Estimating Benchmark Exposure for Air Particulate Matter Using Latent Class Models

We performed benchmark exposure (BME) calculations for particulate matter when multiple dichotomous outcome variables are involved using latent class modeling techniques and generated separate results for both the extra risk and additional risk. The use of latent class models in this study is advantageous because it combined several outcomes into just two classes (namely, a high‐risk class and a low‐risk class) and compared these two classes to obtain the BME levels. This novel approach addresses a key problem in risk estimation—namely, the multiple comparisons problem, where separate regression models are fitted for each outcome variable and the reference exposure will rely on the results of the best‐fitting model. Because of the complex nature of the estimation process, the bootstrap approach was used to estimate the reference exposure level, thereby reducing uncertainty in the obtained values. The methodology developed in this article was applied to environmental data by identifying unmeasured class membership (e.g., morbidity vs. no morbidity class) among infants in utero using observed characteristics that included low birth weight, preterm birth, and small for gestational age.     

Bayesian Hierarchical Structure for Quantifying Population Variability to Inform Probabilistic Health Risk Assessments

Human variability is a very important factor considered in human health risk assessment for protecting sensitive populations from chemical exposure. Traditionally, to account for this variability, an interhuman uncertainty factor is applied to lower the exposure limit. However, using a fixed uncertainty factor rather than probabilistically accounting for human variability can hardly support probabilistic risk assessment advocated by a number of researchers; new methods are needed to probabilistically quantify human population variability. We propose a Bayesian hierarchical model to quantify variability among different populations. This approach jointly characterizes the distribution of risk at background exposure and the sensitivity of response to exposure, which are commonly represented by model parameters. We demonstrate, through both an application to real data and a simulation study, that using the proposed hierarchical structure adequately characterizes variability across different populations.     

Construction of a Dose–Illness Relationship via Modeling Morbidity and Application to Risk Assessment of Wastewater Reuse

A disease burden (DB) evaluation for environmental pathogens is generally performed using disability‐adjusted life years with the aim of providing a quantitative assessment of the health hazard caused by pathogens. A critical step in the preparation for this evaluation is the estimation of morbidity between exposure and disease occurrence. In this study, the method of a traditional dose–response analysis was first reviewed, and then a combination of the theoretical basis of a “single‐hit” and an “infection‐illness” model was performed by incorporating two critical factors: the “infective coefficient” and “infection duration.” This allowed a dose–morbidity model to be built for direct use in DB calculations. In addition, human experimental data for typical intestinal pathogens were obtained for model validation, and the results indicated that the model was well fitted and could be further used for morbidity estimation. On this basis, a real case of a water reuse project was selected for model application, and the morbidity as well as the DB caused by intestinal pathogens during water reuse was evaluated. The results show that the DB attributed to Enteroviruses was significant, while that for enteric bacteria was negligible. Therefore, water treatment technology should be further improved to reduce the exposure risk of Enteroviruses . Since road flushing was identified as the major exposure route, human contact with reclaimed water through this pathway should be limited. The methodology proposed for model construction not only makes up for missing data of morbidity during risk evaluation, but is also necessary to quantify the maximum possible DB.     

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.     

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.     

Methods to Approximate Joint Uncertainty and Variability in Risk

As interest in quantitative analysis of joint uncertainty and interindividual variability (JUV) in risk grows, so does the need for related computational shortcuts. To quantify JUV in risk, Monte Carlo methods typically require nested sampling of JUV in distributed inputs, which is cumbersome and time-consuming. Two approximation methods proposed here allow simpler and more rapid analysis. The first consists of new upper-bound JUV estimators that involve only uncertainty or variability, not both, and so never require nested sampling to calculate. The second is a discrete-probability-calculus procedure that uses only the mean and one upper-tail mean for each input in order to estimate mean and upper-bound risk, which procedure is simpler and more intuitive than similar ones in use. Application of these methods is illustrated in an assessment of cancer risk from residential exposures to chloroform in Kanawah Valley, West Virginia. Because each of the multiple exposure pathways considered in this assessment had separate modeled sources of uncertainty and variability, the assessment illustrates a realistic case where a standard Monte Carlo approach to JUV analysis requires nested sampling. In the illustration, the first proposed method quantified JUV in cancer risk much more efficiently than corresponding nested Monte Carlo calculations. The second proposed method also nearly duplicated JUV-related and other estimates of risk obtained using Monte Carlo methods. Both methods were thus found adequate to obtain basic risk estimates accounting for JUV in a realistically complex risk assessment. These methods make routine JUV analysis more convenient and practical.     

