Monte Carlo Simulation of Rodent Carcinogenicity Bioassays

In this paper we describe a simulation, by Monte Carlo methods, of the results of rodent carcinogenicity bioassays. Our aim is to study how the observed correlation between carcinogenic potency (beta or 1n2/TD50) and maximum tolerated dose (MTD) arises, and whether the existence of this correlation leads to an artificial correlation between carcinogenic potencies in rats and mice. The validity of the bioassay results depends upon, among other things, certain biases in the experimental design of the bioassays. These include selection of chemicals for bioassay and details of the experimental protocol, including dose levels. We use as variables in our simulation the following factors: (1) dose group size, (2) number of dose groups, (3) tumor rate in the control (zero-dose) group, (4) distribution of the MTD values of the group of chemicals as specified by the mean and standard deviation, (5) the degree of correlation between beta and the MTD, as given by the standard deviation of the random error term in the linear regression of log beta on log (1/MTD), and (6) an upper limit on the number of animals with tumors. Monte Carlo simulation can show whether the information present in the existing rodent bioassay database is sufficient to reject the validity of the proposed interspecies correlations at a given level of stringency. We hope that such analysis will be useful for future bioassay design, and more importantly, for discussion of the whole NCI/NTP program.     

Quantitative Risk Assessment for Developmental Neurotoxic Effects

Developmental neurotoxicity concerns the adverse health effects of exogenous agents acting on neurodevelopment. Because human brain development is a delicate process involving many cellular events, the developing fetus is rather susceptible to compounds that can alter the structure and function of the brain. Today, there is clear evidence that early exposure to many neurotoxicants can severely damage the developing nervous system. Although in recent years, there has been much attention given to model development and risk assessment procedures for developmental toxicants, the area of developmental neurotoxicity has been largely ignored. Here, we consider the problem of risk estimation for developmental neurotoxicants from animal bioassay data. Since most responses from developmental neurotoxicity experiments are nonquantal in nature, an adverse health effect will be defined as a response that occurs with very small probability in unexposed animals. Using a two-stage hierarchical normal dose-response model, upper confidence limits on the excess risk due to a given level of added exposure are derived. Equivalently, the model is used to obtain lower confidence limits on dose for a small negligible level of risk. Our method is based on the asymptotic distribution of the likelihood ratio statistic (cf. Crump, 1995). An example is used to provide further illustration.     

Potential Uncertainty Reduction in Model‐Averaged Benchmark Dose Estimates Informed by an Additional Dose Study

A methodology is presented for assessing the information value of an additional dosage experiment in existing bioassay studies. The analysis demonstrates the potential reduction in the uncertainty of toxicity metrics derived from expanded studies, providing insights for future studies. Bayesian methods are used to fit alternative dose‐response models using Markov chain Monte Carlo (MCMC) simulation for parameter estimation and Bayesian model averaging (BMA) is used to compare and combine the alternative models. BMA predictions for benchmark dose (BMD) are developed, with uncertainty in these predictions used to derive the lower bound BMDL. The MCMC and BMA results provide a basis for a subsequent Monte Carlo analysis that backcasts the dosage where an additional test group would have been most beneficial in reducing the uncertainty in the BMD prediction, along with the magnitude of the expected uncertainty reduction. Uncertainty reductions are measured in terms of reduced interval widths of predicted BMD values and increases in BMDL values that occur as a result of this reduced uncertainty. The methodology is illustrated using two existing data sets for TCDD carcinogenicity, fitted with two alternative dose‐response models (logistic and quantal‐linear). The example shows that an additional dose at a relatively high value would have been most effective for reducing the uncertainty in BMA BMD estimates, with predicted reductions in the widths of uncertainty intervals of approximately 30%, and expected increases in BMDL values of 5–10%. The results demonstrate that dose selection for studies that subsequently inform dose‐response models can benefit from consideration of how these models will be fit, combined, and interpreted.     

