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.     

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.     

Multimedia Analysis of PAHs and Nitro-PAH Daughter Products in the Los Angeles Basin

Polycyclic aromatic hydrocarbons (PAHs) that are released into the atmosphere may have health consequences that can be compounded by their nitro-PAH atmospheric transformation products. The available literature suggests that some of the atmospheric nitro-PAH daughter products may increase the overall environmental health risk associated with PAHs. Therefore, an important issue is whether there is merit in considering atmospheric transformation products of air toxins when conducting environmental health-risk analyses. To illustrate the above issue, a comparative analysis of the potential risk that may be imposed by PAHs and their daughter products was carried out for the Los Angeles Basin. The analysis consisted of first assessing the multimedia environmental concentration of selected PAHs and nitro-PAHs using a spatial-compartmental modeling approach coupled with available monitoring data. Multimedia concentrations were then used to estimate chemical media-specific mutagenic densities as well as average daily intake from multiple pathways, followed by cancer risk for the known carcinogens among the study chemicals. The analysis revealed that mutagenic densities of the nitro-PAH daughter products can significantly exceed those of the parent PAHs. The results of this study suggest that there is merit in further investigation of the potential contribution of nitro-PAHs to the overall environmental health risk associated with airborne PAHs.     

A Quantitative Microbial Risk Assessment Model for Legionnaires'' Disease: Animal Model Selection and Dose-Response Modeling

Legionnaires' disease (LD), first reported in 1976, is an atypical pneumonia caused by bacteria of the genus Legionella, and most frequently by L. pneumophila (Lp). Subsequent research on exposure to the organism employed various animal models, and with quantitative microbial risk assessment (QMRA) techniques, the animal model data may provide insights on human dose-response for LD. This article focuses on the rationale for selection of the guinea pig model, comparison of the dose-response model results, comparison of projected low-dose responses for guinea pigs, and risk estimates for humans. Based on both in vivo and in vitro comparisons, the guinea pig (Cavia porcellus) dose-response data were selected for modeling human risk. We completed dose-response modeling for the beta-Poisson (approximate and exact), exponential, probit, logistic, and Weibull models for Lp inhalation, mortality, and infection (end point elevated body temperature) in guinea pigs. For mechanistic reasons, including low-dose exposure probability, further work on human risk estimates for LD employed the exponential and beta-Poisson models. With an exposure of 10 colony-forming units (CFU) (retained dose), the QMRA model predicted a mild infection risk of 0.4 (as evaluated by seroprevalence) and a clinical severity LD case (e.g., hospitalization and supportive care) risk of 0.0009. The calculated rates based on estimated human exposures for outbreaks used for the QMRA model validation are within an order of magnitude of the reported LD rates. These validation results suggest the LD QMRA animal model selection, dose-response modeling, and extension to human risk projections were appropriate.     

Integrating Household Risk Mitigation Behavior in Flood Risk Analysis: An Agent‐Based Model Approach

Recent studies showed that climate change and socioeconomic trends are expected to increase flood risks in many regions. However, in these studies, human behavior is commonly assumed to be constant, which neglects interaction and feedback loops between human and environmental systems. This neglect of human adaptation leads to a misrepresentation of flood risk. This article presents an agent‐based model that incorporates human decision making in flood risk analysis. In particular, household investments in loss‐reducing measures are examined under three economic decision models: (1) expected utility theory, which is the traditional economic model of rational agents; (2) prospect theory, which takes account of bounded rationality; and (3) a prospect theory model, which accounts for changing risk perceptions and social interactions through a process of Bayesian updating. We show that neglecting human behavior in flood risk assessment studies can result in a considerable misestimation of future flood risk, which is in our case study an overestimation of a factor two. Furthermore, we show how behavior models can support flood risk analysis under different behavioral assumptions, illustrating the need to include the dynamic adaptive human behavior of, for instance, households, insurers, and governments. The method presented here provides a solid basis for exploring human behavior and the resulting flood risk with respect to low‐probability/high‐impact risks.     

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.     

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.     

Multi-Stage Model Estimates of Lung Cancer Risk from Exposure to Diesel Exhaust, Based on a U.S. Railroad Worker Cohort

