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There is increasing public concern regarding health risks from multiple chemical exposures and combined exposure to chemical and nonchemical stressors (cumulative risk). These exposures may involve more than one exposure pathway and typically vary over time with respect to the total exposure level and the relative proportions of component chemicals. Research on toxicology and risk assessment of multichemical exposures is complicated further because toxicologic interactions vary with exposure sequence, duration and route, as well as with total dose, relative chemical proportions, and endpoint.

Microbial risk assessors often make simplifying assumptions that lead to the selection of simple concave functions with low-dose linearity, consistent with no-threshold and single-hit hypotheses, as default dose–response model forms. However, evidence is accumulating as the “microbiome revolution” progresses that challenge these assumptions that influence the estimates of the nature and magnitude of uncertainties associated with microbial risks. Scientific advances in the knowledge of the human “superorganism” (hybrid consortium of human plus microbial communities that cooperatively regulates health and disease) enable the design of definitive studies to estimate the pathogen doses overcome by the innate defenses, including the protective microbiota. The systematic investigation of the events of non-typhoid salmonellosis in humans undertaken nearly 2 decades ago was updated to incorporate recent scientific advances in the understanding of impact of the healthy superorganism that strengthens and ex...

Benchmark dose (BMD) modeling is now the state of the science for determining the point of departure for risk assessment. Key advantages include the fact that the modeling takes account of all of the data for a particular effect from a particular experiment, increased consistency, and better accounting for statistical uncertainties. Despite these strong advantages, disagreements remain as to several specific aspects of the modeling, including differences in the recommendations of the US Environmental Protection Agency (US EPA) and the European Food Safety Authority (EFSA). Differences exist in the choice of the benchmark response (BMR) for continuous data, the use of unrestricted models, and the mathematical models used; these can lead to differences in the final BMDL. It is important to take confidence in the model into account in choosing the BMDL, rather than simply choosing the lowest value. The field is moving in the direction of model averaging, which will avoid many of the challenges of choosing a single best model when the underlying biology does not suggest one, but additional research would be useful into methods of incorporating biological considerations into the weights used in the averaging. Additional research is also needed regarding the interplay between the BMR and the UF to ensure appropriate use for studies supporting a lower BMR than default values, such as for epidemiology data. Addressing these issues will aid in harmonizing methods and moving the field of risk assessment forward.

Mixture risk assessments are most often based on toxicology information for the component chemicals, primarily because dose-response information on the mixture of concern is inadequate. The most widely used component methods in mixture risk assessment are based on dose addition or response addition. Two methods described here are derived from dose addition: the hazard index and the relative potency factor method. The hazard index informs safety decisions for specific environmental exposures, while the relative potency factor formula actually estimates the health risk for specific environmental exposures. Use of dose addition is supported when chemicals are toxicologically similar (see Chap. 9). The hazard index is motivated by dose addition and is applied to chemicals having a common toxicological target organ, which is fairly weak evidence of toxicological similarity. A weight of evidence system for binary mixtures allows the hazard index to be modified to incorporate toxicological interactions. Relative potency factors are applied in a dose addition formula and are developed for chemicals that have good evidence of toxicological similarity, e.g., chemicals that share a common adverse outcome pathway (AOP) and are assumed not to elicit toxicological interactions. Two other methods described here are related to response addition, both requiring the assumption of toxicological independence (see Chap. 9). When response is a risk (probability), response addition follows the statistical formula for independent events. When response is a measured effect, the addition is called effect summation, where the component incremental effects are added. This chapter reviews the history and concepts related to component-based methods for health risk assessment of chemical mixtures, illustrates commonly used methods and some modifications, and discusses strengths, limitations, and likely future development.

