Modeling Benzene Pharmacokinetics Across Three Sets of Animal Data: Parametric Sensitivity and Risk Implications

Typically, the uncertainty affecting the parameters of physiologically based pharmacokinetic (PBPK) models is ignored because it is not currently practical to adjust their values using classical parameter estimation techniques. This issue of parametric variability in a physiological model of benzene pharmacokinetics is addressed in this paper. Monte Carlo simulations were used to study the effects on the model output arising from variability in its parameters. The output was classified into two categories, depending on whether the output of the model on a particular run was judged to be generally consistent with published experimental data. Statistical techniques were used to examine sensitivity and interaction in the parameter space. The model was evaluated against the data from three different experiments in order to test for the structural adequacy of the model and the consistency of the experimental results. The regions of the parameter space associated with various inhalation and gavage experiments are distinct, and the model as presently structured cannot adequately represent the outcomes of all experiments. Our results suggest that further effort is required to discern between the structural adequacy of the model and the consistency of the experimental results. The impact of our results on the risk assessment process for benzene is also examined.     

Physiologically-Based Pharmacokinetic Modeling of Benzene in Humans: A Bayesian Approach

Benzene is myelotoxic and leukemogenic in humans exposed at high doses (>1 ppm, more definitely above 10 ppm) for extended periods. However, leukemia risks at lower exposures are uncertain. Benzene occurs widely in the work environment and also indoor air, but mostly below 1 ppm, so assessing the leukemia risks at these low concentrations is important. Here, we describe a human physiologically-based pharmacokinetic (PBPK) model that quantifies tissue doses of benzene and its key metabolites, benzene oxide, phenol, and hydroquinone after inhalation and oral exposures. The model was integrated into a statistical framework that acknowledges sources of variation due to inherent intra- and interindividual variation, measurement error, and other data collection issues. A primary contribution of this work is the estimation of population distributions of key PBPK model parameters. We hypothesized that observed interindividual variability in the dosimetry of benzene and its metabolites resulted primarily from known or estimated variability in key metabolic parameters and that a statistical PBPK model that explicitly included variability in only those metabolic parameters would sufficiently describe the observed variability. We then identified parameter distributions for the PBPK model to characterize observed variability through the use of Markov chain Monte Carlo analysis applied to two data sets. The identified parameter distributions described most of the observed variability, but variability in physiological parameters such as organ weights may also be helpful to faithfully predict the observed human-population variability in benzene dosimetry.     

Linking Indoor Air and Pharmacokinetic Models to Assess Tetrachloroethylene Risk

Physiologically based pharmacokinetic (PBPK) models describing the uptake, metabolism, and excretion of xenobiotic compounds are now proposed for use in regulatory health-risk assessments. In this study we investigate the extent of PCE metabolism arising from domestic respiratory exposure to tetrachloroethylene (PCE) from ground water, as predicted using a PBPK model. Indoor exposure patterns we use as input to the PBPK model are realistic ones generated from a three-compartment model describing volatilization of PCE from domestic water into household air. Values we use for the metabolic parameters of the PBPK model are estimated from data on urinary metabolites in workers exposed to PCE. It is shown that for respiratory PCE exposure due to typical levels of PCE in ground water, use of time-weighted average air concentrations with a steady-state PBPK model yields estimates of total metabolized PCE similar to those obtained using completely dynamic modeling, despite considerable uncertainty in key exposure- and metabolic-model parameters. These findings suggest that, for PCE, risk estimation taking pharmacokinetics into account may be accomplished using a simple analytic approach.     

Sensitivity of Physiologically Based Pharmacokinetic Models to Variation in Model Parameters: Methylene Chloride

The parameters in a physiologically based pharmacokinetic (PBPK) model of methylene chloride were varied systematically, and the resulting variation in a number of model outputs was determined as a function of time for mice and humans at several exposure concentrations. The importance of the various parameters in the model was highly dependent on the conditions (concentration, species) for which the simulation was performed and the model output (dose surrogate) being considered. Model structure also had a significant impact on the results. For sensitivity analysis, particular attention must be paid to conservation equations to ensure that the variational calculations do not alter mass balance, introducing extraneous effects into the model. All of the normalized sensitivity coefficients calculated in this study ranged between −1.12 and 1, and most were much less than 1 in absolute value, indicating that individual input errors are not greatly amplified in the outputs. In addition to ranking parameters in terms of their impact on model predictions, time-dependent sensitivity analysis can also be used as an aid in the design of experiments to estimate parameters by predicting the experimental conditions and sampling points which will maximize parameter identifiability.     

