A Parametric Model for Detecting Hormetic Effects in Developmental Toxicity Studies

Hormetic effects have been observed at low exposure levels based on the dose-response pattern of data from developmental toxicity studies. This indicates that there might actually be a reduced risk of exhibiting toxic effects at low exposure levels. Hormesis implies the existence of a threshold dose level and there are dose-response models that include parameters that account for the threshold. We propose a function that introduces a parameter to account for hormesis. This function is a subset of the set of all functions that could represent a hormetic dose-response relationship at low exposure levels to toxic agents. We characterize the overall dose-response relationship with a piecewise function that consists of a hormetic u-shape curve at low dose levels and a logistic curve at high dose levels. We apply our model to a data set from an experiment conducted at the National Toxicology Program (NTP). We also use the beta-binomial distribution to model the litter response data. It can be seen by observing the structure of these data that current experimental designs for developmental studies employ a limited number of dose groups. These designs may not be satisfactory when the goal is to illustrate the existence of hormesis. In particular, increasing the number of low-level doses improves the power for detecting hormetic effects. Therefore, we also provide the results of simulations that were done to characterize the power of current designs in detecting hormesis and to demonstrate how this power can be improved upon by altering these designs with the addition of only a few low exposure levels.     

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.     

Dose-Response Model for 13 Strains of Salmonella

Data from a human feeding trial with healthy men were used to develop a dose-response model for 13 strains of Salmonella and to determine the effects of strain variation on the shape of the dose-response curve. Dose-response data for individual strains were fit to a three-phase linear model to determine minimum, median, and maximum illness doses, which were used to define Pert distributions in a computer simulation model. Pert distributions for illness dose of individual strains were combined in an Excel spreadsheet using a discrete distribution to model strain prevalence. In addition, a discrete distribution was used to model dose groups and thus create a model that simulated human feeding trials. During simulation of the model with @Risk, an illness dose and a dose consumed were randomly assigned to each consumption event in the simulated feeding trial and if the illness dose was greater than the dose consumed then the model predicted no illness, otherwise the model predicted that an illness would occur. To verify the dose-response model predictions, the original feeding trial was simulated. The dose-response model predicted a median of 69 (range of 43-101) illnesses compared to 74 in the original trial. Thus, its predictions were in agreement with the data used to develop it. However, predictions of the model are only valid for eggnog, healthy men, and the strains and doses of Salmonella used to develop it. When multiple strains of Salmonella were simulated together, the predicted dose-response curves were irregular in shape. Thus, the sigmoid shape of dose-response curves in feeding trials with one strain of Salmonella may not accurately reflect dose response in naturally contaminated food where multiple strains may be present.     

The Importance of Biological Realism in Dioxin Risk Assessment Models Michael

Mechanistic mathematical models of hepatocarcinogenesis in the female rat were constructed to investigate possible relationships among the Ah, estrogen, and EGF receptors in TCDD hepato-carcinogenicity. Each model generates dose-response curves for the expression of biomarker liver proteins CYP1A1, CYP1A2, and residual plasma membrane EGF receptor consequent to exposure to TCDD. The shapes of the response curves were strongly dependent on the assumed mechanisms of constitutive expression of these proteins. Assuming a constant level of the hepatic Ah receptor, a sigmoidal dose-response of hepatic CYP1A1 to total liver TCDD was computed. However, inclusion of induction of the Ah receptor by TCDD in a physiologically realistic dosimetric model produced a linear low-dose response of CYP1A1. This behavior was computed to arise from the net effect of sublinear response of CYP1A1 mRNA to the concentration of the Ah-TCDD complex and supralinear response of the protein concentration to the mRNA level, illustrating the importance of biological realism in dose-response modeling. The dosimetric model also computed effects of TCDD on the hepatic estradiol concentration and consequent effects on the binding capacity of the EGF receptor and suggests plausible mechanisms for tumor promotion by TCDD. Setting circulating estradiol levels in the model to values typical of the male rat indicated possible sources of the differences in the responses of the EGF receptor and in development of tumors in the two sexes.     

