Using the Biological Two-Stage Model to Assess Risk from Short-Term Exposures

Two assumptions used in risk assessment are investigated: (1) the assumption of fraction of lifetime dose rate assumes that the risk from a fractional lifetime exposure at a given dose rate is equal to the risk from full lifetime exposure at that same fraction of the given dose rate; (2) the assumption of fraction of lifetime risk assumes that the risk from a fractional lifetime exposure at a given dose rate is equal to that same fraction of the risk from full lifetime exposure at the same dose rate. These two assumptions are equivalent when risk is a linear function of dose. Thus both can be thought of as generalizations of the assumption that cancer risk is proportional to the total accumulated lifetime dose (or average daily dose), which is often made to assess the risk from short-term exposures. In this paper, the age-specific cumulative hazard functions are derived using the two-stage model developed by Moolgavkar, Venzon, and Knudson for situations when the exposure occurs during a single period or a single instant. The two assumptions described above are examined for three types of carcinogens, initiator, completer, and promoter, in the context of the model. For initiator and completer, these two assumptions are equivalent in the low-dose region; for a promoter, using the fraction of lifetime risk assumption is generally more conservative than that of the fraction of lifetime dose rate assumption. Tables are constructed to show that the use of either the fraction of lifetime dose rate assumption or the fraction lifetime risk assumption can both underestimate and overestimate the true risk for the three types of carcinogens.     

Additive and Multiplicative Models and Multistage Carcinogenesis Theory

In light of the Armitage-Doll multistage carcinogenesis theory, this paper examines the assumption that an additive relative risk relationship is indicative of two carcinogens that affect the same stage in the cancer process. We present formulas to compute excess cancer risks for a variety of patterns for limited exposure durations to two carcinogens that affect the first and penultimate stages; and using an index of synergy proposed by Thomas (1982), we find a number of these patterns to produce additive, or nearly additive, relative risk relationships. The consistent feature of these patterns is that the two exposure periods are of short duration and occur close together.     

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).     

Multistage model interpretation of additive and multiplicative carcinogenic effects

Under the assumption of multistage carcinogenesis, a multiplicative carcinogenic effect would be produced by the action of different carcinogens in a mixture on different stages of the carcinogenic process. An additive effect would be produced by the effect of different carcinogens on the same stage. A mathematical argument for these hypotheses is presented here.     

Quantitative Assessment of the Risk of Lung Cancer Associated with Occupational Exposure to Refractory Ceramic Fibers

We present the results of a quantitative assessment of the lung cancer risk associated with occupational exposure to refractory ceramic fibers (RCF). The primary sources of data for our risk assessment were two long-term oncogenicity studies in male Fischer rats conducted to assess the potential pathogenic effects associated with prolonged inhalation of RCF. An interesting feature of the data was the availability of the temporal profile of fiber burden in the lungs of experimental animals. Because of this information, we were able to conduct both exposure–response and dose–response analyses. Our risk assessment was conducted within the framework of a biologically based model for carcinogenesis, the two-stage clonal expansion model, which allows for the explicit incorporation of the concepts of initiation and promotion in the analyses. We found that a model positing that RCF was an initiator had the highest likelihood. We proposed an approach based on biological considerations for the extrapolation of risk to humans. This approach requires estimation of human lung burdens for specific exposure scenarios, which we did by using an extension of a model due to Yu. Our approach acknowledges that the risk associated with exposure to RCF depends on exposure to other lung carcinogens. We present estimates of risk in two populations: (1) a population of nonsmokers and (2) an occupational cohort of steelworkers not exposed to coke oven emissions, a mixed population that includes both smokers and nonsmokers.     

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.     

