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 wellknown 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.

10abayesian methods10ahierarchical models10ainformative prior distributions10amarkov chain simulation10apharmacokinetics10aposterior predictive checks10asensitivity analysis10atetrachloroethylene10atoxicokinetics1 aGelman, Andrew1 aBois, Frédéric, Y.1 aJiang, Jiming uhttps://indoor.lbl.gov/publications/physiological-pharmacokinetic