Statistical Estimation of Physiologically-based Pharmacokinetic Models: Identifiability, Variation, and Uncertainty with an Illustration of Chronic Exposure to Dioxin and Dioxin-like-compounds.

Assessment of human exposure to environmental chemicals is inherently subject to uncertainty and variability. There are data gaps concerning the inventory, source, duration, and intensity of exposure as well as knowledge gaps regarding pharmacokinetics in general. These gaps result in uncertainties in exposure assessment. The uncertainties compound further with variabilities due to population variations regarding stage of life, life style, and susceptibility, etc. Use of physiologically-based pharmacokinetic (PBPK) models promises to reduce the uncertainties and enhance extrapolation between species, between routes, from high to low dose, and from acute to chronic exposure. However, fitting PBPK models is challenging because of a large number of biochemical and physiological parameters to be estimated. Many of these model parameters are non-identifiable in that their estimates cannot be uniquely determined using statistical criteria. In practice some parameters are fixed in value and some determined through mathematical calibration or computer simulation. These estimated values are subject to substantial uncertainties. The first part of this paper illustrates the use of iteratively-reweighted-nonlinear-least-squares for fitting pharmacokinetic (PK) models, highlighting some common difficulties in obtaining statistical estimates of non-identifiable parameters and use bootstrap confidence interval to quantify uncertainties. Statistical estimation of parameters in physiologically based pharmacokinetic (PBPK) models is a relatively new area of research. Over the past decade or so PBPK models have become important and valuable tools in risk assessment as these models are used to describe the absorption, distribution, metabolism, and excretion of xenobiotics in a biological system such as the human or rat. Because these models incorporate information on biological processes, they are well equipped to describe the kinetic behaviors of chemicals and are useful for extrapolation across dose routes, between species, from high-to-low-doses, and across exposure scenarios. A PBPK model has been developed based on published models in the literature to describe the absorption, distribution, metabolism, and excretion of Dioxin and dioxin like compounds (DLCs) in the rat. Data from the National Toxicology Program (NTP) two year experiment TR-526 is used to illustrate model fitting and statistical estimation of the parameters. Integrating statistical methods into risk assessments is the most efficient way to characterize the variation in parameter values. In this dissertation a Markov Chain Monte Carlo (MCMC) method is used to estimate select parameters of the system and to describe the variation of the select parameters