A Calibrated Human PBPK Model for Benzene Inhalation with Urinary Bladder and Bone Marrow Compartments

A physiologically‐based pharmacokinetic (PBPK) model of benzene inhalation based on a recent mouse model was adapted to include bone marrow (target organ) and urinary bladder compartments. Empirical data on human liver microsomal protein levels and linked CYP2E1 activities were incorporated into the model, and metabolite‐specific conversion rate parameters were estimated by fitting to human biomonitoring data and adjusting for background levels of urinary metabolites. Human studies of benzene levels in blood and breath, and phenol levels in urine were used to validate the rate of human conversion of benzene to benzene oxide, and urinary benzene metabolites from Chinese benzene worker populations provided model validation for rates of human conversion of benzene to muconic acid (MA) and phenylmercapturic acid (PMA), phenol (PH), catechol (CA), hydroquinone (HQ), and benzenetriol (BT). The calibrated human model reveals that while liver microsomal protein and CYP2E1 activities are lower on average in humans compared to mice, the mouse also shows far lower rates of benzene conversion to MA and PMA, and far higher conversion of benzene to BO/PH, and of BO/PH to CA, HQ, and BT. The model also differed substantially from existing human PBPK models with respect to several metabolic rate parameters of importance to interpreting benzene metabolism and health risks in human populations associated with bone marrow doses. The model provides a new methodological paradigm focused on integrating linked human liver metabolism data and calibration using biomonitoring data, thus allowing for model uncertainty analysis and more rigorous validation.     

Evaluating the Risk of Liver Cancer in Humans Exposed to Trichloroethylene Using Physiological Models

Trichloroethylene (TCE) is a widespread environmental pollutant. TCE is classified as a rodent carcinogen by the U.S. Environmental Protection Agency (EPA). Using the rodent cancer bioassay findings and estimates of metabolized dose, the EPA has estimated lifetime exposure cancer risks for humans that ingest TCE in drinking water or inhale TCE. In this study, a physiologically based pharmacokinetic (PB-PK) model for mice was used to simulate selected gavage and inhalation bioassays with TCE. Plausible dose-metrics thought to be linked with the mechanism of action for TCE carcinogenesis were selected. These dose-metrics, adjusted to reflect an average amount per day for a lifetime, were metabolism of TCE (AMET, mg/kg/day) and systemic concentration of TCA (AUCTCA, mg/L/day). These dose-metrics were then used in a linearized multistage model to estimate AMET and AUCTCA values that correspond to liver cancer risks of 1 in 1 million in mice. A human PB-PK model for TCE was then used to predict TCE concentrations in drinking water and air that would provide AMET and AUCTCA values equal to the predicted mice AMET and AUCTCA values that correspond to liver cancer risks of 1 in 1 million. For the dose-metrics, AMET and AUCTCA, the TCE concentrations in air were 10.0 and 0.1 ppb TCE (continuous exposure), respectively, and in water, 7 and 4 μg TCE/L, respectively.     

The Importance of Biological Realism in Dioxin Risk Assessment Models Michael

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

Development of a Screening Approach to Interpret Human Biomonitoring Data on Volatile Organic Compounds: Reverse Dosimetry on Biomonitoring Data for Trichloroethylene

A screening approach is developed for volatile organic compounds (VOCs) to estimate exposures that correspond to levels measured in fluids and/or tissues in human biomonitoring studies. The approach makes use of a generic physiologically-based pharmacokinetic (PBPK) model coupled with exposure pattern characterization, Monte Carlo analysis, and quantitative structure property relationships (QSPRs). QSPRs are used for VOCs with minimal data to develop chemical-specific parameters needed for the PBPK model. The PBPK model is capable of simulating VOC kinetics following multiple routes of exposure, such as oral exposure via water ingestion and inhalation exposure during shower events. Using published human biomonitoring data of trichloroethylene (TCE), the generic model is evaluated to determine how well it estimates TCE concentrations in blood based on the known drinking water concentrations. In addition, Monte Carlo analysis is conducted to characterize the impact of the following factors: (1) uncertainties in the QSPR-estimated chemical-specific parameters; (2) variability in physiological parameters; and (3) variability in exposure patterns. The results indicate that uncertainty in chemical-specific parameters makes only a minor contribution to the overall variability and uncertainty in the predicted TCE concentrations in blood. The model is used in a reverse dosimetry approach to derive estimates of TCE concentrations in drinking water based on given measurements of TCE in blood, for comparison to the U.S. EPA's Maximum Contaminant Level in drinking water. This example demonstrates how a reverse dosimetry approach can be used to facilitate interpretation of human biomonitoring data in a health risk context by deriving external exposures that are consistent with a biomonitoring data set, thereby permitting comparison with health-based exposure guidelines.     