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 Bayesian Semiparametric Model for Radiation Dose‐Response Estimation

In evaluating the risk of exposure to health hazards, characterizing the dose‐response relationship and estimating acceptable exposure levels are the primary goals. In analyses of health risks associated with exposure to ionizing radiation, while there is a clear agreement that moderate to high radiation doses cause harmful effects in humans, little has been known about the possible biological effects at low doses, for example, below 0.1 Gy, which is the dose range relevant to most radiation exposures of concern today. A conventional approach to radiation dose‐response estimation based on simple parametric forms, such as the linear nonthreshold model, can be misleading in evaluating the risk and, in particular, its uncertainty at low doses. As an alternative approach, we consider a Bayesian semiparametric model that has a connected piece‐wise‐linear dose‐response function with prior distributions having an autoregressive structure among the random slope coefficients defined over closely spaced dose categories. With a simulation study and application to analysis of cancer incidence data among Japanese atomic bomb survivors, we show that this approach can produce smooth and flexible dose‐response estimation while reasonably handling the risk uncertainty at low doses and elsewhere. With relatively few assumptions and modeling options to be made by the analyst, the method can be particularly useful in assessing risks associated with low‐dose radiation exposures.     

An Approach for Modeling Noncancer Dose Responses with an Emphasis on Uncertainty

This paper presents an approach for characterizing the probability of adverse effects occurring in a population exposed to dose rates in excess of the Reference Dose (RfD). The approach uses a linear threshold (hockey stick) model of response and is based on the current system of uncertainty factors used in setting RfDs. The approach requires generally available toxicological estimates such as No-Observed-Adverse-Effect Levels (NOAELs) or Benchmark Doses and doses at which adverse effects are observed in 50% of the test animals (ED₅₀s). In this approach, Monte Carlo analysis is used to characterize the uncertainty in the dose response slope based on the range and magnitude of the key sources of uncertainty in setting protective doses. The method does not require information on the shape of the dose response curve for specific chemicals, but is amenable to the inclusion of such data. The approach is applied to four compounds to produce estimates of response rates for dose rates greater than the RfD     

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.     

Characterizing Dose-Response Relationships in Multiple Cancer Bioassays

In the evaluation of chemical compounds for carcinogenic risk, regulatory agencies such as the U.S. Environmental Protection Agency and National Toxicology Program (NTP) have traditionally fit a dose-response model to data from rodent bioassays, and then used the fitted model to estimate a Virtually Safe Dose or the dose corresponding to a very small increase (usually 10(-6)) in risk over background. Much recent interest has been directed at incorporating additional scientific information regarding the properties of the specific chemical under investigation into the risk assessment process, including biological mechanisms of cancer induction, metabolic pathways, and chemical structure and activity. Despite the fact that regulatory agencies are currently poised to allow use of nonlinear dose-response models based on the concept of an underlying threshold for nongenotoxic chemicals, there have been few attempts to investigate the overall relationship between the shape of dose-response curves and mutagenicity. Using data from an historical database of NTP cancer bioassays, the authors conducted a repeated-measures Analysis of the estimated shape from fitting extended Weibull dose-response curves. It was concluded that genotoxic chemicals have dose-response curves that are closer to linear than those for nongenotoxic chemicals, though on average, both types of compounds have dose-response curves that are convex and the effect of genotoxicity is small.     

The Fallacy of Ranking Possible Carcinogen Hazards Using the TD50

Ames et al. have proposed a new model for evaluating carcinogenic hazards in the environment. They advocate ranking possible carcinogens on the basis of the TD50, the estimated dose at which 50% of the test animals would get tumors, and extrapolating that ranking to all other doses. We argue that implicit in this methodology is a simplistic and inappropriate statistical model. All carcinogens are assumed to act similarly and to have dose-response curves of the same shape that differ only in the value of one parameter. We show by counterexample that the rank order of cancer potencies for two chemicals can change over a reasonable range of doses. Ames et al.'s use of these TD50 ranks to compare the hazards from low level exposures to contaminants in our food and environment is wholly inappropriate and inaccurate. Their dismissal of public health concern for environmental exposures, in general, based on these comparisons, is not supported by the data.     

On the risk of mortality to primates exposed to anthrax spores.

Current events have heightened the importance of understanding the risks from inhalation exposure to small numbers of spores of Bacillus anthracis. Previously reported data sets have not been fully assessed using current understanding of microbial dose response. This article presents an assessment of the reported primate dose-response data. At low doses, the risk to large populations of low doses of inhaled spores (e.g., < 100) is not insignificant.     