A California Environmental Protection Agency (Cal/EPA) report concluded that a reasonable and likely explanation for the increased lung cancer rates in numerous epidemiological studies is a causal association between diesel exhaust exposure and lung cancer. A version of the present analysis, based on a retrospective study of a U.S. railroad worker cohort, provided the Cal/EPA report with some of its estimates of lung cancer risk associated with diesel exhaust. The individual data for that cohort study furnish information on age, employment, and mortality for 56,000 workers over 22 years. Related studies provide information on exposure concentrations. Other analyses of the original cohort data reported finding no relation between measures of diesel exhaust and lung cancer mortality, while a Health Effects Institute report found the data unsuitable for quantitative risk assessment. None of those three works used multistage models, which this article uses in finding a likely quantitative, positive relations between lung cancer and diesel exhaust. A seven-stage model that has the last or next-to-last stage sensitive to diesel exhaust provides best estimates of increase in annual mortality rate due to each unit of concentration, for bracketing assumptions on exposure. Using relative increases of risk and multiplying by the background lung cancer mortality rates for California, the 95% upper confidence limit of the 70-year unit risks for lung cancer is estimated to be in the range 2.1 x 10(-4) (microg/m3)(-1) to 5.5 x 10(-4) (microg/m3)(-1). These risks constitute the low end of those in the Cal/EPA report and are below those reported by previous investigators whose estimates were positive using human data.     

Development of Dose‐Response Models to Predict the Relationship for Human Toxoplasma gondii Infection Associated with Meat Consumption

Toxoplasma gondii is a protozoan parasite that is responsible for approximately 24% of deaths attributed to foodborne pathogens in the United States. It is thought that a substantial portion of human T. gondii infections is acquired through the consumption of meats. The dose‐response relationship for human exposures to T. gondii‐infected meat is unknown because no human data are available. The goal of this study was to develop and validate dose‐response models based on animal studies, and to compute scaling factors so that animal‐derived models can predict T. gondii infection in humans. Relevant studies in literature were collected and appropriate studies were selected based on animal species, stage, genotype of T. gondii, and route of infection. Data were pooled and fitted to four sigmoidal‐shaped mathematical models, and model parameters were estimated using maximum likelihood estimation. Data from a mouse study were selected to develop the dose‐response relationship. Exponential and beta‐Poisson models, which predicted similar responses, were selected as reasonable dose‐response models based on their simplicity, biological plausibility, and goodness fit. A confidence interval of the parameter was determined by constructing 10,000 bootstrap samples. Scaling factors were computed by matching the predicted infection cases with the epidemiological data. Mouse‐derived models were validated against data for the dose‐infection relationship in rats. A human dose‐response model was developed as P (d) = 1–exp (–0.0015 × 0.005 × d) or P (d) = 1–(1 + d × 0.003 / 582.414)^?1.479. Both models predict the human response after consuming T. gondii‐infected meats, and provide an enhanced risk characterization in a quantitative microbial risk assessment model for this pathogen.     

Cryptosporidium Infection Risk: Results of New Dose‐Response Modeling

Cryptosporidium human dose‐response data from seven species/isolates are used to investigate six models of varying complexity that estimate infection probability as a function of dose. Previous models attempt to explicitly account for virulence differences among C. parvum isolates, using three or six species/isolates. Four (two new) models assume species/isolate differences are insignificant and three of these (all but exponential) allow for variable human susceptibility. These three human‐focused models (fractional Poisson, exponential with immunity and beta‐Poisson) are relatively simple yet fit the data significantly better than the more complex isolate‐focused models. Among these three, the one‐parameter fractional Poisson model is the simplest but assumes that all Cryptosporidium oocysts used in the studies were capable of initiating infection. The exponential with immunity model does not require such an assumption and includes the fractional Poisson as a special case. The fractional Poisson model is an upper bound of the exponential with immunity model and applies when all oocysts are capable of initiating infection. The beta Poisson model does not allow an immune human subpopulation; thus infection probability approaches 100% as dose becomes huge. All three of these models predict significantly (>10x) greater risk at the low doses that consumers might receive if exposed through drinking water or other environmental exposure (e.g., 72% vs. 4% infection probability for a one oocyst dose) than previously predicted. This new insight into Cryptosporidium risk suggests additional inactivation and removal via treatment may be needed to meet any specified risk target, such as a suggested 10^?4 annual risk of Cryptosporidium infection.     

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

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

A Trichloroethylene Risk Assessment Using a Monte Carlo Analysis of Parameter Uncertainty in Conjunction with Physiologically-Based Pharmacokinetic Modeling

A Monte Carlo simulation is incorporated into a risk assessment for trichloroethylene (TCE) using physiologically-based pharmacokinetic (PBPK) modeling coupled with the linearized multistage model to derive human carcinogenic risk extrapolations. The Monte Carlo technique incorporates physiological parameter variability to produce a statistically derived range of risk estimates which quantifies specific uncertainties associated with PBPK risk assessment approaches. Both inhalation and ingestion exposure routes are addressed. Simulated exposure scenarios were consistent with those used by the Environmental Protection Agency (EPA) in their TCE risk assessment. Mean values of physiological parameters were gathered from the literature for both mice (carcinogenic bioassay subjects) and for humans. Realistic physiological value distributions were assumed using existing data on variability. Mouse cancer bioassay data were correlated to total TCE metabolized and area-under-the-curve (blood concentration) trichloroacetic acid (TCA) as determined by a mouse PBPK model. These internal dose metrics were used in a linearized multistage model analysis to determine dose metric values corresponding to 10^-6 lifetime excess cancer risk. Using a human PBPK model, these metabolized doses were then extrapolated to equivalent human exposures (inhalation and ingestion). The Monte Carlo iterations with varying mouse and human physiological parameters produced a range of human exposure concentrations producing a 10^-6 risk.     