Modeling Human Interindividual Variability in Metabolism and Risk: The Example of 4-Aminobiphenyl

We investigate, through modeling, the impact of interindividual heterogeneity in the metabolism of 4-aminobiphenyl (ABP) and in physiological factors on human cancer risk: A physiological pharmacokinetic model was used to quantify the time course of the formation of the proximate carcinogen, N-hydroxy-4-ABP and the DNA-binding of the active species in the bladder. The metabolic and physiologic model parameters were randomly varied, via Monte Carlo simulations, to reproduce interindividual variability. The sampling means for most parameters were scaled from values developed by Kadlubar et al. (Cancer Res., 51 : 4371, 1991) for dogs; variances were obtained primarily from published human data (e.g., measurements of ABP N-oxidation, and arylamine N-acetylation in human liver tissue). In 500 simulations, theoretically representing 500 humans, DNA-adduct levels in the bladder of the most susceptible individuals are ten thousand times higher than for the least susceptible, and the 5th and 95th percentiles differ by a factor of 160. DNA binding for the most susceptible individual (with low urine pH, low N-acetylation and high N-oxidation activities) is theoretically one million-fold higher than for the least susceptible (with high urine pH, high N-acetylation and low N-oxidation activities). The simulations also suggest that the four factors contributing most significantly to interindividual differences in DNA-binding of ABP in human bladder are urine pH, ABP N-oxidation, ABP N-acetylation and urination frequency.     

Modeling Cholinesterase Activity for Human Dietary Risk Assessment of Carbamate Insecticides

This article demonstrates statistical models to quantify the interaction between a carbamate insecticide and acetylcholinesterase. Carbamates are a class of chemicals that inhibit the activity of acetylcholinesterase in humans, an enzyme involved in the regulation of the neurotransmitter acetylcholine. Following exposure to a carbamate insecticide, we specifically address (1) if acetylcholinesterase activity recovers to its level of preexposure activity; (2) the level of inhibition of acetylcholinesterase activity; (3) the recovery time of acetylcholinesterase activity to its preexposure level for a typical individual; and (4) the upper percentiles of the recovery time of acetycholinesterase activity across individuals. A nonlinear mixed-effects model is fitted to data from a repeated measures experiment conducted with human volunteers randomly assigned to a control and four dose groups. Repeated measurements were taken prior to exposure and at 1, 2, 4, 6, 8, and 21 hours after exposure to the carbamate aldicarb. It was found that full recovery did occur. Inhibition at 1 hour was estimated with maximum inhibition most likely occurring prior to 1-hour postexposure. In addition, recovery was rapid even for sensitive individuals. Given this information, the potential effect from exposure to a carbamate consumed in the diet during a day can be quantitatively assessed.     

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.     