Risk Assessment for Aflatoxin: III. Modeling the Relative Risk of Hepatocellular Carcinoma

Estimates have been made of the cancer potency of aflatoxin exposure among the U.S. population. Risk modeling is used to assess the dose-response relationship between aflatoxin exposure and primary liver cancer, controlling for hepatitis B virus (HBV), based on data provided by the Yeh et al. study in China. A relative risk model is proposed as a more appropriate alternative to the additive ("absolute" risk) model for transportation of risk coefficients between populations with different baseline rates. Several general relative risk models were examined; the exponential model provided the best fit. The Poisson regression method was used to fit the relative risk model to the grouped data. The effects of exposure to aflatoxin (AFB1) and hepatitis B infection were both found to be statistically significant. The risk of death from liver cancer for those exposed to AFB1 relative to the unexposed population, increases by 0.05% per ng/kg/day exposure of AFB1 (p less than 0.001). The results also indicated a 25-fold increase in the risk of death from liver cancer among those infected with hepatitis B virus, relative to noncarriers (p less than 0.0001). With a hepatitis prevalence rate of 1%, the aflatoxin intake level associated with liver cancer lifetime excess risk of 1 x 10(-5) for the U.S. population was estimated as 253 ng/day, based on a liver cancer baseline rate of 3.4/100,000/yr.     

Use of Acute Toxicity to Estimate Carcinogenic Risk

Data on the effects of human exposure to carcinogens are limited, so that estimation of the risks of carcinogens must be obtained indirectly. Current risk estimates are generally based on lifetime animal bioassays which are expensive and which take more than two years to complete. We here show how data on acute toxicity can be used to make a preliminary estimate of carcinogenic risk and give an idea of the uncertainty in that risk estimate. The estimates obtained are biased upwards, and so are useful for setting interim standards and determining whether further study is worthwhile. A general scheme which incorporates the use of such estimates is outlined, and it is shown by example how adoption of the procedures suggested could have prevented regulatory hiatus in the past.     

考虑背景风险的项目投资决策

在项目投资过程中不但面临项目风险,同时还面临背景风险,且背景风险与项目风险之间往往存在着一定的相关性。文章在已有研究的基础上,针对考虑背景风险的项目投资决策问题,分析了风险之间的相关性及相关程度对投资决策的影响。首先讨论了加性背景风险和乘性背景风险单独存在时,背景风险与项目风险之间的相关性对投资决策的影响;其次构建了两种背景风险同时存在情形下的投资模型,进而通过蒙特卡罗仿真方法给出不同相关程度下的仿真结果,在此基础上分析两种背景风险与项目风险之间的相关性及相关程度对投资决策的影响并给出相关研究结论。     

Exposure to Persistent Organochlorines in Canadian Breast Milk: A Probabilistic Assessment

Exposure to persistent organochlorines in breast milk was estimated probabilistically for Canadian infants. Noncancer health effects were evaluated by comparing the predicted exposure distributions to published guidance values. For chemicals identified as potential human carcinogens, cancer risks were evaluated using standard methodology typically applied in Canada, as well as an alternative method developed under the Canadian Environmental Protection Act. Potential health risks associated with exposure to persistent organochlorines were quantitatively and qualitatively weighed against the benefits of breast-feeding. Current levels of the majority of contaminants identified in Canadian breast milk do not pose unacceptable risks to infants. Benefits of breast-feeding are well documented and qualitatively appear to outweigh potential health concerns associated with organochlorine exposure. Furthermore, the risks of mortality from not breast-feeding estimated by Rogan and colleagues exceed the theoretical cancer risks estimated for infant exposure to potential carcinogens in Canadian breast milk. Although levels of persistent compounds have been declining in Canadian breast milk, potentially significant risks were estimated for exposure to polychlorinated biphenyls, dibenzo-p-dioxins, and dibenzofurans. Follow-up work is suggested that would involve the use of a physiologically based toxicokinetic model with probabilistic inputs to predict dioxin exposure to the infant. A more detailed risk analysis could be carried out by coupling the exposure estimates with a dose–response analysis that accounts for uncertainty.     

