Fitting Second-Order Finite Mixture Models to Data with Many Censored Values Using Maximum Likelihood Estimation

Finite mixture models, that is, weighted averages of parametric distributions, provide a powerful way to extend parametric families of distributions to fit data sets not adequately fit by a single parametric distribution. First-order finite mixture models have been widely used in the physical, chemical, biological, and social sciences for over 100 years. Using maximum likelihood estimation, we demonstrate how a first-order finite mixture model can represent the large variability in data collected by the U.S. Environmental Protection Agency for the concentration of Radon 222 in drinking water supplied from ground water, even when 28% of the data fall at or below the minimum reporting level. Extending the use of maximum likelihood, we also illustrate how a second-order finite mixture model can separate and represent both the variability and the uncertainty in the data set.     

An Empirical Approach to Sufficient Similarity: Combining Exposure Data and Mixtures Toxicology Data

When assessing risks posed by environmental chemical mixtures, whole mixture approaches are preferred to component approaches. When toxicological data on whole mixtures as they occur in the environment are not available, Environmental Protection Agency guidance states that toxicity data from a mixture considered “sufficiently similar” to the environmental mixture can serve as a surrogate. We propose a novel method to examine whether mixtures are sufficiently similar, when exposure data and mixture toxicity study data from at least one representative mixture are available. We define sufficient similarity using equivalence testing methodology comparing the distance between benchmark dose estimates for mixtures in both data‐rich and data‐poor cases. We construct a “similar mixtures risk indicator”(SMRI) (analogous to the hazard index) on sufficiently similar mixtures linking exposure data with mixtures toxicology data. The methods are illustrated using pyrethroid mixtures occurrence data collected in child care centers (CCC) and dose‐response data examining acute neurobehavioral effects of pyrethroid mixtures in rats. Our method shows that the mixtures from 90% of the CCCs were sufficiently similar to the dose‐response study mixture. Using exposure estimates for a hypothetical child, the 95th percentile of the (weighted) SMRI for these sufficiently similar mixtures was 0.20 (i.e., where SMRI <1, less concern; >1, more concern).     

Binary Mixtures of Polycyclic Aromatic Hydrocarbons Display Nonadditive Mixture Interactions in an In Vitro Liver Cell Model

Polycyclic aromatic hydrocarbons (PAHs) have been labeled contaminants of concern due to their carcinogenic potential, insufficient toxicological data, environmental ubiquity, and inconsistencies in the composition of environmental mixtures. The Environmental Protection Agency is reevaluating current methods for assessing the toxicity of PAHs, including the assumption of toxic additivity in mixtures. This study was aimed at testing mixture interactions through in vitro cell culture experimentation, and modeling the toxicity using quantitative structure‐activity relationships (QSAR). Clone‐9 rat liver cells were used to analyze cellular proliferation, viability, and genotoxicity of 15 PAHs in single doses and binary mixtures. Tests revealed that many mixtures have nonadditive toxicity, but display varying mixture effects depending on the mixture composition. Many mixtures displayed antagonism, similar to other published studies. QSARs were then developed using the genetic function approximation algorithm to predict toxic activity both in single PAH congeners and in binary mixtures. Effective concentrations inhibiting 50% of the cell populations were modeled, with R² = 0.90, 0.99, and 0.84, respectively. The QSAR mixture algorithms were then adjusted to account for the observed mixture interactions as well as the mixture composition (ratios) to assess the feasibility of QSARs for mixtures. Based on these results, toxic addition is improbable and therefore environmental PAH mixtures are likely to see nonadditive responses when complex interactions occur between components. Furthermore, QSAR may be a useful tool to help bridge these data gaps surrounding the assessment of human health risks that are associated with PAH exposures.     