Duration Adjustment of Acute Exposure Guideline Level Values for Trichloroethylene Using a Physiologically-Based Pharmacokinetic Model

Acute Exposure Guideline Level (AEGL) recommendations are developed for 10-minute, 30-minute, 1-hour, 4-hours, and 8-hours exposure durations and are designated for three levels of severity: AEGL-1 represents concentrations above which acute exposures may cause noticeable discomfort including irritation; AEGL-2 represents concentrations above which acute exposure may cause irreversible health effects or impaired ability to escape; and AEGL-3 represents concentrations above which exposure may cause life-threatening health effects or death. The default procedure for setting AEGL values across durations when applicable data are unavailable involves estimation based on Haber's rule, which has an underlying assumption that cumulative exposure is the determinant of toxicity. For acute exposure to trichloroethylene (TCE), however, experimental data indicate that momentary tissue concentration, and not the cumulative amount of exposure, is important. We employed an alternative approach to duration adjustments in which a physiologically-based pharmacokinetic (PBPK) model was used to predict the arterial blood concentrations [TCE(a)] associated with adverse outcomes appropriate for AEGL-1, -2, or -3-level effects. The PBPK model was then used to estimate the atmospheric concentration that produces equivalent [TCE(a)] at each of the AEGL-specific exposure durations. This approach yielded [TCE(a)] values of 4.89 mg/l for AEGL-1, 18.7 mg/l for AEGL-2, and 310 mg/l for AEGL-3. Duration adjustments based on equivalent target tissue doses should provide similar degrees of toxicity protection at different exposure durations.     

Part II: Quantitative Evaluation of Choices Used in Setting Noncancer Chronic Human Health Reference Values Across Organizations

Environmental and public health organizations, including the World Health Organization (WHO) and the U.S. Environmental Protection Agency (USEPA), develop human health reference values (HHRV) that set “safe” levels of exposure to noncarcinogens. Here, we systematically analyze chronic HHRVs from four organizations: USEPA, Health Canada, RIVM (the Netherlands), and the U.S. Agency for Toxic Substances and Disease Registry. This study is an extension of our earlier work and both closely examines the choices made in setting HHRVs and presents a quantitative method for identifying the primary factors influencing HHRV agreement or disagreement.⁽¹⁾ We evaluated 171 organizational comparisons, developing a quantitative method for identifying the factors to which HHRV agreement (that is, when both organizations considering the same data set the identical HHRV values) is most sensitive. To conduct this analysis, a Bayesian belief network was built using expert judgment, including the specific science policy choices analysis made in the context of setting an HHRV. Based on a sensitivity of findings analysis, HHRV agreement is most sensitive to the point of departure value, followed by the total uncertainty factor (UF), critical study, critical effect, animal model, and point of departure approach. This analysis also considered the specific impacts of individual UFs, with the database UF and the subchronic‐to‐chronic UF being identified as primary factors impacting the total UF differences observed across organizations. The sensitivity of findings analysis results were strengthened and confirmed by frequency analyses evaluating which choices most often disagreed when the HHRV and the total UF disagreed.     

Probabilistic Framework for the Estimation of the Adult and Child Toxicokinetic Intraspecies Uncertainty Factors

Human health risk assessments use point values to develop risk estimates and thus impart a deterministic character to risk, which, by definition, is a probability phenomenon. The risk estimates are calculated based on individuals and then, using uncertainty factors (UFs), are extrapolated to the population that is characterized by variability. Regulatory agencies have recommended the quantification of the impact of variability in risk assessments through the application of probabilistic methods. In the present study, a framework that deals with the quantitative analysis of uncertainty (U) and variability (V) in target tissue dose in the population was developed by applying probabilistic analysis to physiologically-based toxicokinetic models. The mechanistic parameters that determine kinetics were described with probability density functions (PDFs). Since each PDF depicts the frequency of occurrence of all expected values of each parameter in the population, the combined effects of multiple sources of U/V were accounted for in the estimated distribution of tissue dose in the population, and a unified (adult and child) intraspecies toxicokinetic uncertainty factor UFH-TK was determined. The results show that the proposed framework accounts effectively for U/V in population toxicokinetics. The ratio of the 95th percentile to the 50th percentile of the annual average concentration of the chemical at the target tissue organ (i.e., the UFH-TK) varies with age. The ratio is equivalent to a unified intraspecies toxicokinetic UF, and it is one of the UFs by which the NOAEL can be divided to obtain the RfC/RfD. The 10-fold intraspecies UF is intended to account for uncertainty and variability in toxicokinetics (3.2x) and toxicodynamics (3.2x). This article deals exclusively with toxicokinetic component of UF. The framework provides an alternative to the default methodology and is advantageous in that the evaluation of toxicokinetic variability is based on the distribution of the effective target tissue dose, rather than applied dose. It allows for the replacement of the default adult and children intraspecies UF with toxicokinetic data-derived values and provides accurate chemical-specific estimates for their magnitude. It shows that proper application of probability and toxicokinetic theories can reduce uncertainties when establishing exposure limits for specific compounds and provide better assurance that established limits are adequately protective. It contributes to the development of a probabilistic noncancer risk assessment framework and will ultimately lead to the unification of cancer and noncancer risk assessment methodologies.     