Interspecies Extrapolation of Physiological Pharmacokinetic Parameter Distributions

Three methods (multiplicative, additive, and allometric) were developed to extrapolate physiological model parameter distributions across species, specifically from rats to humans. In the multiplicative approach, the rat model parameters are multiplied by the ratio of the mean values between humans and rats. Additive scaling of the distributions is denned by adding the difference between the average human value and the average rat value to each rat value. Finally, allometric scaling relies on established extrapolation relationships using power functions of body weight. A physiologically-based pharmacokinetic model was fitted independently to rat and human benzene disposition data. Human model parameters obtained by extrapolation and by fitting were used to predict the total bone marrow exposure to benzene and the quantity of metabolites produced in bone marrow. We found that extrapolations poorly predict the human data relative to the human model. In addition, the prediction performance depends largely on the quantity of interest. The extrapolated models underpredict bone marrow exposure to benzene relative to the human model. Yet, predictions of the quantity of metabolite produced in bone marrow are closer to the human model predictions. These results indicate that the multiplicative and allometric techniques were able to extrapolate the model parameter distributions, but also that rats do not provide a good kinetic model of benzene disposition in humans.     

Cancer Risk Estimation of Genotoxic Chemicals Based on Target Dose and a Multiplicative Model

A mechanistic model and associated procedures are proposed for cancer risk assessment of genotoxic chemicals. As previously shown for ionizing radiation, a linear multiplicative model was found to be compatible with published experimental data for ethylene oxide, acrylamide, and butadiene. The validity of this model was anticipated in view of the multiplicative interaction of mutation with inherited and acquired growth-promoting conditions. Concurrent analysis led to rejection of an additive model (i.e. the model commonly applied for cancer risk assessment). A reanalysis of data for radiogenic cancer in mouse, dog and man shows that the relative risk coefficient is approximately the same (0.4 to 0.5 percent per rad) for tumours induced in the three species.Doses in vivo, defined as the time-integrated concentrations of ultimate mutagens, expressed in millimol × kg^–1 × h (mMh) are, like radiation doses given in Gy or rad, proportional to frequencies of potentially mutagenic events. The radiation dose equivalents of chemical doses are, calculated by multiplying chemical doses (in mMh) with the relative genotoxic potencies (in rad × mMh^–1) determined in vitro. In this way the relative cancer incidence increments in rats and mice exposed to ethylene oxide were shown to be about 0.4 percent per rad-equivalent, in agreement with the data for radiogenic cancer.Our analyses suggest that values of the relative risk coefficients for genotoxic chemicals are independent of species and that relative cancer risks determined in animal tests apply also to humans. If reliable animal test data are not available, cancer risks may be estimated by the relative potency. In both cases exposure dose/target dose relationships, the latter via macromolecule adducts, should be determined.     

Compliance Versus Risk in Assessing Occupational Exposures

Assessments of occupational exposures to chemicals are generally based upon the practice of compliance testing in which the probability of compliance is related to the exceedance [γ, the likelihood that any measurement would exceed an occupational exposure limit (OEL)] and the number of measurements obtained. On the other hand, workers’ chronic health risks generally depend upon cumulative lifetime exposures which are not directly related to the probability of compliance. In this paper we define the probability of “overexposure” (θ) as the likelihood that individual risk (a function of cumulative exposure) exceeds the risk inherent in the OEL (a function of the OEL and duration of exposure). We regard θ as a relevant measure of individual risk for chemicals, such as carcinogens, which produce chronic effects after long-term exposures but not necessarily for acutely-toxic substances which can produce effects relatively quickly. We apply a random-effects model to data from 179 groups of workers, exposed to a variety of chemical agents, and obtain parameter estimates for the group mean exposure and the within- and between-worker components of variance. These estimates are then combined with OELs to generate estimates of γ and θ. We show that compliance testing can significantly underestimate the health risk when sample sizes are small. That is, there can be large probabilities of compliance with typical sample sizes, despite the fact that large proportions of the working population have individual risks greater than the risk inherent in the OEL. We demonstrate further that, because the relationship between θ and γ depends upon the within- and between-worker components of variance, it cannot be assumed a priori that exceedance is a conservative surrogate for overexposure. Thus, we conclude that assessment practices which focus upon either compliance or exceedance are problematic and recommend that employers evaluate exposures relative to the probabilities of overexposure.     

