Three methods (multiplicative, additive, and allometric) were developed to extrapolate physiological model parameter distributions across species, specifically from rats to humans. In the multiplicative approach, the rat model parameters are multiplied by the ratio of the mean values between humans and rats. Additive scaling of the distributions is defined by adding the difference between the average human value and the average rat value to each rat value. Finally, allometric scaling relies on established extrapolation relationships using power functions of body weight. A physiologically-based pharmacokinetic model was fitted independently to rat and human benzene disposition data. Human model parameters obtained by extrapolation and by fitting were used to predict the total bone marrow exposure to benzene and the quantity of metabolites produced in bone marrow. We found that extrapolations poorly predict the human data relative to the human model. In addition, the prediction performance depends largely on the quantity of interest. The extrapolated models underpredict bone marrow exposure to benzene relative to the human model. Yet, predictions of the quantity of metabolite produced in bone marrow are closer to the human model predictions. These results indicate that the multiplicative and allometric techniques were able to extrapolate the model parameter distributions, but also that rats do not provide a good kinetic model of benzene disposition in humans.

}, keywords = {benzene, interspecies extrapolation, Monte Carlo parameterization, physiologically-based pharmacokinetics}, doi = {10.1111/j.1539-6924.1996.tb00825.x}, author = {Karen H. Watanabe and Fr{\'e}d{\'e}ric Y. Bois} } @article {11040, title = {Physiological pharmacokinetic analysis using population modeling and informative prior distributions}, journal = {Journal of the American Statistical Association}, volume = {91}, number = {436}, year = {1996}, month = {12/1996}, pages = {1400-1412}, abstract = {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 {11030, title = {Population toxicokinetics of benzene. Environmental Health Perspectives}, journal = {Environmental Health Perspectives}, volume = {104}, year = {1996}, month = {12/1996}, pages = {1405-1411}, chapter = {1405}, 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 benzene in humans. We derive statistical distributions for the parameters of a physiological model of benzene, on the basis of existing data. The model adequately fits both prior physiological information and experimental data. An estimate of the relationship between benzene exposure (up to 10 ppm) and fraction metabolized in the bone marrow is obtained and is shown to be linear for the subjects studied. Our median population estimate for the fraction of benzene metabolized, independent of exposure levels, is 52\% (90\% confidence interval, 47-67\%). At levels approaching occupational inhalation exposure (continuous 1 ppm exposure), the estimated quantity metabolized in the bone marrow ranges from 2 to 40 mg/day.

}, url = {http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1469729/}, author = {Fr{\'e}d{\'e}ric Y. Bois and Elise T. Jackson and Kaija Pekari and Martyn T. Smith} } @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} } @article {1705, title = {Human interindividual variability in metabolism and risk: the example of 4-aminobiphenyl}, journal = {Risk Analysis}, volume = {15}, year = {1995}, month = {04/1195}, pages = {205-213}, chapter = {205}, abstract = {We investigate, through modeling, the impact of interindividual heterogeneity in the metabolism of 4-aminobiphenyl (ABP) and in physiological factors on human cancer risk: A physiological pharmacokinetic model was used to quantify the time course of the formation of the proximate carcinogen, N-hydroxy-4-ABP and the DNA-binding of the active species in the bladder. The metabolic and physiologic model parameters were randomly varied, via Monte Carlo simulations, to reproduce interindividual variability. The sampling means for most parameters were scaled from values developed by Kadlubar et al. (Cancer Res., 51: 4371, 1991) for dogs; variances were obtained primarily from published human data (e.g., measurements of ABP N-oxidation, and arylamine N-acetylation in human liver tissue). In 500 simulations, theoretically representing 500 humans, DNA-adduct levels in the bladder of the most susceptible individuals are ten thousand times higher than for the least susceptible, and the 5th and 95th percentiles differ by a factor of 160. DNA binding for the most susceptible individual (with low urine pH, low N-acetylation and high N-oxidation activities) is theoretically one million-fold higher than for the least susceptible (with high urine pH, high N-acetylation and low N-oxidation activities). The simulations also suggest that the four factors contributing most significantly to interindividual differences in DNA-binding of ABP in human bladder are urine pH, ABP N-oxidation, ABP N-acetylation and urination frequency.

}, keywords = {4-Aminobiphenyl, interindividual variability, Monte Carlo Simulations, population heterogeneity, toxicokinetics}, doi = {10.1111/j.1539-6924.1995.tb00314.x}, author = {Fr{\'e}d{\'e}ric Y. Bois and Gail Krowech and Lauren Zeise} } @article {742, title = {Statistical and regulatory considerations for multiple measures in bioequivalence testing}, journal = {Clinical Research and Regulatory Affairs}, volume = {12}, year = {1995}, pages = {249-265}, chapter = {249}, author = {Walter W. Hauck and Terry Hyslop and Sharon Anderson and Fr{\'e}d{\'e}ric Y. Bois and Thomas N. Tozer} }