Symmetry, Identifiability, and Prediction Uncertainties in Multistage Clonal Expansion (MSCE) Models of Carcinogenesis

Many models of exposure-related carcinogenesis, including traditional linearized multistage models and more recent two-stage clonal expansion (TSCE) models, belong to a family of models in which cells progress between successive stages-possibly undergoing proliferation at some stages-at rates that may depend (usually linearly) on biologically effective doses. Biologically effective doses, in turn, may depend nonlinearly on administered doses, due to PBPK nonlinearities. This article provides an exact mathematical analysis of the expected number of cells in the last ("malignant") stage of such a "multistage clonal expansion" (MSCE) model as a function of dose rate and age. The solution displays symmetries such that several distinct sets of parameter values provide identical fits to all epidemiological data, make identical predictions about the effects on risk of changes in exposure levels or timing, and yet make significantly different predictions about the effects on risk of changes in the composition of exposure that affect the pharmacodynamic dose-response relation. Several different predictions for the effects of such an intervention (such as reducing carcinogenic constituents of an exposure) that acts on only one or a few stages of the carcinogenic process may be equally consistent with all preintervention epidemiological data. This is an example of nonunique identifiability of model parameters and predictions from data. The new results on nonunique model identifiability presented here show that the effects of an intervention on changing age-specific cancer risks in an MSCE model can be either large or small, but that which is the case cannot be predicted from preintervention epidemiological data and knowledge of biological effects of the intervention alone. Rather, biological data that identify which rate parameters hold for which specific stages are required to obtain unambiguous predictions. From epidemiological data alone, only a set of equally likely alternative predictions can be made for the effects on risk of such interventions.     

Development of a Screening Approach to Interpret Human Biomonitoring Data on Volatile Organic Compounds: Reverse Dosimetry on Biomonitoring Data for Trichloroethylene

A screening approach is developed for volatile organic compounds (VOCs) to estimate exposures that correspond to levels measured in fluids and/or tissues in human biomonitoring studies. The approach makes use of a generic physiologically-based pharmacokinetic (PBPK) model coupled with exposure pattern characterization, Monte Carlo analysis, and quantitative structure property relationships (QSPRs). QSPRs are used for VOCs with minimal data to develop chemical-specific parameters needed for the PBPK model. The PBPK model is capable of simulating VOC kinetics following multiple routes of exposure, such as oral exposure via water ingestion and inhalation exposure during shower events. Using published human biomonitoring data of trichloroethylene (TCE), the generic model is evaluated to determine how well it estimates TCE concentrations in blood based on the known drinking water concentrations. In addition, Monte Carlo analysis is conducted to characterize the impact of the following factors: (1) uncertainties in the QSPR-estimated chemical-specific parameters; (2) variability in physiological parameters; and (3) variability in exposure patterns. The results indicate that uncertainty in chemical-specific parameters makes only a minor contribution to the overall variability and uncertainty in the predicted TCE concentrations in blood. The model is used in a reverse dosimetry approach to derive estimates of TCE concentrations in drinking water based on given measurements of TCE in blood, for comparison to the U.S. EPA's Maximum Contaminant Level in drinking water. This example demonstrates how a reverse dosimetry approach can be used to facilitate interpretation of human biomonitoring data in a health risk context by deriving external exposures that are consistent with a biomonitoring data set, thereby permitting comparison with health-based exposure guidelines.     

Use of Markov Chain Monte Carlo Analysis with a Physiologically-Based Pharmacokinetic Model of Methylmercury to Estimate Exposures in U.S. Women of Childbearing Age

