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.

Observed versus predicted carboxyhemoglobin levels in cellulose triacetate workers exposed to methylene chloride.

BACKGROUND: Occupational exposure to methylene chloride, together with carboxyhemoglobin concentrations, has not been studied previously. METHODS: Carboxyhemoglobin levels were measured in non-smoking employees exposed to varying concentrations of methylene chloride during the manufacture of cellulose triacetate fibers. The observed carboxyhemoglobin levels were compared to predicted concentrations using a pharmacokinetic model. RESULTS: The presence of carboxyhemoglobin in non-smokers exposed to methylene chloride results primarily from the metabolism of methylene chloride in the liver and exhibits a linear dose-response relationship. The observed levels of carboxyhemoglobin in non-smokers at the end of an 8-hour shift depend upon exposures to methylene chloride that day but are independent of occupational exposures on previous days. The observed daily concentrations of carboxyhemoglobin are consistent with predicted concentrations using a pharmacokinetic model. While varying exposure patterns were shown to change the rate of metabolite formation at the end of shift, these same exposure patterns had almost no effect on the total amount of carbon monoxide in the blood. CONCLUSION: While the present study addresses the relationship between methylene chloride, carbon monoxide, carboxyhemoglobin and ischemic heart disease, it does not address the issue of tumorigenicity, which is also the basis for the current U.S. Occupational Health and Safety workplace exposure limit of 25 ppm. This study provides support for the conclusion that the current American Conference of Governmental Industrial Hygienists 8-hour Threshold Limit Value of 50 ppm adequately protects human health with regard to ischemic heart disease and carboxyhemoglobin formation among non-smokers.

Dose-response implications of the University of Alabama study of lymphohematopoietic cancer among workers exposed to 1,3-butadiene and styrene in the synthetic rubber industry.

New quantitative cancer risk estimates for exposure to 1,3-butadiene are presented. These estimates are based on the most recent human epidemiologic data developed by Drs Delzell and Macaluso and their colleagues at the University of Alabama at Birmingham. The implications of Poisson regression analyses of the relative rate for leukemia are explored using their updated dose estimates and lymphohematopoietic cancer data. The Poisson regression model in these analyses has the same form as in the U.S. Environmental Protection Agency (EPA)'s draft risk assessment of 1,3-butadiene [U.S. Environmental Protection Agency, Health Risk Assessment of 1,3-Butadiene - External Review Draft, National Center for Environmental Assessment, Office of Research and Development, 63 Fed. Reg. 7167 (February 12, 1998) Publication NCEA-W-0267, Washington, 1998]. Consistent with the proposed cancer risk assessment guidelines of the EPA and the EPA's draft risk assessment, the exploration includes the maximum likelihood estimate of the 'effective concentration' (EC(01)) corresponding to an extra risk of leukemia of 0.01 (1%) from a lifetime continuous exposure to 1,3-butadiene based on a linear dose-response model and the cumulative 1,3-butadiene dose metric (ppm-years). The incorporation of the most recent exposure estimates results in a 2.5-fold decrease in the estimates of leukemia risks computed by EPA. In addition, three changes proposed by the American Chemistry Council (formerly the Chemical Manufacturers Association) to the EPA's Science Advisory Board (SAB) for EPA's draft risk assessment of 1,3-butadiene are incorporated into the calculation. This results in approximately an additional fivefold decrease in the risk estimates of leukemia. The leukemia cancer risk estimates in the EPA's draft risk assessment of 1,3-butadiene decrease by approximately a factor of 13-fold when the updated epidemiologic data and the alternative numbers proposed by industry to the SAB are both incorporated. Specifically, the maximum likelihood estimate of the EC(01) increases from EPA's 1.2 ppm to 2.8 ppm on the basis of the updated epidemiologic data and increases further to 15.1 ppm when the CMA's proposed changes are also incorporated.

Risk metrics and cumulative risk assessment methodology for the FQPA.