An Adjustment Factor for Mode-of-Action Uncertainty with Dual-Mode Carcinogens: The Case of Naphthalene-Induced Nasal Tumors in Rats

The U.S. Environmental Protection Agency (USEPA) guidelines for cancer risk assessment recognize that some chemical carcinogens may have a site-specific mode of action (MOA) involving mutation and cell-killing-induced hyperplasia. The guidelines recommend that for such dual MOA (DMOA) carcinogens, judgment should be used to compare and assess results using separate "linear" (genotoxic) versus "nonlinear" (nongenotoxic) approaches to low-level risk extrapolation. Because the guidelines allow this only when evidence supports reliable risk extrapolation using a validated mechanistic model, they effectively prevent addressing MOA uncertainty when data do not fully validate such a model but otherwise clearly support a DMOA. An adjustment-factor approach is proposed to address this gap, analogous to reference-dose procedures used for classic toxicity endpoints. By this method, even when a "nonlinear" toxicokinetic model cannot be fully validated, the effect of DMOA uncertainty on low-dose risk can be addressed. Application of the proposed approach was illustrated for the case of risk extrapolation from bioassay data on rat nasal tumors induced by chronic lifetime exposure to naphthalene. Bioassay data, toxicokinetic data, and pharmacokinetic analyses were determined to indicate that naphthalene is almost certainly a DMOA carcinogen. Plausibility bounds on rat-tumor-type-specific DMOA-related uncertainty were obtained using a mechanistic two-stage cancer risk model adapted to reflect the empirical link between genotoxic and cytotoxic effects of the most potent identified genotoxic naphthalene metabolites, 1,2- and 1,4-naphthoquinone. Bound-specific adjustment factors were then used to reduce naphthalene risk estimated by linear extrapolation (under the default genotoxic MOA assumption), to account for the DMOA exhibited by this compound.     

Apoptosis and Chemical Carcinogenesis

Long recognized as a normal component of organogenesis during development, apoptosis (programmed cell death) has recently been implicated in alterations of cell growth and differentiation. Tissue homeostasis is normally maintained by a balance between cell division and cell death, with apoptosis often functioning in complement to cell growth. Thus, antithetical parallels in chemical carcinogenesis can be drawn between apoptosis and the proliferative events more commonly addressed. While enhanced cell replication may contribute to an increased frequency of mutation, apoptosis within a tissue may counteract chemical carcinogenesis through loss of mutated cells. Many strong carcinogens act as tumor promoters, selectively expanding an initiated cell population advantageously over surrounding cells. Similarly, chemicals with a selective inhibition of apoptosis within an initiated population would offer a growth advantage. In contrast, chemicals causing selective apoptosis of initiated cells would be expected to have an anticarcinogenic effect. Selective apoptosis, in concert with cell-specific replication, may explain the unique promoting effects of different carcinogens such as the peroxisome-proliferating chemicals, phenobarbital, and 2,3,7,8-tetrachloro-dibenzo- p -dioxin (TCDD). Cell turnover, both cell growth and cell death, is central to the process of chemically induced carcinogenesis in animals and understanding its impact is a critical determinant of the relevance of chemically induced effects to man.     

A Quantitative Estimate of Leukemia Mortality Associated with Occupational Exposure to Benzene3

In 1980, the U.S. Supreme Court vacated a revised occupational standard for benzene, stating that the Occupational Safety and Health Administration (OSHA) had failed to demonstrate that significant health risks existed under the current standard. This decision has been interpreted by OSHA as requiring the consideration of quantitative risk assessments, whenever possible, in the development of regulations for occupational carcinogens. In light of this decision, the available epidemiologic evidence was used to generate a quantitative risk assessment for benzene. Uncertainties regarding the levels and lengths of benzene exposure for the studied cohorts were incorporated into the analysis. Based on the one-hit model, the assessment indicates that a working lifetime exposure to benzene at the current permissible exposure level (10 ppm) poses a substantial excess risk of death from leukemia. This report discusses the calculation of the risk estimates, the basis for relying on certain assumptions, and the inherent limitations of using epidemiologic studies to quantify cancer risks.     