Sensitivity Analysis of a Two‐Dimensional Quantitative Microbiological Risk Assessment: Keeping Variability and Uncertainty Separated

The aim of quantitative microbiological risk assessment is to estimate the risk of illness caused by the presence of a pathogen in a food type, and to study the impact of interventions. Because of inherent variability and uncertainty, risk assessments are generally conducted stochastically, and if possible it is advised to characterize variability separately from uncertainty. Sensitivity analysis allows to indicate to which of the input variables the outcome of a quantitative microbiological risk assessment is most sensitive. Although a number of methods exist to apply sensitivity analysis to a risk assessment with probabilistic input variables (such as contamination, storage temperature, storage duration, etc.), it is challenging to perform sensitivity analysis in the case where a risk assessment includes a separate characterization of variability and uncertainty of input variables. A procedure is proposed that focuses on the relation between risk estimates obtained by Monte Carlo simulation and the location of pseudo‐randomly sampled input variables within the uncertainty and variability distributions. Within this procedure, two methods are used—that is, an ANOVA‐like model and Sobol sensitivity indices—to obtain and compare the impact of variability and of uncertainty of all input variables, and of model uncertainty and scenario uncertainty. As a case study, this methodology is applied to a risk assessment to estimate the risk of contracting listeriosis due to consumption of deli meats.     

Linking Indoor Air and Pharmacokinetic Models to Assess Tetrachloroethylene Risk

Physiologically based pharmacokinetic (PBPK) models describing the uptake, metabolism, and excretion of xenobiotic compounds are now proposed for use in regulatory health-risk assessments. In this study we investigate the extent of PCE metabolism arising from domestic respiratory exposure to tetrachloroethylene (PCE) from ground water, as predicted using a PBPK model. Indoor exposure patterns we use as input to the PBPK model are realistic ones generated from a three-compartment model describing volatilization of PCE from domestic water into household air. Values we use for the metabolic parameters of the PBPK model are estimated from data on urinary metabolites in workers exposed to PCE. It is shown that for respiratory PCE exposure due to typical levels of PCE in ground water, use of time-weighted average air concentrations with a steady-state PBPK model yields estimates of total metabolized PCE similar to those obtained using completely dynamic modeling, despite considerable uncertainty in key exposure- and metabolic-model parameters. These findings suggest that, for PCE, risk estimation taking pharmacokinetics into account may be accomplished using a simple analytic approach.     

A Common Rationale for Global Sensitivity Measures and Their Estimation

Measures of sensitivity and uncertainty have become an integral part of risk analysis. Many such measures have a conditional probabilistic structure, for which a straightforward Monte Carlo estimation procedure has a double‐loop form. Recently, a more efficient single‐loop procedure has been introduced, and consistency of this procedure has been demonstrated separately for particular measures, such as those based on variance, density, and information value. In this work, we give a unified proof of single‐loop consistency that applies to any measure satisfying a common rationale. This proof is not only more general but invokes less restrictive assumptions than heretofore in the literature, allowing for the presence of correlations among model inputs and of categorical variables. We examine numerical convergence of such an estimator under a variety of sensitivity measures. We also examine its application to a published medical case study.     

An Empirical,Nonparametric Simulator for Multivariate Random Variables with Differing Marginal Densities and Nonlinear Dependence with Hydroclimatic Applications

Multivariate simulations of a set of random variables are often needed for risk analysis. Given a historical data set, the goal is to develop simulations that reproduce the dependence structure in that data set so that the risk of potentially correlated factors can be evaluated. A nonparametric, copula‐based simulation approach is developed and exemplified. It can be applied to multiple variables or to spatial fields with arbitrary dependence structures and marginal densities. The nonparametric simulator uses logspline density estimation in the univariate setting, together with a sampling strategy to reproduce dependence across variables or spatial instances, through a nonparametric numerical approximation of the underlying copula function. The multivariate data vectors are assumed to be independent and identically distributed. A synthetic example is provided to illustrate the method, followed by an application to the risk of livestock losses in Mongolia.     

