Developing a Hierarchical Error Model Structure to Appropriately Account for Variability in Parameter Estimation Techniques Used in PBPK Models. A. S. Collins, Chemical Industry Institute of Toxicology, Research Triangle Park, NC; T. B. Kepler and M. Davidian, North Carolina State University, Raleigh, NC
Historically, many physiologically based pharmacokinetic (PBPK) models have been analyzed through commercial simulation and optimization software packages such as SimuSolv® and ACSL Tox®. During the parameter estimation process, model parameters are adjusted to maximize the value of the objective function, the log likelihood function (LLF). Parameter estimation of these adjustable PBPK model parameters is usually based on repeated measurement data from multiple individuals. Under the normality assumption, the parameter estimation method implemented in SimuSolv® or ACSL Tox® is correct for data from a single individual when statistical inference is focused solely on that individual. When data from multiple individuals are pooled, a problem arises in using these software packages. Used to derive the LLF, the error model in SimuSolv® and ACSL Tox® is not appropriate because it confounds two sources of variation: intraindividual variability, which is variation among measurements within a given individual, and interindividual variability, which is random variation among individuals. If sources of variation are not taken into proper account, misleading estimates of the parameters and uncertainty in those estimates may result. These two variation components can be taken into appropriate account in a statistical hierarchical or staged model. We used the PBPK models for tert-amyl methyl ether (TAME) and tert-amyl alcohol (TAA) to contrast inference based on the incorrect error model implemented in these software packages and inference based on a hierarchical model. To fit a hierarchical model, maximization of a more complex objective function than that found in SimuSolv® and ACSL Tox® is required. SAS® software is very efficient in implementing hierarchical model fitting for PBPK models. With a hierarchical approach to current PBPK models, the model that most accurately accounts for variation in existing data can be developed, which will allow a more precise extrapolation to humans.
Ms. A. S. Collins is supported by an EPA Science To Achieve Results Fellowship.
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