Use of Mechanistic Models to Estimate Low-Dose Cancer Risks

The utility of mechanistic models of cancer for predicting cancer risks at low doses is examined. Based upon a general approximation to the dose-response that is valid at low doses, it is shown that at low doses the dose-response predicted by a mechanistic model is a linear combination of the dose-responses for each of the physiological parameters in the model that are affected by exposure. This demonstrates that, unless the mechanistic model provides a theoretical basis for determining the dose-responses for these parameters, the extrapolation of risks to low doses using a mechanistic model is basically "curve fitting," just as is the case when extrapolating using statistical models. This suggests that experiments to generate data for use in mechanistic models should emphasize measuring the dose-response for dose-related parameters as accurately as possible and at the lowest feasible doses.     

Risk Assessment of Nongenotoxic Carcinogens Based upon Cell Proliferation/Death Rates in Rodents

Increased cell proliferation increases the opportunity for transformations of normal cells to malignant cells via intermediate cells. Nongenotoxic cytotoxic carcinogens that increase cell proliferation rates to replace necrotic cells are likely to have a threshold dose for cytotoxicity below which necrosis and hence, carcinogenesis do not occur. Thus, low dose cancer risk estimates based upon nonthreshold, linear extrapolation are inappropriate for this situation. However, a threshold dose is questionable if a nongenotoxic carcinogen acts via a cell receptor. Also, a nongenotoxic carcinogen that increases the cell proliferation rate, via the cell division rate and/or cell removal rate by apoptosis, by augmenting an existing endogenous mechanism is not likely to have a threshold dose. Whether or not a threshold dose exists for nongenotoxic carcinogens, it is of interest to study the relationship between lifetime tumor incidence and the cell proliferation rate. The Moolgavkar–Venzon–Knudson biologically based stochastic two-stage clonal expansion model is used to describe a carcinogenic process. Because the variability in cell proliferation rates among animals often makes it impossible to detect changes of less than 20% in the rate, it is shown that small changes in the cell proliferation rate, that may be obscured by the background noise in rates, can produce large changes in the lifetime tumor incidence as calculated from the Moolgavkar–Venzon–Knudson model. That is, dose response curves for cell proliferation and tumor incidence do not necessarily mimic each other. This makes the use of no observed effect levels (NOELs) for cell proliferation rates often inadmissible for establishing acceptable daily intakes (ADIs) of nongenotoxic carcinogens. In those cases where low dose linearity is not likely, a potential alternative to a NOEL is a benchmark dose corresponding to a small increase in the cell proliferation rate, e. g., 1%, to which appropriate safety (uncertainty) factors can be applied to arrive at an ADI.     

Point Estimates of Cancer Risk at Low Doses

There has been considerable discussion regarding the conservativeness of low-dose cancer risk estimates based upon linear extrapolation from upper confidence limits. Various groups have expressed a need for best (point) estimates of cancer risk in order to improve risk/benefit decisions. Point estimates of carcinogenic potency obtained from maximum likelihood estimates of low-dose slope may be highly unstable, being sensitive both to the choice of the dose–response model and possibly to minimal perturbations of the data. For carcinogens that augment background carcinogenic processes and/or for mutagenic carcinogens, at low doses the tumor incidence versus target tissue dose is expected to be linear. Pharmacokinetic data may be needed to identify and adjust for exposure-dose nonlinearities. Based on the assumption that the dose response is linear over low doses, a stable point estimate for low-dose cancer risk is proposed. Since various models give similar estimates of risk down to levels of 1%, a stable estimate of the low-dose cancer slope is provided by ŝ = 0.01/ED01, where ED01 is the dose corresponding to an excess cancer risk of 1%. Thus, low-dose estimates of cancer risk are obtained by, risk = ŝ × dose. The proposed procedure is similar to one which has been utilized in the past by the Center for Food Safety and Applied Nutrition, Food and Drug Administration. The upper confidence limit, s , corresponding to this point estimate of low-dose slope is similar to the upper limit, q ₁ obtained from the generalized multistage model. The advantage of the proposed procedure is that ŝ provides stable estimates of low-dose carcinogenic potency, which are not unduly influenced by small perturbations of the tumor incidence rates, unlike ₁.     

