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.     

Diesel Engine Exhaust and Lung Cancer Mortality: Time‐Related Factors in Exposure and Risk

To develop a quantitative exposure‐response relationship between concentrations and durations of inhaled diesel engine exhaust (DEE) and increases in lung cancer risks, we examined the role of temporal factors in modifying the estimated effects of exposure to DEE on lung cancer mortality and characterized risk by mine type in the Diesel Exhaust in Miners Study (DEMS) cohort, which followed 12,315 workers through December 1997. We analyzed the data using parametric functions based on concepts of multistage carcinogenesis to directly estimate the hazard functions associated with estimated exposure to a surrogate marker of DEE, respirable elemental carbon (REC). The REC‐associated risk of lung cancer mortality in DEMS is driven by increased risk in only one of four mine types (limestone), with statistically significant heterogeneity by mine type and no significant exposure‐response relationship after removal of the limestone mine workers. Temporal factors, such as duration of exposure, play an important role in determining the risk of lung cancer mortality following exposure to REC, and the relative risk declines after exposure to REC stops. There is evidence of effect modification of risk by attained age. The modifying impact of temporal factors and effect modification by age should be addressed in any quantitative risk assessment (QRA) of DEE. Until there is a better understanding of why the risk appears to be confined to a single mine type, data from DEMS cannot reliably be used for QRA.     

Dose-Response and Risk Assessment of Airborne Hexavalent Chromium and Lung Cancer Mortality

This study evaluates the dose-response relationship for inhalation exposure to hexavalent chromium [Cr(VI)] and lung cancer mortality for workers of a chromate production facility, and provides estimates of the carcinogenic potency. The data were analyzed using relative risk and additive risk dose-response models implemented with both Poisson and Cox regression. Potential confounding by birth cohort and smoking prevalence were also assessed. Lifetime cumulative exposure and highest monthly exposure were the dose metrics evaluated. The estimated lifetime additional risk of lung cancer mortality associated with 45 years of occupational exposure to 1 microg/m3 Cr(VI) (occupational exposure unit risk) was 0.00205 (90%CI: 0.00134, 0.00291) for the relative risk model and 0.00216 (90%CI: 0.00143, 0.00302) for the additive risk model assuming a linear dose response for cumulative exposure with a five-year lag. Extrapolating these findings to a continuous (e.g., environmental) exposure scenario yielded an environmental unit risk of 0.00978 (90%CI: 0.00640, 0.0138) for the relative risk model [e.g., a cancer slope factor of 34 (mg/kg-day)-1] and 0.0125 (90%CI: 0.00833, 0.0175) for the additive risk model. The relative risk model is preferred because it is more consistent with the expected trend for lung cancer risk with age. Based on statistical tests for exposure-related trend, there was no statistically significant increased lung cancer risk below lifetime cumulative occupational exposures of 1.0 mg-yr/m3, and no excess risk for workers whose highest average monthly exposure did not exceed the current Permissible Exposure Limit (52 microg/m3). It is acknowledged that this study had limited power to detect increases at these low exposure levels. These cancer potency estimates are comparable to those developed by U.S. regulatory agencies and should be useful for assessing the potential cancer hazard associated with inhaled Cr(VI).     

Risk Assessment for Aflatoxin: An Evaluation Based on the Multistage Model

Lifetime cancer potency of alfatoxin was assessed based on the Yeh et al. study from China in which both aflatoxin exposure and hepatitis B prevalence were measured. This study provides the best available information for estimating the carcinogenic risk posed by aflatoxin to the U.S. population. Cancer potency of aflatoxin was estimated using a biologically motivated risk assessment model. The best estimate of aflatoxin potency was 9 (mg/kg/day)⁻¹ for individuals negative for hepatitis B and 230 (mg/kg/day)⁻¹ for individuals positive for hepatitis B.     

Calculating the Hazard Function and Probability of Tumor for Cancer Risk Assessment When the Parameters Are Time-Dependent

The probability of tumor and hazard function are calculated in a stochastic two-stage model for carcinogenesis when the parameters of the mode are time-dependent. The method used is called the method of characteristics.     

Could Removing Arsenic from Tobacco Smoke Significantly Reduce Smoker Risks of Lung Cancer?