A Bayesian approach, implemented using Markov Chain Monte Carlo (MCMC) analysis, was applied with a physiologically‐based pharmacokinetic (PBPK) model of methylmercury (MeHg) to evaluate the variability of MeHg exposure in women of childbearing age in the U.S. population. The analysis made use of the newly available National Health and Nutrition Survey (NHANES) blood and hair mercury concentration data for women of age 16–49 years (sample size, 1,582). Bayesian analysis was performed to estimate the population variability in MeHg exposure (daily ingestion rate) implied by the variation in blood and hair concentrations of mercury in the NHANES database. The measured variability in the NHANES blood and hair data represents the result of a process that includes interindividual variation in exposure to MeHg and interindividual variation in the pharmacokinetics (distribution, clearance) of MeHg. The PBPK model includes a number of pharmacokinetic parameters (e.g., tissue volumes, partition coefficients, rate constants for metabolism and elimination) that can vary from individual to individual within the subpopulation of interest. Using MCMC analysis, it was possible to combine prior distributions of the PBPK model parameters with the NHANES blood and hair data, as well as with kinetic data from controlled human exposures to MeHg, to derive posterior distributions that refine the estimates of both the population exposure distribution and the pharmacokinetic parameters. In general, based on the populations surveyed by NHANES, the results of the MCMC analysis indicate that a small fraction, less than 1%, of the U.S. population of women of childbearing age may have mercury exposures greater than the EPA RfD for MeHg of 0.1 μg/kgg/day, and that there are few, if any, exposures greater than the ATSDR MRL of 0.3 μgg/kgg/day. The analysis also indicates that typical exposures may be greater than previously estimated from food consumption surveys, but that the variability in exposure within the population of U.S. women of childbearing age may be less than previously assumed.     

A Trichloroethylene Risk Assessment Using a Monte Carlo Analysis of Parameter Uncertainty in Conjunction with Physiologically-Based Pharmacokinetic Modeling

A Monte Carlo simulation is incorporated into a risk assessment for trichloroethylene (TCE) using physiologically-based pharmacokinetic (PBPK) modeling coupled with the linearized multistage model to derive human carcinogenic risk extrapolations. The Monte Carlo technique incorporates physiological parameter variability to produce a statistically derived range of risk estimates which quantifies specific uncertainties associated with PBPK risk assessment approaches. Both inhalation and ingestion exposure routes are addressed. Simulated exposure scenarios were consistent with those used by the Environmental Protection Agency (EPA) in their TCE risk assessment. Mean values of physiological parameters were gathered from the literature for both mice (carcinogenic bioassay subjects) and for humans. Realistic physiological value distributions were assumed using existing data on variability. Mouse cancer bioassay data were correlated to total TCE metabolized and area-under-the-curve (blood concentration) trichloroacetic acid (TCA) as determined by a mouse PBPK model. These internal dose metrics were used in a linearized multistage model analysis to determine dose metric values corresponding to 10^-6 lifetime excess cancer risk. Using a human PBPK model, these metabolized doses were then extrapolated to equivalent human exposures (inhalation and ingestion). The Monte Carlo iterations with varying mouse and human physiological parameters produced a range of human exposure concentrations producing a 10^-6 risk.     

Steady-State Solutions to PBPK Models and Their Applications to Risk Assessment I: Route-to-Route Extrapolation of Volatile Chemicals

Although analysis of in vivo pharmacokinetic data necessitates use of time-dependent physiologically-based pharmacokinetic (PBPK) models, risk assessment applications are often driven primarily by steady-state and/or integrated (e.g., AUC) dosimetry. To that end, we present an analysis of steady-state solutions to a PBPK model for a generic volatile chemical metabolized in the liver. We derive an equivalent model that is much simpler and contains many fewer parameters than the full PBPK model. The state of the system can be specified by two state variables-the rate of metabolism and the rate of clearance by exhalation. For a given oral dose rate or inhalation exposure concentration, the system state only depends on the blood-air partition coefficient, metabolic constants, and the rates of blood flow to the liver and of alveolar ventilation. At exposures where metabolism is close to linear, only the effective first-order metabolic rate is needed. Furthermore, in this case, the relationship between cumulative exposure and average internal dose (e.g., AUCs) remains the same for time-varying exposures. We apply our analysis to oral-inhalation route extrapolation, showing that for any dose metric, route equivalence only depends on the parameters that determine the system state. Even if the appropriate dose metric is unknown, bounds can be placed on the route-to-route equivalence with very limited data. We illustrate this analysis by showing that it reproduces exactly the PBPK-model-based route-to-route extrapolation in EPA's 2000 risk assessment for vinyl chloride. Overall, we find that in many cases, steady-state solutions exactly reproduce or closely approximate the solutions using the full PBPK model, while being substantially more transparent. Subsequent work will examine the utility of steady-state solutions for analyzing cross-species extrapolation and intraspecies variability.     