基于非参多元Expectile模型的原油价格风险测度研究—宏观不确定性视角

当下政治经济环境存在诸多不确定性，原油价格随着不确定性的增加而大幅波动，因此在当前不确定性环境中建立一个有效的风险预测模型具有重要的实际意义。本文基于非参多元Expectile模型，选取2010年1月5日至2020年1月6日的美国西德克萨斯原油价格的日度数据，构建同时包含地缘政治风险、经济政策不确定性等六个宏观不确定性变量的原油价格风险预测模型。此外，引入APARCH模型和基于蒙特卡罗方法的GARCH模型，比较以上三个模型预测能力。最后，基于预测的VaR值计算调整的Sharpe比率。结论表明，整体上，非参多元Expectile模型能较好处理多个宏观变量包含的信息，具有更高的预测能力。在不确定性事件叠加发生的时期预测表现依然优于其他模型，减少了不确定性增加导致原油市场波动幅度增加带来的风险，具有更强的稳定性。因此，在经济转型的关键时期，本研究可为政策制定者和监管当局面临不确定性上升环境下建立有效的原油价格风险预测模型提供参考，制定应对政策防范化解风险，同时也为投资者在当前复杂的国际形势下提供预测参考，尽量规避损失同时获取收益。     

Bounding Analysis of Drinking Water Health Risks from a Spill of Hydraulic Fracturing Flowback Water

A bounding risk assessment is presented that evaluates possible human health risk from a hypothetical scenario involving a 10,000‐gallon release of flowback water from horizontal fracturing of Marcellus Shale. The water is assumed to be spilled on the ground, infiltrates into groundwater that is a source of drinking water, and an adult and child located downgradient drink the groundwater. Key uncertainties in estimating risk are given explicit quantitative treatment using Monte Carlo analysis. Chemicals that contribute significantly to estimated health risks are identified, as are key uncertainties and variables to which risk estimates are sensitive. The results show that hypothetical exposure via drinking water impacted by chemicals in Marcellus Shale flowback water, assumed to be spilled onto the ground surface, results in predicted bounds between 10⁻¹⁰ and 10⁻⁶ (for both adult and child receptors) for excess lifetime cancer risk. Cumulative hazard indices (HI_CUMULATIVE) resulting from these hypothetical exposures have predicted bounds (5th to 95th percentile) between 0.02 and 35 for assumed adult receptors and 0.1 and 146 for assumed child receptors. Predicted health risks are dominated by noncancer endpoints related to ingestion of barium and lithium in impacted groundwater. Hazard indices above unity are largely related to exposure to lithium. Salinity taste thresholds are likely to be exceeded before drinking water exposures result in adverse health effects. The findings provide focus for policy discussions concerning flowback water risk management. They also indicate ways to improve the ability to estimate health risks from drinking water impacted by a flowback water spill (i.e., reducing uncertainty).     

Risk Assessment of Virus in Drinking Water

The reevaluation of drinking water treatment practices in a desire to minimize the formation of disinfection byproducts while assuring minimum levels of public health protection against infectious organisms has caused it to become necessary to consider the problem of estimation of risks posed from exposure to low levels of microorganisms, such as virus or protozoans, found in treated drinking water. This paper outlines a methodology based on risk assessment principles to approach the problem. The methodology is validated by comparison with results obtained in a prospective epidemiological study. It is feasible to produce both point and interval estimates of infection, illness and perhaps mortality by this methodology. Areas of uncertainty which require future data are indicated.     