Route-to-Route Extrapolation of the Toxic Potency of MTBE

MTBE is a volatile organic compound used as an oxygenating agent in gasoline. Inhalation from fumes while refueling automobiles is the principle route of exposure for humans, and toxicity by this route has been well studied. Oral exposures to MTBE exist as well, primarily due to ground-water contamination from leaking stationary sources, such as underground storage tanks. Assessing the potential public health impacts of oral exposures to MTBE is problematic because drinking water studies do not exist for MTBE, and the few oil-gavage studies from which a risk assessment could be derived are limited. This paper evaluates the suitability of the MTBE database for conducting an inhalation route-to-oral route extrapolation of toxicity. This includes evaluating the similarity of critical effect between these two routes, quantifiable differences in absorption, distribution, metabolism, and excretion, and sufficiency of toxicity data by the inhalation route. We conclude that such an extrapolation is appropriate and have validated the extrapolation by finding comparable toxicity between a subchronic gavage oral bioassay and oral doses we extrapolate from a subchronic inhalation bioassay. Our results are extended to the 2-year inhalation toxicity study by Chun et al. (1992) in which rats were exposed to 0, 400, 3000, or 8000 ppm MTBE for 6 hr/d, 5 d/wk. We have estimated the equivalent oral doses to be 0, 130, 940, or 2700 mg/kg/d. These equivalent doses may be useful in conducting noncancer and cancer risk assessments.     

Comparison of the Cancer Risk of Methylene Chloride Predicted from Animal Bioassay Data with the Epidemiologic Evidence

Methylene chloride has been shown to be a lung and liver carcinogen in the mouse; yet, the current epidemiologic data show no adverse health effects associated with chronic exposure to this compound. Hearne et al. have compared the results of a large mortality study on occupational exposure to methylene chloride to the human risk predictions based on the rodent bioassay to point out the inconsistency between the animal toxicologic and human epidemiologic data. The maximum number of lung and liver cancers predicted due to methylene chloride exposure based on the rodent bioassay data was 24 compared to 14 deaths from these cancers actually observed in the Hearne et al. epidemiology study. We assess the minimum risk detectable by the human study in order to calculate the upperbound potency of methylene chloride and compare it to the potency derived from the bioassay data. Results from the epidemiology study imply an upperbound potency of 1.5 x 10(-2) per ppm, compared to 1.4 x 10(-2) per ppm calculated using the most conservative analysis of the animal data. We conclude that the negative epidemiology study of Hearne et al. is not sufficiently powerful to show that the risk is inconsistent with the human risk estimated by modeling the rodent bioassay data. Specifically, the doses to which the workers were exposed, the population studied, and the latency period were not adequate to determine that the risks are outside the bounds of the risk estimates predicted by low-dose modeling of the animal data.     

The Multistage Model with a Time-Dependent Dose Pattern: Applications to Carcinogenic Risk Assessment1

A cancer risk assessment methodology based upon the Armitage–Doll multistage model of cancer is applied to animal bioassay data. The method utilizes the exact time-dependent dose pattern used in a bioassay rather than some single measure of dose such as average dose rate or cumulative dose. The methodology can be used to predict risks from arbitrary exposure patterns including, for example, intermittent exposure and short-term exposure occurring at an arbitrary age. The methodology is illustrated by applying it to a National Cancer Institute bioassay of ethylene dibromide in which dose rates were modified several times during the course of the experiment.     

Reproducibility of the Dose-Response Curve of Steroid-Induced Cleft Palate in Mice

Pregnant CD-1 mice were exposed to cortisone acetate at doses ranging from 20 to 100 mg/kg/ day on days 10-13 by oral and intramuscular routes. Multiple replicate assays were conducted under identical conditions to assess the reproducibility of the dose–response curve for cleft palate. The data were fitted to the probit, logistic, multistage or Armitage-Doll, and Weibull dose-response model separately for each route of exposure. The curves were then tested for parallel slopes (probit and logistic models) or coincidence of model parameters (multistage and Weibull models). The 19 replicate experiments had a wide range of slope estimates, wider for the oral than for the intramuscular experiments. For all models and both routes of exposure the null hypothesis of equality of slopes was rejected at a significant level of p < 0.001. For the intramuscular group of replicates, rejection of slope equality could in part be explained by not maintaining a standard dosing regime. The rejection of equivalence of dose-response curves from replicate studies showed that it is difficult to reproduce dose-response data of a single study within the limits defined by the dose-response model. This has important consequences for quantitative risk assessment, public health measures, or development of mechanistic theories which are typically based on a single animal bioassay.     