Model Uncertainty and Risk Estimation for Experimental Studies of Quantal Responses

Experimental animal studies often serve as the basis for predicting risk of adverse responses in humans exposed to occupational hazards. A statistical model is applied to exposure-response data and this fitted model may be used to obtain estimates of the exposure associated with a specified level of adverse response. Unfortunately, a number of different statistical models are candidates for fitting the data and may result in wide ranging estimates of risk. Bayesian model averaging (BMA) offers a strategy for addressing uncertainty in the selection of statistical models when generating risk estimates. This strategy is illustrated with two examples: applying the multistage model to cancer responses and a second example where different quantal models are fit to kidney lesion data. BMA provides excess risk estimates or benchmark dose estimates that reflects model uncertainty.     

Bayesian Methodology for Model Uncertainty Using Model Performance Data

A simple and useful characterization of many predictive models is in terms of model structure and model parameters. Accordingly, uncertainties in model predictions arise from uncertainties in the values assumed by the model parameters (parameter uncertainty) and the uncertainties and errors associated with the structure of the model (model uncertainty). When assessing uncertainty one is interested in identifying, at some level of confidence, the range of possible and then probable values of the unknown of interest. All sources of uncertainty and variability need to be considered. Although parameter uncertainty assessment has been extensively discussed in the literature, model uncertainty is a relatively new topic of discussion by the scientific community, despite being often the major contributor to the overall uncertainty. This article describes a Bayesian methodology for the assessment of model uncertainties, where models are treated as sources of information on the unknown of interest. The general framework is then specialized for the case where models provide point estimates about a single‐valued unknown, and where information about models are available in form of homogeneous and nonhomogeneous performance data (pairs of experimental observations and model predictions). Several example applications for physical models used in fire risk analysis are also provided.     

The Use of PBPK Models to Inform Human Health Risk Assessment: Case Study on Perchlorate and Radioiodide Human Lifestage Models

Physiologically‐based pharmacokinetic (PBPK) models are often submitted to or selected by agencies, such as the U.S. Environmental Protection Agency (U.S. EPA) and Agency for Toxic Substances and Disease Registry, for consideration for application in human health risk assessment (HHRA). Recently, U.S. EPA evaluated the human PBPK models for perchlorate and radioiodide for their ability to estimate the relative sensitivity of perchlorate inhibition on thyroidal radioiodide uptake for various population groups and lifestages. The most well‐defined mode of action of the environmental contaminant, perchlorate, is competitive inhibition of thyroidal iodide uptake by the sodium‐iodide symporter (NIS). In this analysis, a six‐step framework for PBPK model evaluation was followed, and with a few modifications, the models were determined to be suitable for use in HHRA to evaluate relative sensitivity among human lifestages. Relative sensitivity to perchlorate was determined by comparing the PBPK model predicted percent inhibition of thyroidal radioactive iodide uptake (RAIU) by perchlorate for different lifestages. A limited sensitivity analysis indicated that model parameters describing urinary excretion of perchlorate and iodide were particularly important in prediction of RAIU inhibition; therefore, a range of biologically plausible values available in the peer‐reviewed literature was evaluated. Using the updated PBPK models, the greatest sensitivity to RAIU inhibition was predicted to be the near‐term fetus (gestation week 40) compared to the average adult and other lifestages; however, when exposure factors were taken into account, newborns were found to be populations that need further evaluation and consideration in a risk assessment for perchlorate.     

Physiologically-Based Pharmacokinetic Modeling of Genistein in Rats, Part I: Model Development

Genistein is a phytoestrogen-a plant-derived compound that binds to and activates the estrogen receptor-occurring at high levels in soy beans and food products, leading to widespread human exposure. The numerous scientific publications available describing genistein's dosimetry, mechanisms of action, and identified or putative health effects in both experimental animals and humans make it ideal for examination as an example of endocrine-active compound (EAC). We developed a physiologically-based pharmacokinetic (PBPK) model to quantify the internal, target-tissue dosimetry of genistein in adult rats. Complexities of the model include enterohepatic circulation, binding of both genistein and its conjugates to plasma proteins, and the multiple compartments used to describe transport through the bile duct and gastrointestinal tract. Other aspects of the model are simple perfusion-limited transport to the tissue groups and first-order rates of metabolism, uptake, and excretion. We describe here the model structure and initial calibration of the model by fitting to a large data set for Wistar rats. The model structure can be readily extrapolated to describe genistein dosimetry in humans or modified to describe the dosimetry of other phytoestrogens and phenolic EACs. The model does a fair job of capturing the pharmacokinetics. Although it does not describe the interindividual variability and we have not identified a single set of parameters that provide a good fit to the data for both oral and intravenous exposures, we believe it provides a good initial attempt at PBPK modeling for genistein, which can serve as a template for other phytoestrogens and in the design of future experiments and research that can be used to fill data gaps and better estimate model parameters.     