A Probabilistic Arsenic Exposure Assessment for Children Who Contact Chromated Copper Arsenate (CCA)-Treated Playsets and Decks, Part 2: Sensitivity and Uncertainty Analyses

A probabilistic model (SHEDS-Wood) was developed to examine children's exposure and dose to chromated copper arsenate (CCA)-treated wood, as described in Part 1 of this two-part article. This Part 2 article discusses sensitivity and uncertainty analyses conducted to assess the key model inputs and areas of needed research for children's exposure to CCA-treated playsets and decks. The following types of analyses were conducted: (1) sensitivity analyses using a percentile scaling approach and multiple stepwise regression; and (2) uncertainty analyses using the bootstrap and two-stage Monte Carlo techniques. The five most important variables, based on both sensitivity and uncertainty analyses, were: wood surface residue-to-skin transfer efficiency; wood surface residue levels; fraction of hand surface area mouthed per mouthing event; average fraction of nonresidential outdoor time a child plays on/around CCA-treated public playsets; and frequency of hand washing. In general, there was a factor of 8 for the 5th and 95th percentiles and a factor of 4 for the 50th percentile in the uncertainty of predicted population dose estimates due to parameter uncertainty. Data were available for most of the key model inputs identified with sensitivity and uncertainty analyses; however, there were few or no data for some key inputs. To evaluate and improve the accuracy of model results, future measurement studies should obtain longitudinal time-activity diary information on children, spatial and temporal measurements of residue and soil concentrations on or near CCA-treated playsets and decks, and key exposure factors. Future studies should also address other sources of uncertainty in addition to parameter uncertainty, such as scenario and model uncertainty.     

Percentiles of the Product of Uncertainty Factors for Establishing Probabilistic Reference Doses

Exposure guidelines for potentially toxic substances are often based on a reference dose (RfD) that is determined by dividing a no-observed-adverse-effect-level (NOAEL), lowest-observed-adverse-effect-level (LOAEL), or benchmark dose (BD) corresponding to a low level of risk, by a product of uncertainty factors. The uncertainty factors for animal to human extrapolation, variable sensitivities among humans, extrapolation from measured subchronic effects to unknown results for chronic exposures, and extrapolation from a LOAEL to a NOAEL can be thought of as random variables that vary from chemical to chemical. Selected databases are examined that provide distributions across chemicals of inter- and intraspecies effects, ratios of LOAELs to NOAELs, and differences in acute and chronic effects, to illustrate the determination of percentiles for uncertainty factors. The distributions of uncertainty factors tend to be approximately lognormally distributed. The logarithm of the product of independent uncertainty factors is approximately distributed as the sum of normally distributed variables, making it possible to estimate percentiles for the product. Hence, the size of the products of uncertainty factors can be selected to provide adequate safety for a large percentage (e.g., approximately 95%) of RfDs. For the databases used to describe the distributions of uncertainty factors, using values of 10 appear to be reasonable and conservative. For the databases examined the following simple "Rule of 3s" is suggested that exceeds the estimated 95th percentile of the product of uncertainty factors: If only a single uncertainty factor is required use 33, for any two uncertainty factors use 3 x 33 approximately 100, for any three uncertainty factors use a combined factor of 3 x 100 = 300, and if all four uncertainty factors are needed use a total factor of 3 x 300 = 900. If near the 99th percentile is desired use another factor of 3. An additional factor may be needed for inadequate data or a modifying factor for other uncertainties (e.g., different routes of exposure) not covered above.     