Comparison of the EU T25 Single Point Estimate Method with Benchmark Dose Response Modeling for Estimating Potency of Carcinogens

The T25 single-point estimate method of evaluating the carcinogenic potency of a chemical, which is currently used by the European Union (EU) and is denoted the EU approach, is based on the selection of a single dose in a chronic bioassay with an incidence rate that is significantly higher than the background rate. The T25 is determined from that single point by a linear extrapolation or interpolation to the chronic dose (in mg/kg/day), at which a 25% increase in the incidence of the specified tumor type is expected, corrected for the background rate. Another method used to obtain a carcinogenic potency value based on a 25% increase in incidence above the background rate is the estimation of a T25 derived from a benchmark dose (BMD) response model fit to the chronic bioassay data for the specified tumor type. A comparison was made between these two methods using 276 chronic bioassays conducted by the National Toxicology Program. In each of the 2-year bioassays, a tumor type was selected based on statistical and biological significance, and both EU T25 and BMD T25 estimates were determined for that end point. In addition, simulations were done using underlying cumulative probability distributions to examine the effect of dose spacing, the number of animals per dose group, the possibility of a dose threshold, and variation in the background incidence rates on the EU T25 and BMD estimates. The simulations showed that in the majority of cases the EU T25 method underestimated the true T25 dose and overestimated the carcinogenic potency. The BMD estimate is generally less biased and has less variation about the true T25 value than the EU estimate.     

Extrapolation of Carcinogenicity Between Species: Qualitative and Quantitative Factors

Prediction of human cancer risk from the results of rodent bioassays requires two types of extrapolation: a qualitative extrapolation from short-lived rodent species to long-lived humans, and a quantitative extrapolation from near-toxic doses in the bioassay to low-level human exposures. Experimental evidence on the accuracy of prediction between closely related species tested under similar experimental conditions (rats, mice, and hamsters) indicates that: (1) if a chemical is positive in one species, it will be positive in the second species about 75% of the time; however, since about 50% of test chemicals are positive in each species, by chance alone one would expect a predictive value between species of about 50%. (2) If a chemical induces tumors in a particular target organ in one species, it will induce tumors in the same organ in the second species about 50% of the time. Similar predictive values are obtained in an analysis of prediction from humans to rats or from humans to mice for known human carcinogens. Limitations of bioassay data for use in quantitative extrapolation are discussed, including constraints on both estimates of carcinogenic potency and of the dose-response in experiments with only two doses and a control. Quantitative extrapolation should be based on an understanding of mechanisms of carcinogenesis, particularly mitogenic effects that are present at high and not low doses.     

Estimating Noncancer Uncertainty Factors: Are Ratios NOAELs Informative?

The prominent role of animal bioassay evidence in environmental regulatory decisions compels a careful characterization of extrapolation uncertainties. In noncancer risk assessment, uncertainty factors are incorporated to account for each of several extrapolations required to convert a bioassay outcome into a putative subthreshold dose for humans. Measures of relative toxicity taken between different dosing regimens, different endpoints, or different species serve as a reference for establishing the uncertainty factors. Ratios of no observed adverse effect levels (NOAELs) have been used for this purpose; statistical summaries of such ratios across sets of chemicals are widely used to guide the setting of uncertainty factors. Given the poor statistical properties of NOAELs, the informativeness of these summary statistics is open to question. To evaluate this, we develop an approach to calibrate the ability of NOAEL ratios to reveal true properties of a specified distribution for relative toxicity. A priority of this analysis is to account for dependencies of NOAEL ratios on experimental design and other exogenous factors. Our analysis of NOAEL ratio summary statistics finds (1) that such dependencies are complex and produce pronounced systematic errors and (2) that sampling error associated with typical sample sizes (50 chemicals) is non-negligible. These uncertainties strongly suggest that NOAEL ratio summary statistics cannot be taken at face value; conclusions based on such ratios reported in well over a dozen published papers should be reconsidered.     