The Food Quality Protection Act (FQPA) of 1996 mandates that the U.S. Environmental Protection Agency consider both aggregate and cumulative risks. Aggregate assessments account for multiple sources and routes of exposure for a single chemical. Cumulative assessments combine exposures to two or more chemicals that share a common mechanism of toxicity. Probabilistic risk assessment methods are described for determining a population's distribution of the dose from exposure and the combination of that exposure characterization with appropriate toxicological information to form a risk assessment. An individual's dose from exposure is characterized as a set of chemical- and route-specific dose profiles over time. For each individual and each chemical and route, a margin of exposure (MOE) is calculated by dividing a toxicologically relevant benchmark dose (e.g., an ED(10)) by the individual's dose from exposure. The set of these MOEs for an individual is combined into the individual's Total MOE. The distribution of the Total MOEs in a population is compared to an Acceptable MOE. Advantages of the Total MOE approach over approaches based on reference doses are discussed. Some general comments on risk metrics are made, and some general guidance for cumulative risk assessments is provided.

Monograph: reassessment of human cancer risk of aldrin/dieldrin.

In 1987, the US Environmental Protection Agency (EPA) classified aldrin and dieldrin as category B2 carcinogens, i.e. probable human carcinogens, based largely on the increase in liver tumors in mice fed either organochlorine insecticide. At that date, the relevant epidemiology was deemed inadequate to influence the cancer risk assessment. More time has now elapsed since early exposures of manufacturing workers to aldrin/dieldrin; therefore, updated epidemiological data possess more power to detect exposure-related differences in cancer risk and mortality. Also, recent experimental studies provide a plausible mode of action to explain the mouse specificity of dieldrin-induced hepatocarcinogenesis and call into question the relevance of this activity to human cancer risk. This monograph places this new information within the historic and current perspectives of human cancer risk assessment, including EPA's 1996 Proposed Guidelines for Carcinogen Risk Assessment. Updated epidemiological studies of manufacturing workers in which lifetime exposures to aldrin/dieldrin have been quantified do not indicate increased mortality or cancer risk. In fact, at the middle range of exposures, there is evidence of a decrease in both mortality from all causes and cancer. Recent experimental studies indicate that dieldrin-induced hepatocarcinogenesis in mice occurs through a nongenotoxic mode of action, in which the slow oxidative metabolism of dieldrin is accompanied by an increased production of reactive oxygen species, depletion of hepatic antioxidant defenses (particularly alpha-tocopherol), and peroxidation of liver lipids. Dieldrin-induced oxidative stress or its sequelae apparently result in modulation of gene expression that favors expansion of initiated mouse, but not rat, liver cells; thus, dieldrin acts as a nongenotoxic promoter/accelerator of background liver tumorigenesis in the mouse. Within the framework of EPA's Proposed Guidelines for Carcinogen Risk Assessment, it is proposed that the most appropriate cancer risk descriptor for aldrin/dieldrin, relating to the mouse liver tumor response, is 'not likely a human carcinogen', a descriptor consistent with the example of phenobarbital cited by EPA.

Cancer dose-response modeling of epidemiological data on worker exposures to aldrin and dieldrin.

The paper applies classical statistical principles to yield new tools for risk assessment and makes new use of epidemiological data for human risk assessment. An extensive clinical and epidemiological study of workers engaged in the manufacturing and formulation of aldrin and dieldrin provides occupational hygiene and biological monitoring data on individual exposures over the years of employment and provides unusually accurate measures of individual lifetime average daily doses. In the cancer dose-response modeling, each worker is treated as a separate experimental unit with his own unique dose. Maximum likelihood estimates of added cancer risk are calculated for multistage, multistage-Weibull, and proportional hazards models. Distributional characterizations of added cancer risk are based on bootstrap and relative likelihood techniques. The cancer mortality data on these male workers suggest that low-dose exposures to aldrin and dieldrin do not significantly increase human cancer risk and may even decrease the human hazard rate for all types of cancer combined at low doses (e.g., 1 microgram/kg/day). The apparent hormetic effect in the best fitting dose-response models for this data set is statistically significant. The decrease in cancer risk at low doses of aldrin and dieldrin is in sharp contrast to the U.S. Environmental Protection Agency's upper bound on cancer potency based on mouse liver tumors. The EPA's upper bound implies that lifetime average daily doses of 0.0000625 and 0.00625 microgram/kg body weight/day would correspond to increased cancer risks of 0.000001 and 0.0001, respectively. However, the best estimate from the Pernis epidemiological data is that there is no increase in cancer risk in these workers at these doses or even at doses as large as 2 micrograms/kg/day.

