We describe a general approach using Bayesian analysis for the estimation of parameters in physiological pharmacokinetic models. The chief statistical difficulty in estimation with these models is that any physiological model that is even approximately realistic will have a large number of parameters, often comparable to the number of observations in a typical pharmacokinetic experiment (e.g., 28 measurements and 15 parameters for each subject). In addition, the parameters are generally poorly identified, akin to the well\known ill-conditioned problem of estimating a mixture of declining exponentials. Our modeling includes (a) hierarchical population modeling, which allows partial pooling of information among different experimental subjects; (b) a pharmacokinetic model including compartments for well-perfused tissues, poorly perfused tissues, fat, and the liver; and (c) informative prior distributions for population parameters, which is possible because the parameters represent real physiological variables. We discuss how to estimate the models using Bayesian posterior simulation, a method that automatically includes the uncertainty inherent in estimating such a large number of parameters. We also discuss how to check model fit and sensitivity to the prior distribution using posterior predictive simulationY We illustrate the application to the toxicokinetics of tetrachloroethylene (perchloroethylene [PERC]), the problem that motivated this work.

}, keywords = {bayesian methods, hierarchical models, informative prior distributions, markov chain simulation, pharmacokinetics, posterior predictive checks, sensitivity analysis, tetrachloroethylene, toxicokinetics}, doi = {10.2307/2291566}, author = {Andrew Gelman and Fr{\'e}d{\'e}ric Y. Bois and Jiming Jiang} } @article {11029, title = {Population toxicokinetics of tetrachloroethylene}, journal = {Archives of Toxicology}, volume = {70}, year = {1996}, pages = {347-355}, abstract = {In assessing the distribution and metabolism of toxic compounds in the body, measurements are not always feasible for ethical or technical reasons. Computer modeling offers a reasonable alternative, but the variability and complexity of biological systems pose unique challenges in model building and adjustment. Recent tools from population pharmacokinetics, Bayesian statistical inference, and physiological modeling can be brought together to solve these problems. As an example, we modeled the distribution and metabolism of tetrachloroethylene (PERC) in humans. We derive statistical distributions for the parameters of a physiological model of PERC, on the basis of data from Monster et al. (1979). The model adequately fits both prior physiological information and experimental data. An estimate of the relationship between PERC exposure and fraction metabolized is obtained. Our median population estimate for the fraction of inhaled tetrachloroethylene that is metabolized, at exposure levels exceeding current occupational standards, is 1.5\% [95\% confidence interval (0.52\%, 4.1\%)]. At levels approaching ambient inhalation exposure (0.001 ppm), the median estimate of the fraction metabolized is much higher, at 36\% [95\% confidence interval (15\%, 58\%)]. This disproportionality should be taken into account when deriving safe exposure limits for tetrachloroethylene and deserves to be verified by further experiments.

}, keywords = {human metabolism, pharmacokinetics, population toxicokinetics, tetrachloroethylene}, author = {Fr{\'e}d{\'e}ric Y. Bois and Andrew Gelman and Jiming Jiang and Don Maszle and Lauren Zeise and George Alexeeff} }