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).     

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

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

An Integrated Physical Dispersion and Behavioral Response Model for Risk Assessment of Radiological Dispersion Device (RDD) Events

A radiological dispersion device (RDD) or "dirty" bomb is a conventional explosive wrapped in radiological material. Terrorists may use an RDD to disperse radioactive material across a populated area, causing casualties and/or economic damage. Nearly all risk assessment models for RDDs make unrealistic assumptions about public behavior in their health assessments, including assumptions that the public would stand outside in a single location indefinitely. In this article, we describe an approach for assessing the risks of RDD events incorporating both physical dispersion and behavioral response variables. The general approach is tested using the City of Pittsburgh, Pennsylvania as a case study. Atmospheric models simulate an RDD attack and its likely fallout, while radiation exposure models assess fatal cancer risk. We model different geographical distributions of the population based on time of day. We evaluate aggregate health impacts for different public responses (i.e., sheltering-in-place, evacuating). We find that current RDD models in use can be improved with the integration of behavioral components. Using the results from the model, we show how risk varies across several behavioral and physical variables. We show that the best policy to recommend to the public depends on many different variables, such as the amount of trauma at ground zero, the capability of emergency responders to get trauma victims to local hospitals quickly and efficiently, how quickly evacuations can take place in the city, and the amount of shielding available for shelterers. Using a parametric analysis, we develop behaviorally realistic risk assessments, we identify variables that can affect an optimal risk reduction policy, and we find that decision making can be improved by evaluating the tradeoff between trauma and cancer fatalities for various RDD scenarios before they occur.     

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.     

A Search for Thresholds and Other Nonlinearities in the Relationship Between Hexavalent Chromium and Lung Cancer

The exposure-response relationship for airborne hexavalent chromium exposure and lung cancer mortality is well described by a linear relative rate model. However, categorical analyses have been interpreted to suggest the presence of a threshold. This study investigates nonlinear features of the exposure response in a cohort of 2,357 chemical workers with 122 lung cancer deaths. In Poisson regression, a simple model representing a two-step carcinogenesis process was evaluated. In a one-stage context, fractional polynomials were investigated. Cumulative exposure dose metrics were examined corresponding to cumulative exposure thresholds, exposure intensity (concentration) thresholds, dose-rate effects, and declining burden of accumulated effect on future risk. A simple two-stage model of carcinogenesis provided no improvement in fit. The best-fitting one-stage models used simple cumulative exposure with no threshold for exposure intensity and had sufficient power to rule out thresholds as large as 30 microg/m3 CrO3 (16 microg/m3 as Cr+6) (one-sided 95% confidence limit, likelihood ratio test). Slightly better-fitting models were observed with cumulative exposure thresholds of 0.03 and 0.5 mg-yr/m3 (as CrO3) with and without an exposure-race interaction term, respectively. With the best model, cumulative exposure thresholds as large as 0.4 mg-yr/m3 CrO3 were excluded (two-sided upper 95% confidence limit, likelihood ratio test). A small departure from dose-rate linearity was observed, corresponding to (intensity)0.8 but was not statistically significant. Models in which risk-inducing damage burdens declined over time, based on half-lives ranging from 0.1 to 40 years, fit less well than assuming a constant burden. A half-life of 8 years or less was excluded (one-sided 95% confidence limit). Examination of nonlinear features of the hexavalent chromium-lung cancer exposure response in a population used in a recent risk assessment supports using the traditional (lagged) cumulative exposure paradigm: no intensity (concentration) threshold, linearity in intensity, and constant increment in risk following exposure.     

需求不确定条件下的制造商订单分配模型

制造商的订单分配作为供应链模型微观层面的重要组成部分,对提升整个供应链效率有很大影响,但需求层面的不确定因素加大了订单分配的难度。以按比例分配为原则,讨论在需求不确定条件下完全信息与不完全信息两类多供应商-单制造商的订单分配模型。重点研究完全信息条件下各方的分散决策和集中决策,由于后者能避免各参与方对其他决策方的边际影响,所以能够实现供应链总利润的最大化;其次又将不完全信息引入模型,讨论制造商如何通过折算因子结合已有信息对供应商的私人信息进行估计,进而做出决策。最后以需求服从正态分布为例对两类模型进行验证。     

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

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