If a specific biological mechanism could be determined by which a carcinogen increases lung cancer risk, how might this knowledge be used to improve risk assessment? To explore this issue, we assume (perhaps incorrectly) that arsenic in cigarette smoke increases lung cancer risk by hypermethylating the promoter region of gene p16INK4a, leading to a more rapid entry of altered (initiated) cells into a clonal expansion phase. The potential impact on lung cancer of removing arsenic is then quantified using a three‐stage version of a multistage clonal expansion (MSCE) model. This refines the usual two‐stage clonal expansion (TSCE) model of carcinogenesis by resolving its intermediate or “initiated” cell compartment into two subcompartments, representing experimentally observed “patch” and “field” cells. This refinement allows p16 methylation effects to be represented as speeding transitions of cells from the patch state to the clonally expanding field state. Given these assumptions, removing arsenic might greatly reduce the number of nonsmall cell lung cancer cells (NSCLCs) produced in smokers, by up to two‐thirds, depending on the fraction (between 0 and 1) of the smoking‐induced increase in the patch‐to‐field transition rate prevented if arsenic were removed. At present, this fraction is unknown (and could be as low as zero), but the possibility that it could be high (close to 1) cannot be ruled out without further data.     

Assessment of the Effectiveness of Radon Screening Programs in Reducing Lung Cancer Mortality

The present study was aimed at assessing the health consequences of the presence of radon in Quebec homes and the possible impact of various screening programs on lung cancer mortality. Lung cancer risk due to this radioactive gas was estimated according to the cancer risk model developed by the Sixth Committee on Biological Effects of Ionizing Radiations. Objective data on residential radon exposure, population mobility, and tobacco use in the study population were integrated into a Monte‐Carlo‐type model. Participation rates to radon screening programs were estimated from published data. According to the model used, approximately 10% of deaths due to lung cancer are attributable to residential radon exposure on a yearly basis in Quebec. In the long term, the promotion of a universal screening program would prevent less than one death/year on a province‐wide scale (0.8 case; IC 99%: –3.6 to 5.2 cases/year), for an overall reduction of 0.19% in radon‐related mortality. Reductions in mortality due to radon by (1) the implementation of a targeted screening program in the region with the highest concentrations, (2) the promotion of screening on a local basis with financial support, or (3) the realization of systematic investigations in primary and secondary schools would increase to 1%, 14%, and 16.4%, respectively, in the each of the populations targeted by these scenarios. Other than the battle against tobacco use, radon screening in public buildings thus currently appears as the most promising screening policy for reducing radon‐related lung cancer.     

An Exposure‐Response Threshold for Lung Diseases and Lung Cancer Caused by Crystalline Silica

Whether crystalline silica (CS) exposure increases risk of lung cancer in humans without silicosis, and, if so, whether the exposure‐response relation has a threshold, have been much debated. Epidemiological evidence is ambiguous and conflicting. Experimental data show that high levels of CS cause lung cancer in rats, although not in other species, including mice, guinea pigs, or hamsters; but the relevance of such animal data to humans has been uncertain. This article applies recent insights into the toxicology of lung diseases caused by poorly soluble particles (PSPs), and by CS in particular, to model the exposure‐response relation between CS and risk of lung pathologies such as chronic inflammation, silicosis, fibrosis, and lung cancer. An inflammatory mode of action is described, having substantial empirical support, in which exposure increases alveolar macrophages and neutrophils in the alveolar epithelium, leading to increased reactive oxygen species (ROS) and nitrogen species (RNS), pro‐inflammatory mediators such as TNF‐alpha, and eventual damage to lung tissue and epithelial hyperplasia, resulting in fibrosis and increased lung cancer risk among silicotics. This mode of action involves several positive feedback loops. Exposures that increase the gain factors around such loops can create a disease state with elevated levels of ROS, TNF‐alpha, TGF‐beta, alveolar macrophages, and neutrophils. This mechanism implies a “tipping point” threshold for the exposure‐response relation. Applying this new model to epidemiological data, we conclude that current permissible exposure levels, on the order of 0.1 mg/m³, are probably below the threshold for triggering lung diseases in humans.     

Using Average Lifetime Dose Rate for Intermittent Exposures to Carcinogens

The effect of using the average dose rate over a lifetime as a representative measure of exposure to carcinogens is investigated by comparing the true theoretical multistage intermittent-dosing lifetime low-dose excess risk to the theoretical multistage continuous-dosing lifetime risk corresponding to the average lifetime dose rate. It is concluded that low-dose risk estimates based on the average lifetime dose rate may overestimate the true risk by several orders of magnitude, but that they never underestimate the true risk by more than a factor of k/r, where k is the total number of stages in the multistage model and r is the number of stages that are dose-related.     