Summary of the Workshop on Issues in Risk Assessment: Quantitative Methods for Developmental Toxicology

This report summarizes the proceedings of a conference on quantitative methods for assessing the risks of developmental toxicants. The conference was planned by a subcommittee of the National Research Council's Committee on Risk Assessment Methodology ⁴ in conjunction with staff from several federal agencies, including the U.S. Environmental Protection Agency, U.S. Food and Drug Administration, U.S. Consumer Products Safety Commission, and Health and Welfare Canada. Issues discussed at the workshop included computerized techniques for hazard identification, use of human and animal data for defining risks in a clinical setting, relationships between end points in developmental toxicity testing, reference dose calculations for developmental toxicology, analysis of quantitative dose-response data, mechanisms of developmental toxicity, physiologically based pharmacokinetic models, and structure-activity relationships. Although a formal consensus was not sought, many participants favored the evolution of quantitative techniques for developmental toxicology risk assessment, including the replacement of lowest observed adverse effect levels (LOAELs) and no observed adverse effect levels (NOAELs) with the benchmark dose methodology.     

Health-Based Screening Levels to Evaluate U.S. Geological Survey Ground water Quality Data

Federal and state drinking-water standards and guidelines do not exist for many contaminants analyzed by the U.S. Geological Survey's National Water-Quality Assessment Program, limiting the ability to evaluate the potential human-health relevance of water-quality findings. Health-based screening levels (HBSLs) were developed collaboratively to supplement existing drinking-water standards and guidelines as part of a six-year, multi-agency pilot study. The pilot study focused on ground water samples collected prior to treatment or blending in areas of New Jersey where groundwater is the principal source of drinking water. This article describes how HBSLs were developed and demonstrates the use of HBSLs as a tool for evaluating water-quality data in a human-health context. HBSLs were calculated using standard U.S. Environmental Protection Agency (USEPA) methodologies and toxicity information. New HBSLs were calculated for 12 of 32 contaminants without existing USEPA drinking-water standards or guidelines, increasing the number of unregulated contaminants (those without maximum contaminant levels (MCLs)) with human-health benchmarks. Concentrations of 70 of the 78 detected contaminants with human-health benchmarks were less than MCLs or HBSLs, including all 12 contaminants with new HBSLs, suggesting that most contaminant concentrations were not of potential human-health concern. HBSLs were applied to a state-scale groundwater data set in this study, but HBSLs also may be applied to regional and national evaluations of water-quality data. HBSLs fulfill a critical need for federal, state, and local agencies, water utilities, and others who seek tools for evaluating the occurrence of contaminants without drinking-water standards or guidelines.     

Characterizing the Noncancer Toxicity of Mixtures Using Concepts from the TTC and Quantitative Models of Uncertainty in Mixture Toxicity

This article explores the use of an approach for setting default values for the noncancer toxicity, developed as part of the Threshold of Toxicological Concern (TTC), for the evaluation of the chronic noncarcinogenic effects of certain chemical mixtures. Individuals are exposed to many mixtures where there are little or no toxicological data on some or all of the mixture components. The approach developed in the TTC can provide a basis for conservative estimates of the toxicity of the mixture components when compound-specific data are not available. The application of this approach to multiple chemicals in a mixture, however, has implications for the statistical assumptions made in developing component-based estimates of mixtures. Specifically, conservative assumptions that are appropriate for one compound may become overly conservative when applied to all components of a mixture. This overestimation can be investigated by modeling the uncertainty in toxicity standards. In this article the approach is applied to both hypothetical and actual examples of chemical mixtures and the potential for overestimation is investigated. The results indicate that the use of the approach leads to conservative estimates of mixture toxicity and therefore its use is most appropriate for screening assessments of mixtures.     

Predictive Bayesian Microbial Dose-Response Assessment Based on Suggested Self-Organization in Primary Illness Response: Cryptosporidium parvum

The probability of illness caused by very low doses of pathogens cannot generally be tested due to the numbers of subjects that would be needed, though such assessments of illness dose response are needed to evaluate drinking water standards. A predictive Bayesian dose-response assessment method was proposed previously to assess the unconditional probability of illness from available information and avoid the inconsistencies of confidence-based approaches. However, the method uses knowledge of the conditional dose-response form, and this form is not well established for the illness endpoint. A conditional parametric dose-response function for gastroenteric illness is proposed here based on simple numerical models of self-organized host-pathogen systems and probabilistic arguments. In the models, illnesses terminate when the host evolves by processes of natural selection to a self-organized critical value of wellness. A generalized beta-Poisson illness dose-response form emerges for the population as a whole. Use of this form is demonstrated in a predictive Bayesian dose-response assessment for cryptosporidiosis. Results suggest that a maximum allowable dose of 5.0 x 10(-7) oocysts/exposure (e.g., 2.5 x 10(-7) oocysts/L water) would correspond with the original goals of the U.S. Environmental Protection Agency Surface Water Treatment Rule, considering only primary illnesses resulting from Poisson-distributed pathogen counts. This estimate should be revised to account for non-Poisson distributions of Cryptosporidium parvum in drinking water and total response, considering secondary illness propagation in the population.     