An Evaluation of the Rai and Van Ryzin Dose-Response Model in Teratology

The underlying assumptions of the Rai and Van Ryzin dose-response model for reproductive toxicological data are evaluated on the basis of existing experimental data. The model under consideration is unusual in its use of litter size to completely account for extra-binomial variation in the data by associating litter size with reproductive outcome. The experimental data show that controlling litter size is not sufficient to account for the litter-to-litter variability in responses. It is also shown that the two linear components of the Rai and Van Ryzin model are inappropriate. For the component which applies to the dam, the data suggest a strong nonlinearity, supported by rejection of the linear model via statistical hypothesis tests. In the component involving litter size, a relationship with dose is not apparent. The litter size parameters offer considerable potential for bias in estimation; bias which is at least partly masked by the model having good prediction characteristics due to the increased number of parameters. A simulation study is presented to illustrate how the Rai and Van Ryzin model can exaggerate litter size effects on the probability of response when the simulated data arise from a model involving a nonlinear dam component, common to this type of data, and no effect of litter size.     

Learning from Nuclear Accident Experience

Statistical procedures are developed to estimate accident occurrence rates from historical event records, to predict future rates and trends, and to estimate the accuracy of the rate estimates and predictions. Maximum likelihood estimation is applied to several learning models and results are compared to earlier graphical and analytical estimates. The models are based on (1) the cumulative number of operating years, (2) the cumulative number of plants built, and (3) accidents (explicitly), with the accident rate distinctly different before and after an accident. The statistical accuracies of the parameters estimated are obtained in analytical form using the Fisher information matrix. Using data on core damage accidents in electricity producing plants , it is estimated that the probability for a plant to have a serious flaw has decreased from 0.1 to 0.01 during the developmental phase of the nuclear industry. At the same time the equivalent frequency of accidents has decreased from 0.04 per reactor year to 0.0004 per reactor year, partly due to the increasing population of plants.     

Reassessing Benzene Cancer Risks Using Internal Doses

Human cancer risks from benzene exposure have previously been estimated by regulatory agencies based primarily on epidemiological data, with supporting evidence provided by animal bioassay data. This paper reexamines the animal-based risk assessments for benzene using physiologically-based pharmacokinetic (PBPK) models of benzene metabolism in animals and humans. It demonstrates that internal doses (interpreted as total benzene metabolites formed) from oral gavage experiments in mice are well predicted by a PBPK model developed by Travis et al. Both the data and the model outputs can also be accurately described by the simple nonlinear regression model total metabolites = 76.4x/(80.75 + x), where x = administered dose in mg/kg/day. Thus, PBPK modeling validates the use of such nonlinear regression models, previously used by Bailer and Hoel. An important finding is that refitting the linearized multistage (LMS) model family to internal doses and observed responses changes the maximum-likelihood estimate (MLE) dose-response curve for mice from linear-quadratic to cubic, leading to low-dose risk estimates smaller than in previous risk assessments. This is consistent with the conclusion for mice from the Bailer and Hoel analysis. An innovation in this paper is estimation of internal doses for humans based on a PBPK model (and the regression model approximating it) rather than on interspecies dose conversions. Estimates of human risks at low doses are reduced by the use of internal dose estimates when the estimates are obtained from a PBPK model, in contrast to Bailer and Hoel's findings based on interspecies dose conversion. Sensitivity analyses and comparisons with epidemiological data and risk models suggest that our finding of a nonlinear MLE dose-response curve at low doses is robust to changes in assumptions and more consistent with epidemiological data than earlier risk models.     