Ethylene oxide cancer risk assessment based on epidemiological data: application of revised regulatory guidelines.

Ethylene oxide (EO) research has significantly increased since the 1980s, when regulatory risk assessments were last completed on the basis of the animal cancer chronic bioassays. In tandem with the new scientific understanding, there have been evolutionary changes in regulatory risk assessment guidelines, that encourage flexibility and greater use of scientific information. The results of an updated meta-analysis of the findings from 10 unique EO study cohorts from five countries, including nearly 33,000 workers, and over 800 cancers are presented, indicating that EO does not cause increased risk of cancers overall or of brain, stomach or pancreatic cancers. The findings for leukemia and non-Hodgkin's lymphoma (NHL) are inconclusive. Two studies with the requisite attributes of size, individual exposure estimates and follow up are the basis for dose-response modeling and added lifetime risk predictions under environmental and occupational exposure scenarios and a variety of plausible alternative assumptions. A point of departure analysis, with various margins of exposure, is also illustrated using human data. The two datasets produce remarkably similar leukemia added risk predictions, orders of magnitude lower than prior animal-based predictions under conservative, default assumptions, with risks on the order of 1 x 10(-6) or lower for exposures in the low ppb range. Inconsistent results for "lymphoid" tumors, a non-standard grouping using histologic information from death certificates, are discussed. This assessment demonstrates the applicability of the current risk assessment paradigm to epidemiological data.

Some implications for quantitative risk assessment if hormesis exists.

The existence of hormesis should impact quantitative risk assessment in at least seven fundamental ways. (1) The dose-response models for bioassay and epidemiological data should have greater flexibility to fit the observed shape of the dose-response data and no longer be forced to always be linearly increasing at low doses. (2) Experimental designs should be altered to provide greater opportunity to identify the hormetic component of a dose-response relationship. (3) Rather than a lifetime average daily dose or its analog for shorter time periods, dose scales or metrics should be used that reflect the age or time dependence of the dose level. (4) Low-dose risk characterization should include the likelihood of beneficial effects and the likelihood that a dose level has reasonable certainty of no appreciable adverse health effects. (5) Exposure assessments should make greater efforts to characterize the distribution of actual doses from exposure rather than just upper bounds. (6) Uncertainty characterizations should be expanded to include both upper and lower bounds, and there should be an increased explicit use of expert judgement and weight-of-evidence based distributional analyses reflecting more of the available relevant dose-response information and alternative risk characterizations. (7) Risk should be characterized in terms of the net effect of a dose on health rather than a dose's effect on a single factor affecting health - for example, risk would be better expressed in terms of mortality from all causes combined rather than a specific type of fatal disease.

Modeling to incorporate defense mechanisms into the estimation of dose responses.

Several adverse health effects (including cancer and noncancer effects) may be the result of an imbalance between exogenous and endogenous invading substances and defense mechanisms. In these cases the probability of an adverse effect depends on how much the exposure to a substance increases or decreases the number of defenders or their efficiency as well as increasing or decreasing the number of invaders. Rather than using a dose scale such as parts per million or milligram/kilogram/day in these cases, dose-response models can directly incorporate the impact of defense mechanisms by using a dose scale that corresponds to the number of invaders that break through the defenders and become free to do their damage. The number of breakthroughs at a specific age, the cumulative number of breakthroughs by a specific age, or the cumulative number of breakthroughs in a window of time would usually be the appropriate age-dependent dose. Although a lifetime average daily dose level can be used as a surrogate for an age-dependent dose in simplistic dose-response models, the age-dependent dose itself can be used in more biologically based models that include time, reflect the key role of feedback mechanisms, and treat the human body as an age-dependent dynamic system responding to internal and external stimuli and not as a system at equilibrium. Some illustrative biologic examples of defense mechanisms and invader-defender interactions are presented. Several numerical examples are given in which the dose incorporates the age-dependent effects of a substance on the number of invaders, the number of defenders, and/or the defenders' efficiencies.

Using PBPK modeling and comprehensive realism methodology for the quantitative cancer risk assessment of butadiene.