Treating and Drinking Well Water in the Presence of Health Risks from Arsenic Contamination: Results from a U.S. Hot Spot

The Safe Drinking Water Act of 1974 regulates water quality in public drinking water supply systems but does not pertain to private domestic wells, often found in rural areas throughout the country. The recent decision to tighten the drinking water standard for arsenic from 50 parts per billion (ppb) to 10 ppb may therefore affect some households in rural communities, but may not directly reduce health risks for those on private wells. The article reports results from a survey conducted in a U.S. arsenic hot spot, the rural area of Churchill County, Nevada. This area has elevated levels of arsenic in groundwater. We find that a significant proportion of households on private wells are consuming drinking water with arsenic levels that pose a health risk. The decision to treat tap water for those on private wells in this area is modeled, and the predicted probability of treatment is used to help explain drinking water consumption. This probability represents behaviors relating to the household's perception of risk.     

A Look at State‐Level Risk Assessment in the United States: Making Decisions in the Absence of Federal Risk Values

State environmental agencies in the United States are charged with making risk management decisions that protect public health and the environment while managing limited technical, financial, and human resources. Meanwhile, the federal risk assessment community that provides risk assessment guidance to state agencies is challenged by the rapid growth of the global chemical inventory. When chemical toxicity profiles are unavailable on the U.S. Environmental Protection Agency's Integrated Risk Information System or other federal resources, each state agency must act independently to identify and select appropriate chemical risk values for application in human health risk assessment. This practice can lead to broad interstate variation in the toxicity values selected for any one chemical. Within this context, this article describes the decision‐making process and resources used by the federal government and individual U.S. states. The risk management of trichloroethylene (TCE) in the United States is presented as a case study to demonstrate the need for a collaborative approach among U.S. states toward identification and selection of chemical risk values while awaiting federal risk values to be set. The regulatory experience with TCE is contrasted with collaborative risk science models, such as the European Union's efforts in risk assessment harmonization. Finally, we introduce State Environmental Agency Risk Collaboration for Harmonization, a free online interactive tool designed to help to create a collaborative network among state agencies to provide a vehicle for efficiently sharing information and resources, and for the advancement of harmonization in risk values used among U.S. states when federal guidance is unavailable.     

Incorporating Risk Assessment and Benefit-Cost Analysis in Environmental Management1

Using data from interviews with a key set of individuals at the U.S. Environmental Protection Agency, this study examines intraagency views about the incorporation of risk assessment and benefit-cost analysis in environment management.     

Carcinogenic Mixtures

Human populations are generally exposed simultaneously to a number of toxicants present in the environment, including complex mixtures of unknown and variable origin. While scientific methods for evaluating the potential carcinogenic risks of pure compounds are relatively well established, methods for assessing the risks of complex mixtures are somewhat less developed. This article provides a report of a recent workshop on carcinogenic mixtures sponsored by the Committee on Toxicology of the U.S. National Research Council, in which toxicological, epidemiological, and statistical approaches to carcinogenic risk assessment for mixtures were discussed. Complex mixtures, such as diesel emissions and tobacco smoke, have been shown to have carcinogenic potential. Bioassay-directed fractionation based on short-term screening test for genotoxicity has also been used in identifying carcinogenic components of mixtures. Both toxicological and epidemiological studies have identified clear interactions between chemical carcinogens, including synergistic effects at moderate to high doses. To date, laboratory studies have demonstrated over 900 interactions involving nearly 200 chemical carcinogens. At lower doses, theoretical arguments suggest that risks may be near additive. Thus, additivity at low doses has been invoked as as a working hypothesis by regulatory authorities in the absence of evidence to the contrary. Future studies of the joint effects of carcinogenic agents may serve to elucidate the mechanisms by which interactions occur at higher doses.     