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.     

Benchmark Dose Analysis via Nonparametric Regression Modeling

Estimation of benchmark doses (BMDs) in quantitative risk assessment traditionally is based upon parametric dose‐response modeling. It is a well‐known concern, however, that if the chosen parametric model is uncertain and/or misspecified, inaccurate and possibly unsafe low‐dose inferences can result. We describe a nonparametric approach for estimating BMDs with quantal‐response data based on an isotonic regression method, and also study use of corresponding, nonparametric, bootstrap‐based confidence limits for the BMD. We explore the confidence limits’ small‐sample properties via a simulation study, and illustrate the calculations with an example from cancer risk assessment. It is seen that this nonparametric approach can provide a useful alternative for BMD estimation when faced with the problem of parametric model uncertainty.     

Comparative Potency Method for Cancer Risk Assessment: Application to Diesel Particulate Emissions1

An estimation of the human lung cancer “unit risk” from diesel engine particulate emissions has been made using a comparative potency approach. This approach involves evaluating the tumorigenic and mutagenic potencies of the particulates from four diesel and one gasoline engine in relation to other combustion and pyrolysis products (coke oven, roofing tar, and cigarette smoke) that cause lung cancer in humans. The unit cancer risk is predicated on the linear nonthreshold extrapolation model and is the individual lifetime excess lung cancer risk from continuous exposure to 1 μg carcinogen per m³ inhaled air. The human lung cancer unit risks obtained from the epidemiologic data for coke oven workers, roofing tar applicators, and cigarette smokers were, respectively, 9.3 × 10^?4, 3.6 × 10^?4, and 2.2 × 10^?6 per μg particulate organics per m³ air. The comparative potencies of these three materials and the diesel and gasoline engine exhaust particulates (as organic extracts) were evaluated by in vivo tumorigenicity bioassays involving skin initiation and skin carcinogenicity in SENCAR mice and by the in vitro bioassays that proved suitable for this analysis: Ames Salmonella microsome bioassay, L5178Y mouse lymphoma cell mutagenesis bioassay, and sister chromatid exchange bioassay in Chinese hamster ovary cells. The relative potencies of the coke oven, roofing tar, and cigarette smoke emissions, as determined by the mouse skin initiation assay, were within a factor of 2 of those determined using the epidemiologic data. The relative potencies, from the in vitro bioassays as compared to the human data, were similar for coke oven and roofing tar, but for the cigarette smoke condensate the in vitro tests predicted a higher relative potency. The mouse skin initiation bioassay was used to determine the unit lung cancer risk for the most potent of the diesel emissions. Based on comparisons with coke oven, roofing tar, and cigarette smoke, the unit cancer risk averaged 4.4 × 10^?4. The unit lung cancer risks for the other, less potent motor-vehicle emissions were determined from their comparative potencies relative to the most potent diesel using three in vitro bioassays. There was a high correlation between the in vitro and in vivo bioassays in their responses to the engine exhaust particulate extracts. The unit lung cancer risk per μg particulates per m³ for the automotive diesel and gasoline exhaust particulates ranged from 0.20 × 10^?4 to 0.60 × 10^?4; that for the heavy-duty diesel engine was 0.02 × 10^?4. These unit risks provide the basis for a future assessment of human lung cancer risks when combined with human population exposure to automotive emissions.     