Experimental Design of Bioassays for Screening and Low Dose Extrapolation

Relatively high doses of chemicals generally are employed in animal bioassays to detect potential carcinogens with relatively small numbers of animals. The problem investigated here is the development of experimental designs which are effective for high to low dose extrapolation for tumor incidence as well as for screening (detecting) carcinogens. Several experimental designs are compared over a wide range of different dose response curves. Linear extrapolation is used below the experimental data range to establish an upper bound on carcinogenic risk at low doses. The goal is to find experimental designs which minimize the upper bound on low dose risk estimates (i.e., maximize the allowable dose for a given level of risk). The maximum tolerated dose (MTD) is employed for screening purposes. Among the designs investigated, experiments with doses at the MTD, 1/2 MTD, 1/4 MTD, and controls generally provide relatively good data for low dose extrapolation with relatively good power for detecting carcinogens. For this design, equal numbers of animals per dose level perform as well as unequal allocations.     

Modeling Receptor-Mediated Processes with Dioxin: Implications for Pharmacokinetics and Risk Assessment

Dioxin (2,3,7,8-tetrachlorodibenzo- p -dioxin; TCDD), a widespread polychlorinated aromatic hydrocarbon, caused tumors in the liver and other sites when administered chronically to rats at doses as low as 0.01 μg/kg/day. It functions in combination with a cellular protein, the Ah receptor, to alter gene regulation, and this resulting modulation of gene expression is believed to be obligatory for both dioxin toxicity and carcinogenicity. The U.S. EPA is reevaluating its dioxin risk assessment and, as part of this process, will be developing risk assessment approaches for chemicals, such as dioxin, whose toxicity is receptor-mediated. This paper describes a receptor-mediated physiologically based pharmacokinetic (PB-PK) model for the tissue distribution and enzyme-inducing properties of dioxin and discusses the potential role of these models in a biologically motivated risk assessment. In this model, ternary interactions among the Ah receptor, dioxin, and DNA binding sites lead to enhanced production of specific hepatic proteins. The model was used to examine the tissue disposition of dioxin and the induction of both a dioxin-binding protein (presumably, cytochrome P4501A2), and cytochrome P4501A1. Tumor promotion correlated more closely with predicted induction of P4501A1 than with induction of hepatic binding proteins. Although increased induction of these proteins is not expected to be causally related to tumor formation, these physiological dosimetry and gene-induction response models will be important for biologically motivated dioxin risk assessments in determining both target tissue dose of dioxin and gene products and in examining the relationship between these gene products and the cellular events more directly involved in tumor promotion.     

Bogen's Critique of Linear‐No‐Threshold Default Assumptions

In an article recently published in this journal, Bogen⁽¹⁾ concluded that an NRC committee's recommendations that default linear, nonthreshold (LNT) assumptions be applied to dose– response assessment for noncarcinogens and nonlinear mode of action carcinogens are not justified. Bogen criticized two arguments used by the committee for LNT: when any new dose adds to a background dose that explains background levels of risk (additivity to background or AB), or when there is substantial interindividual heterogeneity in susceptibility (SIH) in the exposed human population. Bogen showed by examples that SIH can be false. Herein is outlined a general proof that confirms Bogen's claim. However, it is also noted that SIH leads to a nonthreshold population distribution even if individual distributions all have thresholds, and that small changes to SIH assumptions can result in LNT. Bogen criticizes AB because it only applies when there is additivity to background, but offers no help in deciding when or how often AB holds. Bogen does not contradict the fact that AB can lead to LNT but notes that, even if low‐dose linearity results, the response at higher doses may not be useful in predicting the amount of low‐dose linearity. Although this is theoretically true, it seems reasonable to assume that generally there is some quantitative relationship between the low‐dose slope and the slope suggested at higher doses. Several incorrect or misleading statements by Bogen are noted.     

