameters. The performance of this new estimator using covariates was compared with that of the usual Bayesian estimation.