Statistical Modeling of Animal Bioassay Data with Variable Dosing Regimens: Example—Vinyl Chloride

We consider animal bioassay experiments with variable dosing regimens in which groups of animals are dosed beginning at different ages and for varying durations. Two response models are discussed and then applied to data from an experiment on vinyl chloride exposure of F-344 rats, B6C3F1 and Swiss CD-1 mice, and Syrian Golden hamsters. The multistage model of Armitage and Doll, as extended by Whittemore, Day and Brown, and Crump and Howe, is used to estimate the dose effect on the ordered stages of tumor development. The data for all endpoints and species/strains examined consistently indicate a predominant effect on the first stage, suggesting that vinyl chloride is primarily a tumor initiator. This is consistent with evidence from two-stage experiments on this chemical. The second response model, new to this article, adjusts for survival nonparametrically. It is used to test for an age difference in susceptibility, to evaluate alternative exposure durations, and to compare the effectiveness of alternative dosing regimens for detecting carcinogenicity.     

A Comparison of Unconstraining Methods to Improve Revenue Management Systems

Asuccessful revenue management system requires accurate demand forecasts for each customer segment. The forecasts are used to set booking limits for lower value customers to ensure an adequate supply for higher value customers. The very use of booking limits, however, constrains the historical demand data needed for an accurate forecast. Ignoring this interaction leads to substantial penalties in a firm's potential revenues. We review existing unconstraining methods and propose a new method that includes some attractive properties not found in the existing methods. We evaluate several of the common unconstraining methods against our proposed method by testing them on intentionally constrained simulated data. Results indicate our proposed method outperforms other methods in two of three data sets. We also test the revenue impact of our proposed method, expectation maximization (EM), and “no unconstraining” on actual booking data from a hotel/casino. We show that performance varies with the initial starting protection limits and a lack of unconstraining leads to significant revenue losses.     

Uncertainties in Pharmacokinetic Modeling for Perchloroethylene. I. Comparison of Model Structure, Parameters, and Predictions for Low-Dose Metabolism Rates for Models Derived by Different Authors

In recent years physiologically based pharmacokinetic models have come to play an increasingly important role in risk assessment for carcinogens. The hope is that they can help open the black box between external exposure and carcinogenic effects to experimental observations, and improve both high-dose to low-dose and interspecies projections of risk. However, to date, there have been only relatively preliminary efforts to assess the uncertainties in current modeling results. In this paper we compare the physiologically based pharmacokinetic models (and model predictions of risk-related overall metabolism) that have been produced by seven different sets of authors for perchloroethylene (tetrachloroethylene). The most striking conclusion from the data is that most of the differences in risk-related model predictions are attributable to the choice of the data sets used for calibrating the metabolic parameters. Second, it is clear that the bottom-line differences among the model predictions are appreciable. Overall, the ratios of low-dose human to bioassay rodent metabolism spanned a 30-fold range for the six available human/rat comparisons, and the seven predicted ratios of low-dose human to bioassay mouse metabolism spanned a 13-fold range. (The greater range for the rat/human comparison is attributable to a structural assumption by one author group of competing linear and saturable pathways, and their conclusion that the dangerous saturable pathway constitutes a minor fraction of metabolism in rats.) It is clear that there are a number of opportunities for modelers to make different choices of model structure, interpretive assumptions, and calibrating data in the process of constructing pharmacokinetic models for use in estimating "delivered" or "biologically effective" dose for carcinogenesis risk assessments. We believe that in presenting the results of such modeling studies, it is important for researchers to explore the results of alternative, reasonably likely approaches for interpreting the available data--and either show that any conclusions they make are relatively insensitive to particular interpretive choices, or to acknowledge the differences in conclusions that would result from plausible alternative views of the world.     

The Value of Animal Test Information in Environmental Control Decisions

Value of information (VOI)analytic techniques are used to evaluate the benefit of performing animal bioassays to provide information about the cancer potency of specific chemical compounds. These tools allow the identification of the conditions in which the cost of reducing uncertainty about potency, by performing a subchronic or chronic bioassay, is justified by the benefit of having improved information for making control decisions. The decision analytic results are readily scaled to apply to a range of human contact rates (exposures)and a variety of control strategies. The sensitivity of results to uncertainty about animal to human extrapolation and the design of the bioassay is explored. An evaluation of the possible gains in general understanding about the mechanisms of carcinogenicity resulting from chronic bioassays is beyond the scope of this approach.     