A Simple Toxicokinetic Model Exhibiting Complex Dynamics and Nonlinear Exposure Response

Uncertainty in model predictions of exposure response at low exposures is a problem for risk assessment. A particular interest is the internal concentration of an agent in biological systems as a function of external exposure concentrations. Physiologically based pharmacokinetic (PBPK) models permit estimation of internal exposure concentrations in target tissues but most assume that model parameters are either fixed or instantaneously dose-dependent. Taking into account response times for biological regulatory mechanisms introduces new dynamic behaviors that have implications for low-dose exposure response in chronic exposure. A simple one-compartment simulation model is described in which internal concentrations summed over time exhibit significant nonlinearity and nonmonotonicity in relation to external concentrations due to delayed up- or downregulation of a metabolic pathway. These behaviors could be the mechanistic basis for homeostasis and for some apparent hormetic effects.     

A Calibrated Human PBPK Model for Benzene Inhalation with Urinary Bladder and Bone Marrow Compartments

A physiologically‐based pharmacokinetic (PBPK) model of benzene inhalation based on a recent mouse model was adapted to include bone marrow (target organ) and urinary bladder compartments. Empirical data on human liver microsomal protein levels and linked CYP2E1 activities were incorporated into the model, and metabolite‐specific conversion rate parameters were estimated by fitting to human biomonitoring data and adjusting for background levels of urinary metabolites. Human studies of benzene levels in blood and breath, and phenol levels in urine were used to validate the rate of human conversion of benzene to benzene oxide, and urinary benzene metabolites from Chinese benzene worker populations provided model validation for rates of human conversion of benzene to muconic acid (MA) and phenylmercapturic acid (PMA), phenol (PH), catechol (CA), hydroquinone (HQ), and benzenetriol (BT). The calibrated human model reveals that while liver microsomal protein and CYP2E1 activities are lower on average in humans compared to mice, the mouse also shows far lower rates of benzene conversion to MA and PMA, and far higher conversion of benzene to BO/PH, and of BO/PH to CA, HQ, and BT. The model also differed substantially from existing human PBPK models with respect to several metabolic rate parameters of importance to interpreting benzene metabolism and health risks in human populations associated with bone marrow doses. The model provides a new methodological paradigm focused on integrating linked human liver metabolism data and calibration using biomonitoring data, thus allowing for model uncertainty analysis and more rigorous validation.     

Exposure Reconstruction for the TCDD-Exposed NIOSH Cohort Using a Concentration- and Age-Dependent Model of Elimination

Recent studies demonstrating a concentration dependence of elimination of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) suggest that previous estimates of exposure for occupationally exposed cohorts may have underestimated actual exposure, resulting in a potential overestimate of the carcinogenic potency of TCDD in humans based on the mortality data for these cohorts. Using a database on U.S. chemical manufacturing workers potentially exposed to TCDD compiled by the National Institute for Occupational Safety and Health (NIOSH), we evaluated the impact of using a concentration- and age-dependent elimination model (CADM) (Aylward et al., 2005) on estimates of serum lipid area under the curve (AUC) for the NIOSH cohort. These data were used previously by Steenland et al. (2001) in combination with a first-order elimination model with an 8.7-year half-life to estimate cumulative serum lipid concentration (equivalent to AUC) for these workers for use in cancer dose-response assessment. Serum lipid TCDD measurements taken in 1988 for a subset of the cohort were combined with the NIOSH job exposure matrix and work histories to estimate dose rates per unit of exposure score. We evaluated the effect of choices in regression model (regression on untransformed vs. ln-transformed data and inclusion of a nonzero regression intercept) as well as the impact of choices of elimination models and parameters on estimated AUCs for the cohort. Central estimates for dose rate parameters derived from the serum-sampled subcohort were applied with the elimination models to time-specific exposure scores for the entire cohort to generate AUC estimates for all cohort members. Use of the CADM resulted in improved model fits to the serum sampling data compared to the first-order models. Dose rates varied by a factor of 50 among different combinations of elimination model, parameter sets, and regression models. Use of a CADM results in increases of up to five-fold in AUC estimates for the more highly exposed members of the cohort compared to estimates obtained using the first-order model with 8.7-year half-life. This degree of variation in the AUC estimates for this cohort would affect substantially the cancer potency estimates derived from the mortality data from this cohort. Such variability and uncertainty in the reconstructed serum lipid AUC estimates for this cohort, depending on elimination model, parameter set, and regression model, have not been described previously and are critical components in evaluating the dose-response data from the occupationally exposed populations.