Bounding Poorly Characterized Risks: A Lung Cancer Example

For diseases with more than one risk factor, the sum of probabilistic estimates of the number of cases caused by each individual factor may exceed the total number of cases observed, especially when uncertainties about exposure and dose response for some risk factors are high. In this study, we outline a method of bounding the fraction of lung cancer fatalities not due to specific well-studied causes. Such information serves as a "reality check" for estimates of the impacts of the minor risk factors, and, as such, complements the traditional risk analysis. With lung cancer as our example, we allocate portions of the observed lung cancer mortality to known causes (such as smoking, residential radon, and asbestos fibers) and describe the uncertainty surrounding those estimates. The interactions among the risk factors are also quantified, to the extent possible. We then infer an upper bound on the residual mortality due to "other" causes, using a consistency constraint on the total number of deaths, the maximum uncertainty principle, and the mathematics originally developed of imprecise probabilities.     

How Do Cancer Risks Predicted From Animal Bioassays Compare with the Epidemiologic Evidence? The Case of Ethylene Dibromide

Cancer risks for ethylene dibromide (EDB) were estimated by fitting several linear non-threshold additive models to data from a gavage bioassay. Risks predicted by these models were compared to the observed cancer mortality among a cohort of workers occupationally exposed to the same chemical. Models that accounted for the shortened latency period in the gavaged rats predicted upper bound risks that were within a factor of 3 of the observed cancer deaths. Data from an animal inhalation study of EDB also were compatible with the epidemiologic data. These findings contradict those of Ramsey et al. (1978), who reported that extrapolation from animal data produced highly exaggerated risk estimates for EDB-exposed workers. This paper explores the reasons for these discrepant findings.     

Quantifying Potential Health Impacts of Cadmium in Cigarettes on Smoker Risk of Lung Cancer: A Portfolio-of-Mechanisms Approach

This article introduces an approach to estimating the uncertain potential effects on lung cancer risk of removing a particular constituent, cadmium (Cd), from cigarette smoke, given the useful but incomplete scientific information available about its modes of action. The approach considers normal cell proliferation; DNA repair inhibition in normal cells affected by initiating events; proliferation, promotion, and progression of initiated cells; and death or sparing of initiated and malignant cells as they are further transformed to become fully tumorigenic. Rather than estimating unmeasured model parameters by curve fitting to epidemiological or animal experimental tumor data, we attempt rough estimates of parameters based on their biological interpretations and comparison to corresponding genetic polymorphism data. The resulting parameter estimates are admittedly uncertain and approximate, but they suggest a portfolio approach to estimating impacts of removing Cd that gives usefully robust conclusions. This approach views Cd as creating a portfolio of uncertain health impacts that can be expressed as biologically independent relative risk factors having clear mechanistic interpretations. Because Cd can act through many distinct biological mechanisms, it appears likely (subjective probability greater than 40%) that removing Cd from cigarette smoke would reduce smoker risks of lung cancer by at least 10%, although it is possible (consistent with what is known) that the true effect could be much larger or smaller. Conservative estimates and assumptions made in this calculation suggest that the true impact could be greater for some smokers. This conclusion appears to be robust to many scientific uncertainties about Cd and smoking effects.     

Mesothelioma: Risk Apportionment Among Asbestos Exposure Sources

The mesothelioma epidemic in the United States, which peaked during the 2000–2004 period, can be traced to high‐level asbestos exposures experienced by males in occupational settings prior to the full recognition of the disease‐causing potential of asbestos and the establishment of enforceable asbestos exposure limits by the Occupational Safety and Health Administration (OSHA) in 1971. Many individuals diagnosed with mesothelioma where asbestos has been identified as a contributing cause of the disease have filed claims seeking compensation from asbestos settlement trusts or through the court system. An individual with mesothelioma typically has been exposed to asbestos in more than one setting and from more than one asbestos product. Apportioning risk for mesothelioma among contributing factors is an ongoing problem faced by occupational disease compensation boards, juries, parties responsible for paying damages, and currently by the U.S. Senate in its efforts to formulate a bill establishing an asbestos settlement trust. In this article we address the following question: If an individual with mesothelioma where asbestos has been identified as a contributing cause were to be compensated for his or her disease, how should that compensation be apportioned among those responsible for the asbestos exposures? For the purposes of apportionment, we assume that asbestos is the only cause of mesothelioma and that every asbestos exposure contributes, albeit differentially, to the risk. We use an extension of the mesothelioma risk model initially proposed in the early 1980s to quantify the contribution to risk of each exposure as a percentage of the total risk. The percentage for each specific discrete asbestos exposure depends on the start and end dates, the intensity, and the asbestos fiber type for the exposure. We provide justification for the use of the mesothelioma risk model for apportioning risk and discuss how to assess uncertainty associated with its application.     