The National Academy of Sciences and many others have noted the need for quantitative health risk assessment methodology that goes beyond a simple screening analysis based on upper bounds on risk. The Academy recommended adoption of methodologies which provide a higher-tier analysis based on realistic estimates of risk which reflect more of the available biological information. In recent years, scientists have challenged the assumption of low-dose linearity and other default assumptions in cancer risk assessment. These challenges have stimulated the continued evolution of quantitative risk assessment methodologies, because effective risk management requires accurate characterizations of uncertainty and greater utilization of cost-benefit analyses for decision making. "Comprehensive Realism" is an emerging quantitative weight-of-evidence based risk assessment methodology for both cancer and noncancer health effects which utilizes probability distributions and decision analysis techniques to reflect more of the available human and animal dose-response data. The current state of knowledge about the relative plausibility of alternative dose-response analyses is also addressed in this approach. The framework discussed here should lead to a higher-tier assessment of butadiene.

Oncogenicity testing of 2-ethylhexanol in Fischer 344 rats and B6C3F1 mice.

2-Ethylhexanol (2EH) is a weak nongenotoxic hepatic peroxisome proliferator in the rat. It is a high-volume chemical intermediate in the preparation of the plasticizers bis-(2-ethylhexyl) adipate (DEHA), bis-(2-ethylhexyl) phthalate (DEHP), and tris-(2-ethylhexyl) phosphate (TEHP), which are weak hepatocellular tumorigens in female mice. In consequence, the oncogenic potential of 2EH was evaluated in male (M) and female (F) rats and mice (50 animals/sex/group). Oral gavage doses of 2EH in 0.005% aqueous Cremophor EL (polyoxyl-35 castor oil) were given five times a week to rats: 0 (water), 0 (vehicle), 50, 150, and 500 mg/kg for 24 months, and to mice: 0 (water), 0 (vehicle), 50, 200, and 750 mg/kg for 18 months. Statistical comparisons of data were made between vehicle controls and treatment groups. There were no differences of biological significance between data from vehicle and water control groups. In rats, there were no dose-related changes at 50 mg/kg. There was reduced body weight gain at 150 mg/kg (M, 16; F, 12%) and 500 mg/kg (M, 33; F, 31%) and an increased incidence of lethargy and unkemptness. There were dose-related increases in relative liver, stomach, brain, kidney, and testis weights at sacrifice. Female rat mortality was markedly increased at 500 mg/kg. There was marked aspiration-induced bronchopneumonia in rats at 500 mg/kg; hematologic, gross, and microscopic changes, including tumors, were otherwise comparable among all rat groups. In mice at 50 and 200 mg/kg there were no dose-related changes and essentially no time-dependent or time-independent adverse trends in liver tumor incidence at the 5% significance level. At 750 mg/kg mouse body weight gain was reduced (M, 26; F, 24%), and mortality increased (M and F, 30%) versus vehicle controls. At 750 mg/kg there was a slight increase in nonneoplastic focal hyperplasia in the forestomach of mice (M 5/50, F 4/50) versus vehicle controls (M 1/50, F 1/50). There were increases in mouse relative liver (F, 21%) and stomach (M, 13%; F, 19%) weights at 750 mg/kg. There was a 12% incidence of hepatic basophilic foci and an 18% incidence of hepatocellular carcinomas in male mice at 750 mg/kg, not statistically significant compared with either control by Fisher's exact test. There was a 12% incidence of hepatic basophilic foci and a 10% incidence of hepatocellular carcinomas in female mice at 750 mg/kg, statistically significant (p < 0.05) compared with vehicle but not with water controls by Fisher's exact test. There were no metastases. Time-dependent and -independent statistical analyses showed an adverse trend in the incidence of hepatocellular carcinomas in male and female mice, correlated with toxicity (expressed as mortality) at 750 mg/kg. The time-adjusted incidence of hepatocellular carcinomas in male mice (18.8%) was within the historical normal range at the testing facility (0-22%), but that in females (13.1%) lay outside the normal range (0-2%). Under the conditions of these studies 2EH was not oncogenic in rats, but there were weak adverse trends in hepatocellular carcinoma incidence in mice at high dose levels which may have been associated with toxicity. The major effects of chronic dosing were mortality in female rats at 500 mg/kg and in male and female mice at 750 mg/kg, accompanied by reductions in body weight gain in rats at 150 and 500 mg/kg and in mice at 750 mg/kg. Direct comparison of any tumorogenic effects of 2EH given alone to female mice with those due to 2EH formed in vivo from DEHA, DEHP, or TEHP is limited by the high mortality caused by 2ER in female mice at equivalent doses of 2EH. While 2EH may be a contributing factor in the hepatocellular carcinogenesis in female mice associated with the chronic administration of DEHA and DEHP, it is unlikely to be the entire proximate carcinogen.