Sensitivity Analysis of a Two-Dimensional Probabilistic Risk Assessment Model Using Analysis of Variance

This article demonstrates application of sensitivity analysis to risk assessment models with two-dimensional probabilistic frameworks that distinguish between variability and uncertainty. A microbial food safety process risk (MFSPR) model is used as a test bed. The process of identifying key controllable inputs and key sources of uncertainty using sensitivity analysis is challenged by typical characteristics of MFSPR models such as nonlinearity, thresholds, interactions, and categorical inputs. Among many available sensitivity analysis methods, analysis of variance (ANOVA) is evaluated in comparison to commonly used methods based on correlation coefficients. In a two-dimensional risk model, the identification of key controllable inputs that can be prioritized with respect to risk management is confounded by uncertainty. However, as shown here, ANOVA provided robust insights regarding controllable inputs most likely to lead to effective risk reduction despite uncertainty. ANOVA appropriately selected the top six important inputs, while correlation-based methods provided misleading insights. Bootstrap simulation is used to quantify uncertainty in ranks of inputs due to sampling error. For the selected sample size, differences in F values of 60% or more were associated with clear differences in rank order between inputs. Sensitivity analysis results identified inputs related to the storage of ground beef servings at home as the most important. Risk management recommendations are suggested in the form of a consumer advisory for better handling and storage practices.     

A Bayesian Semiparametric Model for Radiation Dose‐Response Estimation

In evaluating the risk of exposure to health hazards, characterizing the dose‐response relationship and estimating acceptable exposure levels are the primary goals. In analyses of health risks associated with exposure to ionizing radiation, while there is a clear agreement that moderate to high radiation doses cause harmful effects in humans, little has been known about the possible biological effects at low doses, for example, below 0.1 Gy, which is the dose range relevant to most radiation exposures of concern today. A conventional approach to radiation dose‐response estimation based on simple parametric forms, such as the linear nonthreshold model, can be misleading in evaluating the risk and, in particular, its uncertainty at low doses. As an alternative approach, we consider a Bayesian semiparametric model that has a connected piece‐wise‐linear dose‐response function with prior distributions having an autoregressive structure among the random slope coefficients defined over closely spaced dose categories. With a simulation study and application to analysis of cancer incidence data among Japanese atomic bomb survivors, we show that this approach can produce smooth and flexible dose‐response estimation while reasonably handling the risk uncertainty at low doses and elsewhere. With relatively few assumptions and modeling options to be made by the analyst, the method can be particularly useful in assessing risks associated with low‐dose radiation exposures.     

A Comparative Cancer Risk Evaluation of MTBE and Other Compounds (Including Naturally Occurring Compounds) in Drinking Water in New Hampshire

Methyl tert-butyl ether (MTBE) was added to gasoline in New Hampshire (NH) between 1995 and 2006 to comply with the oxygenate requirements of the 1990 Amendments to the Clean Air Act. Leaking tanks and spills released MTBE into groundwater, and as a result, MTBE has been detected in drinking water in NH. We conducted a comparative cancer risk assessment and a margin-of-safety (MOS) analysis for several constituents, including MTBE, detected in NH drinking water. Using standard risk assessment methods, we calculated cancer risks from exposure to 12 detected volatile organic compounds (VOCs), including MTBE, and to four naturally occurring compounds (i.e., arsenic, radium-226, radium-228, and radon-222) detected in NH public water supplies. We evaluated exposures to a hypothetical resident ingesting the water, dermally contacting the water while showering, and inhaling compounds volatilizing from water in the home. We then compared risk estimates for MTBE to those of the other 15 compounds. From our analysis, we concluded that the high-end cancer risk from exposure to MTBE in drinking water is lower than the risks from all the other VOCs evaluated and several thousand times lower than the risks from exposure to naturally occurring constituents, including arsenic, radium, and radon. We also conducted an MOS analysis in which we compared toxicological points of departure to the NH maximum contaminant level (MCL) of 13 µg/L. All of the MOSs were greater than or equal to 160,000, indicating a large margin of safety and demonstrating the health-protectiveness of the NH MCL for MTBE.     