Significance of Exposure Assessment to Analysis of Cancer Risk from Inorganic Arsenic in Drinking Water in Taiwan

The primary source of evidence that inorganic arsenic in drinking water is associated with increased mortality from cancer at internal sites (bladder, liver, lung, and other organs) is a large ecologic study conducted in regions of Southwest Taiwan endemic to Blackfoot disease. The dose-response patterns for lung, liver, and bladder cancers display a nonlinear dose-response relationship with arsenic exposure. The data do not appear suitable, however, for the more refined task of dose-response assessment, particularly for inference of risk at the low arsenic concentrations found in some U.S. water supplies. The problem lies in variable arsenic concentrations between the wells within a village, largely due to a mix of shallow wells and deep artesian wells, and in having only one well test for 24 (40%) of the 60 villages. The current analysis identifies 14 villages where the exposure appears most questionable, based on criteria described in the text. The exposure values were then changed for seven of the villages, from the median well test being used as a default to some other point in the village's range of well tests that would contribute to smoothing the appearance of a dose-response curve. The remaining seven villages, six of which had only one well test, were deleted as outliers. The resultant dose-response patterns showed no evidence of excess risk below arsenic concentrations of 0.1 mg/l. Of course, that outcome is dependent on manipulation of the data, as described. Inclusion of the seven deleted villages would make estimates of risk much higher at low doses. In those seven villages, the cancer mortality rates are significantly high for their exposure levels, suggesting that their exposure values may be too low or that other etiological factors need to be taken into account.     

Cancer Risk Assessment with Intermittent Exposure

Applications of methods for carcinogenic risk assessment often focus on estimating lifetime cancer risk. With intermittent or time-dependent exposures, lifetime risk is often approximated on the basis of a lifetime average daily dose (LADD). In this article, we show that there exists a lifetime equivalent constant dose (LECD) which leads to the same lifetime risk as the actual time-dependent exposure pattern. The ratio C = LECD/LADD then provides a measure of accuracy of risk estimates based on the LADD, as well as a basis for correcting such estimates. Theoretical results derived under the classical multistage model and the two-stage birth-death-mutation model suggest that the maximum value of C, which represents the factor by which the LADD may lead to underestimates of risk, will often lie in the range of 2- to 5-fold. The practical application of these results is illustrated in the case of astronauts subjected to relatively short-term exposure to volatile organics in a closed space station environment, and in the case of the ingestion of pesticide residues in food where consumption patterns vary with age.     

A Stochastic Two-Stage Model for Cancer Risk Assessment. II. The Number and Size of Premalignant Clones

Mathematical expressions are derived, under different dosing patterns, for the number and size of premalignant clones within the framework of a two-mutation model for carcinogenesis, which has previously been shown to be consistent with a large body of epidemiologic and experimental data.     

Modeling Long-Term Exposure of the Whole Population to Chemicals in Food

This paper discusses a statistical exposure model (STEM) that can be used to estimate the percentage of the population exceeding ingestion intake criteria (e.g., ADI or TDI). In addition, STEM may be linked to toxicokinetic models to evaluate the interindividual variability in internal doses that results from variability in consumption habits. The assumptions of STEM are investigated by analyzing dioxin and cadmium intake data for the Dutch population.     

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 g/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 g/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 g/kg/day.     

Peak Exposures in Epidemiologic Studies and Cancer Risks: Considerations for Regulatory Risk Assessment

We review approaches for characterizing “peak” exposures in epidemiologic studies and methods for incorporating peak exposure metrics in dose–response assessments that contribute to risk assessment. The focus was on potential etiologic relations between environmental chemical exposures and cancer risks. We searched the epidemiologic literature on environmental chemicals classified as carcinogens in which cancer risks were described in relation to “peak” exposures. These articles were evaluated to identify some of the challenges associated with defining and describing cancer risks in relation to peak exposures. We found that definitions of peak exposure varied considerably across studies. Of nine chemical agents included in our review of peak exposure, six had epidemiologic data used by the U.S. Environmental Protection Agency (US EPA) in dose–response assessments to derive inhalation unit risk values. These were benzene, formaldehyde, styrene, trichloroethylene, acrylonitrile, and ethylene oxide. All derived unit risks relied on cumulative exposure for dose–response estimation and none, to our knowledge, considered peak exposure metrics. This is not surprising, given the historical linear no‐threshold default model (generally based on cumulative exposure) used in regulatory risk assessments. With newly proposed US EPA rule language, fuller consideration of alternative exposure and dose–response metrics will be supported. “Peak” exposure has not been consistently defined and rarely has been evaluated in epidemiologic studies of cancer risks. We recommend developing uniform definitions of “peak” exposure to facilitate fuller evaluation of dose response for environmental chemicals and cancer risks, especially where mechanistic understanding indicates that the dose response is unlikely linear and that short‐term high‐intensity exposures increase risk.