Challenges to default assumptions stimulate comprehensive realism as a new tier in quantitative cancer risk assessment.

The current practice in carcinogen risk assessment of using a linearized multistage model and assuming low-dose linearity is based on several false premises. In many cases linearity at low doses would not be expected based on the interaction between the multiple components in the carcinogenic process. The two-stage growth models, involving multiple mutations and cell birth and death rates, provide one means of exploring these interactions. In addition, if carcinogenesis is considered to be the imbalance between invading substances and defense mechanisms, then the cancer probability depends on how much the substance increases or decrease the number of defenders or their efficiency as well as increasing or decreasing the number of invaders. Challenges to low-dose linearity and other default assumptions have stimulated the development of new risk assessment methodologies as have the need for more realistic estimates of risk, better uncertainty characterization, and greater utilization of cost-benefit analyses, and other tools for risk management decision making. "Comprehensive realism" is an emerging quantitative weight-of-evidence risk assessment methodology which is designed to reflect all of the relevant and available information and the current state of knowledge about the health risks associated with a substance.

Reconsideration of the genetic risk assessment for ethylene oxide exposures.

The US Environmental Protection Agency (EPA) developed a genetic risk assessment model for exposures to ethylene oxide utilizing data on the induction of reciprocal translocations in male germ cells [Rhomberg et al. 1990]. This particular approach served as a reasonable initial attempt, albeit somewhat limited with regard to endpoint and only partially attentive to the mechanisms of induction of genetic alterations and the behavior of chromosomes during meiosis. The present paper discusses the scientific basis for a reassessment of the EPA model, providing data and hypotheses related to effective dose to the target cells and shape of the dose-response relationship at low doses, and dose rates. While the present genetic risk assessment approach is discussed in terms of ethylene oxide, it would be applicable to most mutagenic chemicals. The outcome of the discussion is that the genetic risk for exposed males from reciprocal translocation induction will be negligible at low doses since the dose-response curve is likely to be a function of the square of the dose. In addition, the proportion of genetically unbalanced live born offspring in humans arising from reciprocal translocation carriers is less than 10% of the frequency formed through meiotic segregation and fertilization for such carriers. Simply from a consideration of mechanism--namely, the very high probability of DNA repair prior to the next S-phase for a resting oocyte--it would be predicted that there would be a very low to negligible frequency of translocations in female germ cells from ethylene oxide exposure. It is further stressed that additional components of a genetic risk model require a consideration of all germ cell stages in the male, and the inclusion of calculations for point and deletion mutations. Some indications of likely response are presented with these points in mind.

Use of probabilistic expert judgment in uncertainty analysis of carcinogenic potency.

A new approach to characterizing the state of knowledge about carcinogenic potency is described. In this approach, the carcinogenic risk posed by a specific dose is characterized by a probability distribution, indicating the relative likelihood of different risk estimates. The approach utilizes expert judgment and a probability tree and is illustrated in a case study of chloroform exposure. Experts in cancer biology/toxicology, pharmacokinetics, and dose-response modeling were identified by a panel of science-policy specialists. In a workshop, experts reviewed the chloroform data, received training in probability elicitation, and constructed a consensual probability tree based on biological theories of cancer causation. Distributions of carcinogenic risk were developed based on the probability tree, chloroform data, judgmental probabilities provided by the experts, and classical statistical techniques. Risk distributions varied considerably between experts, with some predicting essentially no risk from 100 ppb chloroform in drinking water while other have at least some probability on risks generally considered of regulatory significance. Estimated human risk was much lower when extrapolating from liver tumors in animals than from kidney tumors. Issues of scientific disagreement leading to different risk distributions between experts are discussed. The resulting risk distributions are compared to standard EPA risk calculations for the same exposure scenario as well as to the expert judgement of epidemiologists about cancer risks of chlorinated drinking water. Issues in combining expert judgments are discussed, and several alternative methods are presented. Strengths and weaknesses of the distributional approach are discussed.