Mlonte Carlo Techniques for Quantitative Uncertainty Analysis in Public Health Risk Assessments

Most public health risk assessments assume and combine a series of average, conservative, and worst-case values to derive a conservative point estimate of risk. This procedure has major limitations. This paper demonstrates a new methodology for extended uncertainty analyses in public health risk assessments using Monte Carlo techniques. The extended method begins as do some conventional methods--with the preparation of a spreadsheet to estimate exposure and risk. This method, however, continues by modeling key inputs as random variables described by probability density functions (PDFs). Overall, the technique provides a quantitative way to estimate the probability distributions for exposure and health risks within the validity of the model used. As an example, this paper presents a simplified case study for children playing in soils contaminated with benzene and benzo(a)pyrene (BaP).     

Bayesian Modeling of Measurement Errors and Pesticide Concentration in Dietary Risk Assessments

We propose new models for dealing with various sources of variability and uncertainty that influence risk assessments for dietary exposure. The uncertain or random variables involved can interact in complex ways, and the focus is on methodology for integrating their effects and on assessing the relative importance of including different uncertainty model components in the calculation of dietary exposures to contaminants, such as pesticide residues. The combined effect is reflected in the final inferences about the population of residues and subsequent exposure assessments. In particular, we show how measurement uncertainty can have a significant impact on results and discuss novel statistical options for modeling this uncertainty. The effect of measurement error is often ignored, perhaps due to the laboratory process conforming to the relevant international standards, for example, or is treated in an  ad hoc  way. These issues are common to many dietary risk analysis problems, and the methods could be applied to any food and chemical of interest. An example is presented using data on carbendazim in apples and consumption surveys of toddlers.     

Subsea Release of Oil from a Riser: An Ecological Risk Assessment

This study illustrates a newly developed methodology, as a part of the U.S. EPA ecological risk assessment (ERA) framework, to predict exposure concentrations in a marine environment due to underwater release of oil and gas. It combines the hydrodynamics of underwater blowout, weathering algorithms, and multimedia fate and transport to measure the exposure concentration. Naphthalene and methane are used as surrogate compounds for oil and gas, respectively. Uncertainties are accounted for in multimedia input parameters in the analysis. The 95th percentile of the exposure concentration (EC_95%) is taken as the representative exposure concentration for the risk estimation. A bootstrapping method is utilized to characterize EC_95% and associated uncertainty. The toxicity data of 19 species available in the literature are used to calculate the 5th percentile of the predicted no observed effect concentration (PNEC_5%) by employing the bootstrapping method. The risk is characterized by transforming the risk quotient (RQ), which is the ratio of EC_95% to PNEC_5%, into a cumulative risk distribution. This article describes a probabilistic basis for the ERA, which is essential from risk management and decision‐making viewpoints. Two case studies of underwater oil and gas mixture release, and oil release with no gaseous mixture are used to show the systematic implementation of the methodology, elements of ERA, and the probabilistic method in assessing and characterizing the risk.     

Risk/Benefit Assessments of Human Diseases: Optimum Dose for Intervention

A simple procedure is proposed in order to quantify the tradeoff between a loss suffered from an illness due to exposure to a microbial pathogen and a loss due to a toxic effect, perhaps a different illness, induced by a disinfectant employed to reduce the microbial exposure. Estimates of these two types of risk as a function of disinfectant dose and their associated relative losses provide information for the estimation of the optimum dose of disinfectant that minimizes the total expected loss. The estimates of the optimum dose and expected relative total loss were similar regardless of whether the beta-Poisson, log-logistic, or extreme value function was used to model the risk of illness due to exposure to a microbial pathogen. This is because the optimum dose of the disinfectant and resultant expected minimum loss depend upon the estimated slope (first derivative) of the models at low levels of risk, which appear to be similar for these three models at low levels of risk. Similarly, the choice among these three models does not appear critical for estimating the slope at low levels of risk for the toxic effect induced by the use of a disinfectant. For the proposed procedure to estimate the optimum disinfectant dose, it is not necessary to have absolute values for the losses due to microbial-induced or disinfectant-induced illness, but only relative losses are required. All aspects of the problem are amenable to sensitivity analyses. The issue of risk/benefit tradeoffs, more appropriately called risk/risk tradeoffs, does not appear to be an insurmountable problem.