Improving Cancer Dose–Response Characterization by Using Physiologically Based Pharmacokinetic Modeling: An Analysis of Pooled Data for Acrylonitrile-Induced Brain Tumors to Assess Cancer Potency in the Rat

Historically, U.S. regulators have derived cancer slope factors by using applied dose and tumor response data from a single key bioassay or by averaging the cancer slope factors of several key bioassays. Recent changes in U.S. Environmental Protection Agency (EPA) guidelines for cancer risk assessment have acknowledged the value of better use of mechanistic data and better dose–response characterization. However, agency guidelines may benefit from additional considerations presented in this paper. An exploratory study was conducted by using rat brain tumor data for acrylonitrile (AN) to investigate the use of physiologically based pharmacokinetic (PBPK) modeling along with pooling of dose–response data across routes of exposure as a means for improving carcinogen risk assessment methods. In this study, two contrasting assessments were conducted for AN-induced brain tumors in the rat on the basis of (1) the EPA's approach, the dose–response relationship was characterized by using administered dose/concentration for each of the key studies assessed individually; and (2) an analysis of the pooled data, the dose–response relationship was characterized by using PBPK-derived internal dose measures for a combined database of ten bioassays. The cancer potencies predicted for AN by the contrasting assessments are remarkably different (i.e., risk-specific doses differ by as much as two to four orders of magnitude), with the pooled data assessments yielding lower values. This result suggests that current carcinogen risk assessment practices overestimate AN cancer potency. This methodology should be equally applicable to other data-rich chemicals in identifying (1) a useful dose measure, (2) an appropriate dose–response model, (3) an acceptable point of departure, and (4) an appropriate method of extrapolation from the range of observation to the range of prediction when a chemical's mode of action remains uncertain.     

Comparing Toxicologic and Epidemiologic Studies: Methylene Chloride-A Case Study

Exposure to methylene chloride induces lung and liver cancers in mice. The mouse bioassay data have been used as the basis for several cancer risk assessments. ^(1,2) The results from epidemiologic studies of workers exposed to methylene chloride have been mixed with respect to demonstrating an increased cancer risk. The results from a negative epidemiologic study of Kodak workers have been used by two groups of investigators to test the predictions from the EPA risk assessment models.^(3,4) These two groups used very different approaches to this problem, which resulted in opposite conclusions regarding the consistency between the animal model predictions and the Kodak study results. The results from the Kodak study are used to test the predictions from OSHA's multistage models of liver and lung cancer risk. Confidence intervals for the standardized mortality ratios (SMRs) from the Kodak study are compared with the predicted confidence intervals derived from OSHA's risk assessment models. Adjustments for the "healthy worker effect," differences in length of follow-up, and dosimetry between animals and humans were incorporated into these comparisons. Based on these comparisons, we conclude that the negative results from the Kodak study are not inconsistent with the predictions from OSHA's risk assessment model.     

A Malformation Incidence Dose-Response Model Incorporating Fetal Weight and/or Litter Size as Covariates

A dose-response model is often fit to bioassay data to provide a mathematical relationship between the incidence of a developmental malformation and dose of a toxicant. To utilize the interrelations among the fetal weight, incidence of malformation and number of the live fetuses, a conditional Gaussian regression chain model is proposed to model the dose-response function for developmental malformation incidence using the litter size and/or the fetal weight as covariates. The litter size is modeled as a function of dose, the fetal weight is modeled as a function of dose conditional on the litter size, and the malformation incidence is modeled as a function of dose conditional on both the litter size and the fetal weight, which itself is also conditional on the litter size. Data from a developmental experiment conducted at the National Center for Toxicological Research to investigate the growth stunting and increased incidence of cleft palate induced by Dexamethasone (DEX) exposure in rats was used as an illustration.