Risk Assessment of Multistate Progression of Breast Tumor with State‐Dependent Genetic and Environmental Covariates

Few studies have focused on the different roles risk factors play in the multistate temporal natural course of breast cancer. We proposed a three‐state Markov regression model to predict the risk from free of breast cancer (FBC) to the preclinical screen‐detectable phase (PCDP) and from the PCDP to the clinical phase (CP). We searched the initiators and promoters affecting onset and subsequent progression of breast tumor to build up a three‐state temporal natural history model with state‐dependent genetic and environmental covariates. This risk assessment model was applied to a 1 million Taiwanese women cohort. The proposed model was verified by external validation with another independent data set. We identified three kinds of initiators, including the BRCA gene, seven single nucleotides polymorphism, and breast density. ER, Ki‐67, and HER‐2 were found as promoters. Body mass index and age at first pregnancy both played a role. Among women carrying the BRCA gene, the 10‐year predicted risk for the transition from FBC to CP was 25.83%, 20.31%, and 13.84% for the high‐, intermediate‐, and low‐risk group, respectively. The corresponding figures were 1.55%, 1.22%, and 0.76% among noncarriers. The mean sojourn time of staying at the PCDP ranged from 0.82 years for the highest risk group to 6.21 years for the lowest group. The lack of statistical significance for external validation () revealed the adequacy of our proposed model. The three‐state model with state‐dependent covariates of initiators and promoters was proposed for achieving individually tailored screening and also for personalized clinical surveillance of early breast cancer.     

Zum Verhältnis von Wertadditivität bei Sicherheitsäquivalenten und Risikoanalyse — Replik zu den Anmerkungen „Sicherheitsäquivalente sind nicht überflüssig!“ von Björn Häckel, Christian Holtz und Hans Ulrich Buhl

Zusammenfassung  Die Forderung nach Geldmarktinvarianz in der Risikoanalyse impliziert weder Invarianz des Sicherheits?quivalentes im Hinblick auf den Kassenbestand (additive Konstante) noch Invarianz im Hinblick auf die Finanzierungsstruktur (multiplikative Konstante) des Investors. Hingegen kann sowohl konstante absolute Risikoaversion (Invarianz bezüglich additiver Konstanten) also auch konstante relative Risikoaversion (Invarianz bezüglich multiplikativer Konstanten) durchaus kompatibel mit Geldmarktinvarianz sein. Aus der Wertadditivit?t des Sicherheits?quivalentes bezüglich additiver Konstanten folgt jedoch Geldmarktinvarianz.

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On the relationship between value additivity of certainty equivalents and risk analysis

Summary  If the valuation of risky cash flow streams is independent of transactions in a perfect money market (as required in the so-called risk analysis), this does neither imply value additivity of the certainty equivalent with respect to additive constants, i.e. cash holdings, nor with respect to multiplicative constant, i.e. the capital structure of the investor. But both, constant absolute and constant relative risk aversion, i.e. value additivity with respect to additive and multiplicative constants, respectively, can be consistent with money market invariance. However, value additivity regarding additive constants implies money market invariance.

     

Determination of Less-Than-Lifetime Exposures to Point Source Emissions

This paper presents a method of estimating long-term exposures to point source emissions. The method consists of a Monte Carlo exposure model (PSEM or Point Source Exposure Model) that combines data on population mobility and mortality with information on daily activity patterns. The approach behind the model can be applied to a wide variety of exposure scenarios. In this paper, PSEM is used to characterize the range and distribution of lifetime equivalent doses received by inhalation of air contaminated by the emissions of a point source. The output of the model provides quantitative information on the dose, age, and gender of highly exposed individuals. The model is then used in an example risk assessment. Finally, future uses of the model's approach are discussed.