Statistical Distributions of Daily Breathing Rates for Narrow Age Groups of Infants and Children

Children may be more susceptible to toxicity from some environmental chemicals than adults. This susceptibility may occur during narrow age periods (windows), which can last from days to years depending on the toxicant. Breathing rates specific to narrow age periods are useful to assess inhalation dose during suspected windows of susceptibility. Because existing breathing rates used in risk assessment are typically for broad age ranges or are based on data not representative of the population, we derived daily breathing rates for narrow age ranges of children designed to be more representative of the current U.S. children's population. These rates were derived using the metabolic conversion method of Layton (1993) and energy intake data adjusted to represent the U.S. population from a relatively recent dietary survey (CSFII 1994–1996, 1998). We calculated conversion factors more specific to children than those previously used. Both nonnormalized (L/day) and normalized (L/kg-day) breathing rates were derived and found comparable to rates derived using energy estimates that are accurate for the individuals sampled but not representative of the population. Estimates of breathing rate variability within a population can be used with stochastic techniques to characterize the range of risk in the population from inhalation exposures. For each age and age-gender group, we present the mean, standard error of the mean, percentiles (50th, 90th, and 95th), geometric mean, standard deviation, 95th percentile, and best-fit parametric models of the breathing rate distributions. The standard errors characterize uncertainty in the parameter estimate, while the percentiles describe the combined interindividual and intra-individual variability of the sampled population. These breathing rates can be used for risk assessment of subchronic and chronic inhalation exposures of narrow age groups of children.     

An Improved Framework for Uncertainty Analysis: Accounting for Unsuspected Errors

I use an analogy with the history of physical measurements, population and energy projections, and analyze the trends in several data sets to quantify the overconfidence of the experts in the reliability of their uncertainty estimates. Data sets include (i) time trends in the sequential measurements of the same physical quantity; (ii) national population projections; and (iii) projections for the U.S., energy sector. Probabilities of large deviations for the true values are parametrized by an exponential distribution with the slope determined by the data. Statistics of past errors can be used in probabilistic risk assessment to hedge against unsuspected uncertainties and to include the possibility of human error into the framework of uncertainty analysis. By means of a sample Monte Carlo simulation of cancer risk caused by ingestion of benzene in soil, I demonstrate how the upper 95th percentiles of risk are changed when unsuspected uncertainties are included. I recommend to inflate the estimated uncertainties by default safety factors determined from the relevant historical data sets.     

Estimation of the Likelihood of Fecal–Oral HEV Transmission Among Pigs

Sources for human hepatitis E virus (HEV) infections of genotype 3 are largely unknown. Pigs are potential animal reservoirs for HEV. Intervention at pig farms may be desired when pigs are confirmed as a source for human infections, requiring knowledge about transmission routes. These routes are currently understudied. The current study aims to quantify the likelihood of pig feces in causing new HEV infections in pigs due to oral ingestion. We estimated the daily infection risk for pigs by modeling the fate of HEV in the fecal–oral (F–O) pathway. Using parameter values deemed most plausible by the authors based on current knowledge the daily risk of infection was 0.85 (95% interval: 0.03–1). The associated expected number of new infections per day was ～4 (2.5% limit 0.1, the 97% limit tending to infinity) compared to 0.7 observed in a transmission experiment with pigs, and the likelihood of feces causing the transmission approached 1. In alternative scenarios, F–O transmission of HEV was also very likely to cause new infections. By reducing the total value of all explanatory variables by 2 orders of magnitude, the expected numbers of newly infected pigs approached the observed number. The likelihood of F–O transmission decreased by decreasing parameter values, allowing for at most 94% of infections being caused by additional transmission routes. Nevertheless, in all scenarios F–O transmission was estimated to contribute to HEV transmission. Thus, despite the difficulty in infecting pigs with HEV via oral inoculation, the F–O route is likely to cause HEV transmission among pigs.     