Optimal Designs for Estimating the Effective Dose in Developmental Toxicity Experiments

Recent advances in risk assessment have led to the development of joint dose-response models to describe prenatal death and fetal malformation rates in developmental toxicity experiments. These models can be used to estimate the effective dose corresponding to a 5% excess risk for both these toxicological endpoints, as well as for overall toxicity. In this article, we develop optimal experimental designs for the estimation of the effective dose for developmental toxicity using joint Weibull dose-response models for prenatal death and fetal malformation. Based on an extended series of developmental studies, near-optimal designs for prenatal death, malformation, and overall toxicity were found to involve three dose groups: an unexposed control group, a high dose equal to the maximum tolerated dose, and a low dose above or comparable to the effective dose. The effect on the optimal designs of changing the number of implants and the degree of intra-litter correlation is also investigated. Although the optimal design has only three dose groups in most cases, practical considerations involving model lack of fit and estimation of the shape of the dose-response curve suggest that, in practice, suboptimal designs with more than three doses will often be preferred.     

Comparison of Six Dose-Response Models for Use with Food-Borne Pathogens

Food-related illness in the United States is estimated to affect over six million people per year and cost the economy several billion dollars. These illnesses and costs could be reduced if minimum infectious doses were established and used as the basis of regulations and monitoring. However, standard methodologies for dose-response assessment are not yet formulated for microbial risk assessment. The objective of this study was to compare dose-response models for food-borne pathogens and determine which models were most appropriate for a range of pathogens. The statistical models proposed in the literature and chosen for comparison purposes were log-normal, log-logistic, exponential, -Poisson and Weibull-Gamma. These were fit to four data sets also taken from published literature, Shigella flexneri, Shigella dysenteriae,Campylobacter jejuni, and Salmonella typhosa, using the method of maximum likelihood. The Weibull-gamma, the only model with three parameters, was also the only model capable of fitting all the data sets examined using the maximum likelihood estimation for comparisons. Infectious doses were also calculated using each model. Within any given data set, the infectious dose estimated to affect one percent of the population ranged from one order of magnitude to as much as nine orders of magnitude, illustrating the differences in extrapolation of the dose response models. More data are needed to compare models and examine extrapolation from high to low doses for food-borne pathogens.     

Addressing Nonlinearity in the Exposure-Response Relationship for a Genotoxic Carcinogen: Cancer Potency Estimates for Ethylene Oxide

Ethylene oxide (EO) has been identified as a carcinogen in laboratory animals. Although the precise mechanism of action is not known, tumors in animals exposed to EO are presumed to result from its genotoxicity. The overall weight of evidence for carcinogenicity from a large body of epidemiological data in the published literature remains limited. There is some evidence for an association between EO exposure and lympho/hematopoietic cancer mortality. Of these cancers, the evidence provided by two large cohorts with the longest follow-up is most consistent for leukemia. Together with what is known about human leukemia and EO at the molecular level, there is a body of evidence that supports a plausible mode of action for EO as a potential leukemogen. Based on a consideration of the mode of action, the events leading from EO exposure to the development of leukemia (and therefore risk) are expected to be proportional to the square of the dose. In support of this hypothesis, a quadratic dose-response model provided the best overall fit to the epidemiology data in the range of observation. Cancer dose-response assessments based on human and animal data are presented using three different assumptions for extrapolating to low doses: (1) risk is linearly proportionate to dose; (2) there is no appreciable risk at low doses (margin-of-exposure or reference dose approach); and (3) risk below the point of departure continues to be proportionate to the square of the dose. The weight of evidence for EO supports the use of a nonlinear assessment. Therefore, exposures to concentrations below 37 microg/m3 are not likely to pose an appreciable risk of leukemia in human populations. However, if quantitative estimates of risk at low doses are desired and the mode of action for EO is considered, these risks are best quantified using the quadratic estimates of cancer potency, which are approximately 3.2- to 32-fold lower, using alternative points of departure, than the linear estimates of cancer potency for EO. An approach is described for linking the selection of an appropriate point of departure to the confidence in the proposed mode of action. Despite high confidence in the proposed mode of action, a small linear component for the dose-response relationship at low concentrations cannot be ruled out conclusively. Accordingly, a unit risk value of 4.5 x 10(-8) (microg/m3)(-1) was derived for EO, with a range of unit risk values of 1.4 x 10(-8) to 1.4 x 10(-7) (microg/m3)(-1) reflecting the uncertainty associated with a theoretical linear term at low concentrations.