Statistical issues in toxicokinetic modeling: A Bayesian perspective

Determining the relationship between an exposure and the resulting target tissue dose is a critical issue encountered in quantitative risk assessment (QRA). Classical or physiologically based toxicokinetic (PBTK) models can be useful in performing that task. Interest in using these models to improve extrapolations between species, routes, and exposure levels in ORA has therefore grown considerably in recent years. In parallel, PBTK models have become increasingly sophisticated. However, development of a strong statistical foundation to support PBTK model calibration and use has received little attention. There is a critical need for methods that address the uncertainties inherent in toxicokinetic data and the variability in the human populations for which risk predictions are made and to take advantage of a priori information on parameters during the calibration process. Natural solutions to these problems can be found in a Bayesian statistical framework with the help of computational techniques such as Markov chain Monte Carlo methods. Within such a framework, we have developed an approach to toxicokinetic modeling that can be applied to heterogeneous human or animal populations. This approach also expands the possibilities for uncertainty analysis. We present a review of these efforts and other developments in these areas. Appropriate statistical treatment of uncertainty and variability within the modeling process will increase confidence in model results and ultimately contribute to an improved scientific basis for the estimation of occupational and environmental health risks.