Dose-Response Assessment of Airborne Methyl Isothiocyanate (MITC) Following a Metam Sodium Spill

A tank car derailment in northern California in 1991 spilled metam sodium into the Sacramento River, and released its breakdown product, methyl isothiocyanate (MITC), into the air. This paper describes the risk evaluation process used. Over 240 individuals reported symptoms such as eye and throat irritation, dizziness, and shortness of breath. Reference exposure levels (RELs) for 1 hr were developed for MITC and compared to exposure concentrations. Ocular irritation in cats was the most sensitive endpoint reported. The no observed adverse effect level (NOAEL), divided by an uncertainty factor (UF) of 100, produced an REL of 0.5 ppb of MITC in air to prevent discomfort. An REL to prevent disability was estimated to be 40 ppb. An REL to prevent life-threatening injury was estimated to be 150 ppb. Measured MITC levels ranged from 0.2-37 ppb and estimated peak levels ranged from 140-1600 ppb. The usefulness of RELs for emergency planning is discussed.     

Combining Food Frequency and Survey Data to Quantify Long-Term Dietary Exposure: A Methyl Mercury Case Study

Twenty-four-hour recall data from the Continuing Survey of Food Intake by Individuals (CSFII) are frequently used to estimate dietary exposure for risk assessment. Food frequency questionnaires are traditional instruments of epidemiological research; however, their application in dietary exposure and risk assessment has been limited. This article presents a probabilistic method of bridging the National Health and Nutrition Examination Survey (NHANES) food frequency and the CSFII data to estimate longitudinal (usual) intake, using a case study of seafood mercury exposures for two population subgroups (females 16 to 49 years and children 1 to 5 years). Two hundred forty-nine CSFII food codes were mapped into 28 NHANES fish/shellfish categories. FDA and state/local seafood mercury data were used. A uniform distribution with minimum and maximum blood-diet ratios of 0.66 to 1.07 was assumed. A probabilistic assessment was conducted to estimate distributions of individual 30-day average daily fish/shellfish intakes, methyl mercury exposure, and blood levels. The upper percentile estimates of fish and shellfish intakes based on the 30-day daily averages were lower than those based on two- and three-day daily averages. These results support previous findings that distributions of "usual" intakes based on a small number of consumption days provide overestimates in the upper percentiles. About 10% of the females (16 to 49 years) and children (1 to 5 years) may be exposed to mercury levels above the EPA's RfD. The predicted 75th and 90th percentile blood mercury levels for the females in the 16-to-49-year group were similar to those reported by NHANES. The predicted 90th percentile blood mercury levels for children in the 1-to-5-year subgroup was similar to NHANES and the 75th percentile estimates were slightly above the NHANES.     

Part I––Comparing Noncancer Chronic Human Health Reference Values: An Analysis of Science Policy Choices

The goal of this study was to systematically evaluate the choices made in deriving a chronic oral noncancer human health reference value (HHRV) for a given chemical by different organizations, specifically those from the U.S. Environmental Protection Agency, Health Canada, RIVM (the Netherlands), and the U.S. Agency for Toxic Substances and Disease Registry. This analysis presents a methodological approach for comparing both the HHRVs and the specific choices made in the process of deriving an HHRV across these organizations. Overall, across the 96 unique chemicals and 171 two‐way organizational comparisons, the HHRV agreed approximately 26% of the time. A qualitative method for identifying the primary factors influencing these HHRV differences was also developed, using arrays of HHRVs across organizations for the same chemical. The primary factors identified were disagreement on the critical or principal study and differential application of the total uncertainty factor across organizations. Of the cases where the total UF was the primary factor influencing HHRV disagreement, the database UF had the greatest influence.     

期权定价方法综述

介绍了期权定价理论的产生和发展; 然后对期权定价方法及其实证研究进行了较详细的 分类综述, 突出综述了既适用于完全金融市场, 又适用于非完全的金融市场的确定性套利定价 方法、区间定价方法和E2套利定价方法; 最后, 对各种方法的条件和特点进行了讨论和评价.