Science Policy Choices and the Estimation of Cancer Risk Associated with Exposure to TCDD

United States regulatory agencies use no-threshold models for estimating carcinogenic risks. Other countries use no-threshold models for carcinogens that are genotoxic and threshold models for carcinogens that are not genotoxic, such as 2, 3, 7, 8-tetrachlorodibenzo-p-dioxin (TCDD or "dioxin"). The U.S. Environmental Protection Agency has proposed a revision of the carcinogenic potency estimate for TCDD that is based on neither a threshold nor a no-threshold model; instead, it is a compromise between risk numbers generated by the two irreconcilably different models. This paper discusses the revision and its implications.     

Resolution of the Long-Term Performance Issues at the Waste Isolation Pilot Plant

The Waste Isolation Pilot Plant (WIPP) is a geological repository for disposal of U.S. defense transuranic radioactive waste. Built and operated by the U.S. Department of Energy (DOE), it is located in the Permian age salt beds in southeastern New Mexico at a depth of 655 m. Performance assessment for the repository's compliance with the 10,000-year containment standards was completed in 1996 and the U.S. Environmental Protection Agency (EPA) certified in 1998 that the repository meets compliance with the EPA standards 40 CFR 191 and 40 CFR 194. The Environmental Evaluation Group (EEG) review of the DOE's application for certification identified a number of issues. These related to the scenarios, conceptual models, and values of the input parameters used in the calculations. It is expected that these issues will be addressed and resolved during the first 5-year recertification process that began with the first receipt of waste at WIPP on March 26, 1999, and scheduled to be completed in March 2004.     

The Use of PBPK Models to Inform Human Health Risk Assessment: Case Study on Perchlorate and Radioiodide Human Lifestage Models

Physiologically‐based pharmacokinetic (PBPK) models are often submitted to or selected by agencies, such as the U.S. Environmental Protection Agency (U.S. EPA) and Agency for Toxic Substances and Disease Registry, for consideration for application in human health risk assessment (HHRA). Recently, U.S. EPA evaluated the human PBPK models for perchlorate and radioiodide for their ability to estimate the relative sensitivity of perchlorate inhibition on thyroidal radioiodide uptake for various population groups and lifestages. The most well‐defined mode of action of the environmental contaminant, perchlorate, is competitive inhibition of thyroidal iodide uptake by the sodium‐iodide symporter (NIS). In this analysis, a six‐step framework for PBPK model evaluation was followed, and with a few modifications, the models were determined to be suitable for use in HHRA to evaluate relative sensitivity among human lifestages. Relative sensitivity to perchlorate was determined by comparing the PBPK model predicted percent inhibition of thyroidal radioactive iodide uptake (RAIU) by perchlorate for different lifestages. A limited sensitivity analysis indicated that model parameters describing urinary excretion of perchlorate and iodide were particularly important in prediction of RAIU inhibition; therefore, a range of biologically plausible values available in the peer‐reviewed literature was evaluated. Using the updated PBPK models, the greatest sensitivity to RAIU inhibition was predicted to be the near‐term fetus (gestation week 40) compared to the average adult and other lifestages; however, when exposure factors were taken into account, newborns were found to be populations that need further evaluation and consideration in a risk assessment for perchlorate.     

An Upper‐Bound Assessment of the Benefits of Reducing Perchlorate in Drinking Water

The Environmental Protection Agency plans to issue new federal regulations to limit drinking water concentrations of perchlorate, which occurs naturally and results from the combustion of rocket fuel. This article presents an upper‐bound estimate of the potential benefits of alternative maximum contaminant levels for perchlorate in drinking water. The results suggest that the economic benefits of reducing perchlorate concentrations in drinking water are likely to be low, i.e., under $2.9 million per year nationally, for several reasons. First, the prevalence of detectable perchlorate in public drinking water systems is low. Second, the population especially sensitive to effects of perchlorate, pregnant women who are moderately iodide deficient, represents a minority of all pregnant women. Third, and perhaps most importantly, reducing exposure to perchlorate in drinking water is a relatively ineffective way of increasing iodide uptake, a crucial step linking perchlorate to health effects of concern.     