A distributional approach to characterizing low-dose cancer risk.

Since cancer risk at very low doses cannot be directly measured in humans or animals, mathematical extrapolation models and scientific judgment are required. This article demonstrates a probabilistic approach to carcinogen risk assessment that employs probability trees, subjective probabilities, and standard bootstrapping procedures. The probabilistic approach is applied to the carcinogenic risk of formaldehyde in environmental and occupational settings. Sensitivity analyses illustrate conditional estimates of risk for each path in the probability tree. Fundamental mechanistic uncertainties are characterized. A strength of the analysis is the explicit treatment of alternative beliefs about pharmacokinetics and pharmacodynamics. The resulting probability distributions on cancer risk are compared with the point estimates reported by federal agencies. Limitations of the approach are discussed as well as future research directions.

Another flaw in the linearized multistage model upper bounds on human cancer potency.

The statistical methodology used by the EPA and other federal agencies to characterize human cancer potencies based on animal experiments greatly exaggerates the estimates and bounds for human cancer risks in some instances. The current methodology incorporates simplified assumptions and approximations that fail to properly assess the impact of quantitative differences in human and experimental animal background transition rates from stage to stage in the multistage carcinogenic process. Because the majority of tumorigenic responses in rats and mice occur in organs with a high background tumor incidence and, hence, high background stage transition rates, the current simplified methodology often significantly overstates human risk. This newly recognized flaw in conjunction with the several previously recognized flaws in the current characterizations of human cancer potencies argues strongly for a change away from the current characterizations based solely on a default screening methodology to a more comprehensive, biologically based risk assessment methodology.

Incorporating additional biological phenomena into two-stage cancer models.

Several difficulties arise in the implementation of the Armitage-Doll-type carcinogenesis model. Some of these difficulties have been briefly discussed herein, with particular attention to the recent finding that the magnitude of current animal-based bounds on human cancer potency is influenced by animal background transition rates. Although the ideal method of accounting for the background transition rates necessitates more direct biological information, this paper offers risk assessors some alternatives for improving current quantitative cancer potency assessment. Computer software has been developed to facilitate the use of not only the multistage model but also other dose-response models, including the following: 1) tolerance models (probit, logit, multihit, and Weibull), which assume that a distribution of tolerances exists in the population and that when a tolerance is exceeded, a carcinogenic response occurs; 2) multihit models, which assume that a carcinogenic response occurs when a tissue receives more than a specified number of hits; 3) Armitage-Doll multistage models, which explicitly model the time and/or dose dependence of each transition stage; 4) time-to-response extensions of the multistage model; and 5) extensions of the multistage model including cell proliferation (Lu and Sielken 1991, Holland and Sielken 1993). In any of the dose-response models, the dose scale is not restricted to the administered dose scale. Computer software that facilitates the use of more biologically relevant dose scales (such as delivered and biologically effective dose scales) is now available. Furthermore, the differences between species and routes of exposure in the amount of delivered or biologically effective dose corresponding to a particular administered dose can be incorporated. The dependence of an individual's dose on not only the individual's administered dose but also the individual's background dose and susceptibility can be incorporated as well. Hence, interindividual variability in dose levels and probabilities of a carcinogenic response can be considered (Holland and Sielken 1993). The possibility also exists of incorporating more cell biology into carcinogenesis theory using the MVK two-stage model. In this model, cell proliferation parameters are included, in contrast to models of the Armitage-Doll family. The MVK model offers increased potential for obtaining estimates of low-dose behavior that reflect more of the available biological data, including microdosimetry data. A Monte Carlo simulator for this model can be used in cases in which more complex biological mechanisms are included, information other than the means of population distributions is desired, and information on subpopulations is desired.(ABSTRACT TRUNCATED AT 400 WORDS)