Impact of physiologically based pharmacokinetic modeling on benchmark dose calculations for TCDD-induced biochemical responses

Approaches for applications of physiologically based pharmacokinetic models in risk assessment

Physiologically based pharmacokinetic (PBPK) models are particularly useful for simulating exposures to environmental toxicants for which, unlike pharmaceuticals, there is often little or no human data available to estimate the internal dose of a putative toxic moiety in a target tissue or an appropriate surrogate. This article reviews the current state of knowledge and approaches for application of PBPK models in the process of deriving reference dose, reference concentration, and cancer risk estimates. Examples drawn from previous U.S. Environmental Protection Agency (EPA) risk assessments and human health risk assessments in peer-reviewed literature illustrate the ways and means of using PBPK models to quantify the pharmacokinetic component of the interspecies and intraspecies uncertainty factors as well as to conduct route to route, high dose to low dose and duration extrapolations. The choice of the appropriate dose metric is key to the use of the PBPK models for the various applications in risk assessment. Issues related to whether uncertainty factors are most appropriately applied before or after derivation of human equivalent dose (or concentration) continue to be explored. Scientific progress in the understanding of life stage and genetic differences in dosimetry and their impacts on variability in susceptibility, as well as ongoing development of analytical methods to characterize uncertainty in PBPK models, will make their use in risk assessment increasingly likely. As such, it is anticipated that when PBPK models are used to express adverse tissue responses in terms of the internal target tissue dose of the toxic moiety rather than the external concentration, the scientific basis of, and confidence in, risk assessments will be enhanced.

Comparing experimental designs for benchmark dose calculations for continuous endpoints

The BMD (benchmark dose) method that is used in risk assessment of chemical compounds was introduced by Crump (1984) and is based on dose-response modeling. To take uncertainty in the data and model fitting into account, the lower confidence bound of the BMD estimate (BMDL) is suggested to be used as a point of departure in health risk assessments. In this article, we study how to design optimum experiments for applying the BMD method for continuous data. We exemplify our approach by considering the class of Hill models. The main aim is to study whether an increased number of dose groups and at the same time a decreased number of animals in each dose group improves conditions for estimating the benchmark dose. Since Hill models are nonlinear, the optimum design depends on the values of the unknown parameters. That is why we consider Bayesian designs and assume that the parameter vector has a prior distribution. A natural design criterion is to minimize the expected variance of the BMD estimator. We present an example where we calculate the value of the design criterion for several designs and try to find out how the number of dose groups, the number of animals in the dose groups, and the choice of doses affects this value for different Hill curves. It follows from our calculations that to avoid the risk of unfavorable dose placements, it is good to use designs with more than four dose groups. We can also conclude that any additional information about the expected dose-response curve, e.g., information obtained from studies made in the past, should be taken into account when planning a study because it can improve the design.

Estimated cancer risk of dioxins to humans using a bioassay and physiologically based pharmacokinetic model

The health risk of dioxins and dioxin-like compounds to humans was analyzed quantitatively using experimental data and mathematical models. To quantify the toxicity of a mixture of three dioxin congeners, we calculated the new relative potencies (REPs) for 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD), 1,2,3,7,8-pentachlorodibenzo-p-dioxin (PeCDD), and 2,3,4,7,8- pentachlorodibenzofuran (PeCDF), focusing on their tumor promotion activity. We applied a liver foci formation assay to female SD rats after repeated oral administration of dioxins. The REP of dioxin for a rat was determined using dioxin concentration and the number of the foci in rat liver. A physiologically based pharmacokinetic model (PBPK model) was used for interspecies extrapolation targeting on dioxin concentration in liver. Toxic dose for human was determined by back-estimation with a human PBPK model, assuming that the same concentration in the target tissue may cause the same level of effect in rats and humans, and the REP for human was determined by the toxic dose obtained. The calculated REPs for TCDD, PeCDD, and PeCDF were 1.0, 0.34, and 0.05 for rats, respectively, and the REPs for humans were almost the same as those for rats. These values were different from the toxic equivalency factors (TEFs) presented previously (Van den Berg, M., Birnbaum, L., Bosveld, A.T.C., Brunstrom, B., Cook, P., Feeley, M., Giesy, J.P., Hanberg, A., Hasegawa, R., Kennedy, S.W., Kubiak, T., Larsen, J.C., Rolaf van Leeuwen, F.X., Liem, A.K.D., Nolt, C., Peterson, R.E., Poellinger. L., Safe, S., Schrenk, D., Tillitt, D, Tysklind, M., Younes, M., Waern, F., Zacharewski, T., 1998. Toxic equivalency factors (TEFs) for PCBs, PCDDs, PCDFs for humans and wildlife. Environ. Health Perspect. 106, 775-792). The relative risk of excess liver cancer for Japanese people in general was 1.7-6.5 x 10(-7) by TCDD only, and 2.9-11 x 10(-7) by the three dioxins at the present level of contamination.

Analysis of nonlinear regression models: a cautionary note

Regression models are routinely used in many applied sciences for describing the relationship between a response variable and an independent variable. Statistical inferences on the regression parameters are often performed using the maximum likelihood estimators (MLE). In the case of nonlinear models the standard errors of MLE are often obtained by linearizing the nonlinear function around the true parameter and by appealing to large sample theory. In this article we demonstrate, through computer simulations, that the resulting asymptotic Wald confidence intervals cannot be trusted to achieve the desired confidence levels. Sometimes they could underestimate the true nominal level and are thus liberal. Hence one needs to be cautious in using the usual linearized standard errors of MLE and the associated confidence intervals.

Identification of a Critical Dose Level for Risk Assessment: Developments in Benchmark Dose Analysis of Continuous Endpoints

The benchmark dose (BMD) method has been recommended to replace the no-observed-adverse-effect-level (NOAEL) approach in health risk assessment of chemical substances. In the present article, developments in BMD analysis from continuous experimental data are proposed. The suggested approach defines the BMD as the dose at which the slope of the S-shaped dose-response relationship changes the most in the low-dose region. This dose resides in a region where the sensitivity to chemical exposure may start to change noticeably. It is shown that the response (defined as a percent change relative to the magnitude, or size, of response) corresponding to the dose where the slope changes the most depends on the geometrical shape of the dose-response curve; the response becomes lower as the curve becomes more asymmetrical and threshold-like in the low-dose region. Given a symmetrical case, described by the Hill function, the response associated with the critical dose level becomes 21% (defined as a percent change relative to the magnitude, or size, of response). According to a limiting case of asymmetry and threshold-like characteristics, reflected by a Gompertz curve, the response corresponding to the dose of interest becomes as low as 7.3% (defined as a percent change relative to the magnitude, or size, of response). Use of a response in the range of 5-10% when estimating the BMD conservatively accounts for uncertainties associated with the proposed strategy, and may be appropriate in a risk assessment point of view. The present investigation also indicated that a BMD defined according to the suggested procedure may be estimated more precisely relative to BMDs defined under other approaches for continuous data.