Probabilistic Integrated Human Mixture Risk Assessment of Multiple Metals Through Seafood Consumption

Inorganic arsenic (iAs), cadmium (Cd), lead (Pb), and methylmercury (MeHg) are toxic metals that cause substantial health concern and are present in various seafood items. This study linked probabilistic risk assessment to the interactive hazard index (HI_INT) approach to assess the human mixture risk posed by the dietary intake of iAs, Cd, Pb, and MeHg from seafood for different age populations, and joint toxic actions and toxic interactions among metals were also considered in the assessment. We found that, in combination, an iAs–Cd–Pb–MeHg mixture synergistically causes neurological toxicity. Furthermore, an iAs–Cd–Pb mixture antagonistically causes renal and hematological effects and additively causes cardiovascular effect. Our results demonstrated that if toxic interactions are not considered, the health risk may be overestimated or underestimated. The 50th percentile HI_INT estimates in all age populations for neurological, renal, cardiovascular, and hematological effects were lower than 1; however, the 97.5th percentile HI_INT estimates might exceed 1. In particular, toddlers and preschoolers had the highest neurological risk, with 0.16 and 0.19 probabilities, respectively, of neurological HI_INT exceeding 1. Saltwater fish consumption was the principal contributor to the health risk. We suggest that regular monitoring of metal levels in seafood, more precise dietary surveys, further toxicological data, and risk–benefit analysis of seafood consumption are warranted to improve the accuracy of human mixture risk assessment and determine optimal consumption.     

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.     

Emissions from Mass Burn Resource Recovery Facilities

Recent resource recovery facility stack tests have increased the available pool of data on emissions from these facilities. This has led to more accurate predictions of emissions from proposed facilities. The source, type, and rate of emissions presented are based upon a review of the literature, theoretical approaches, stack test data from existing facilities, permit levels of other facilities, and discussions with equipment manufacturers. The pollutants selected for study are those regulated by United States Environmental Protection Agency (USEPA) Prevention of Significant Deterioration (PSD) regulations and other pollutants of concern. The pollutants studied are particulate matter, sulfur dioxide, nitrogen oxides, carbon monoxide, nonmethane hydrocarbons, hydrogen sulfide, reduced sulfide, reduced sulfur compounds, total reduced sulfur, lead, mercury, beryllium, arsenic, cadmium, chromium, chromium +6, copper, manganese, nickel, vanadium, zinc, hydrogen chloride, fluorides, sulfuric acid mist, polynuclear aromatic hydrocarbons, polychlorinated biphenyls, vinyl chloride, dioxins, furans, formaldehyde, and asbestos.     

Modeling U‐Shaped Exposure‐Response Relationships for Agents that Demonstrate Toxicity Due to Both Excess and Deficiency

Essential elements such as copper and manganese may demonstrate U‐shaped exposure‐response relationships due to toxic responses occurring as a result of both excess and deficiency. Previous work on a copper toxicity database employed CatReg, a software program for categorical regression developed by the U.S. Environmental Protection Agency, to model copper excess and deficiency exposure‐response relationships separately. This analysis involved the use of a severity scoring system to place diverse toxic responses on a common severity scale, thereby allowing their inclusion in the same CatReg model. In this article, we present methods for simultaneously fitting excess and deficiency data in the form of a single U‐shaped exposure‐response curve, the minimum of which occurs at the exposure level that minimizes the probability of an adverse outcome due to either excess or deficiency (or both). We also present a closed‐form expression for the point at which the exposure‐response curves for excess and deficiency cross, corresponding to the exposure level at which the risk of an adverse outcome due to excess is equal to that for deficiency. The application of these methods is illustrated using the same copper toxicity database noted above. The use of these methods permits the analysis of all available exposure‐response data from multiple studies expressing multiple endpoints due to both excess and deficiency. The exposure level corresponding to the minimum of this U‐shaped curve, and the confidence limits around this exposure level, may be useful in establishing an acceptable range of exposures that minimize the overall risk associated with the agent of interest.