Researchers in numerous fields (e.g., pharmacology, entomology, toxicology, and epidemiology) have attempted to model the joint action of chemicals using simple formulas based only on knowledge of individual chemical toxicity or pharmacological effect (i.e., dose-response relationships). Collectively, these formulas are referred to as “additivity models,” and they are based on concepts of additivity that include dose addition, independent action, integrated addition, and effect summation. In toxicology, additivity-based predictions are often compared to observed mixture data to assess the presence and magnitude of interactions (greater-than-additive or less-than-additive) among chemicals. These models can also be used to estimate the toxicity of a defined mixture for comparison to the observed toxicity of a related, but more complex, mixture. Alternatively, additivity models have been used to explore mechanisms of joint action. In general, the steps for investigating joint toxicity using additivity models include (1) deciding on which additivity model(s) to apply (e.g., dose addition, independent action, or both), (2) collecting dose-response data on individual chemicals and the mixture, (3) incorporating individual chemical data in an additivity model to generate predictions, and (4) comparing predicted to observed mixture responses. Many of the additivity models have a long and sometimes controversial history. This chapter provides background on several of the common additivity models, illustrates their application with examples, and discusses their advantages and limitations.

In assessing environmental health risks, the risk characterization step synthesizes information gathered in evaluating exposures to stressors together with dose-response relationships, characteristics of the exposed population, and external environmental conditions. This manuscript summarizes key steps of a cumulative risk assessment (CRA) followed by a discussion of considerations for characterizing cumulative risks. Cumulative risk characterizations differ considerably from single chemical- or single source-based risk characterization. CRAs typically focus on a specific population instead of a pollutant or pollutant source and should include an evaluation of all relevant sources contributing to the exposures in the population and other factors that influence dose-response relationships. Second, CRAs may include influential environmental and population-specific conditions, involving multiple chemical and nonchemical stressors. Third, a CRA could examine multiple health effects, reflecting joint toxicity and the potential for toxicological interactions. Fourth, the complexities often necessitate simplifying methods, including judgment-based and semiquantitative indices that collapse disparate data into numerical scores. Fifth, because of the higher dimensionality and potentially large number of interactions, information needed to quantify risk is typically incomplete, necessitating an uncertainty analysis. Three approaches that could be used for characterizing risks in a CRA are presented: the multiroute hazard index, stressor grouping by exposure and toxicity, and indices for screening multiple factors and conditions. Other key roles of the risk characterization in CRAs are also described, mainly the translational aspect of including a characterization summary for lay readers (in addition to the technical analysis), and placing the results in the context of the likely risk-based decisions.

Previously, we reported that acute treatment with propoxur or carbaryl decreased the duration of the photic after discharge (PhAD) of flash evoked potentials (FEPs). In the current studies, we compared the effects of acute or repeated exposure to a mixture of carbaryl and propoxur (1:1.45 ratio; propoxur:carbaryl) on the duration of the PhAD and brain ChE activity in Long Evans rats. Animals were exposed (po) either to a single dose (0, 3, 10, 45 or 75 mg/kg), or 14 daily dosages (0, 3, 10, 30, 45 mg/kg), of the mixture. Acute and repeated treatment with 3mg/kg (or greater) of the mixture produced dose-related inhibition of brain ChE activity. Compared to controls, the PhAD duration decreased after acute administration of 75 mg/kg or repeated treatment with 30 mg/kg of the mixture. The linear relationship between the percent of control brain ChE activity and the PhAD duration was similar for both exposure paradigms. Dose-response models for the acute and repeated exposure data did not differ for brain ChE activity or the duration of the PhAD. Repeated treatment with the mixture resulted in slightly less (13-22%) erythrocyte ChE inhibition than acute exposure. Both acute and repeated treatment resulted in dose-additive results for the PhAD duration and less than dose-additive responses (6-16%) for brain ChE activity for the middle range of dosages. Acute treatment resulted in greater than dose-additive erythrocyte ChE inhibition (15-18%) at the highest dosages. In contrast, repeated treatment resulted in less than dose-additive erythrocyte ChE inhibition (16-22%) at the middle dosages. Brain and plasma levels of propoxur and carbaryl did not differ between the acute and repeated dosing paradigms. In summary, a physiological measure of central nervous system function and brain ChE activity had similar responses after acute or repeated treatment with the carbamate mixture, and brain ChE showed only small deviations from dose-additivity. Erythrocyte ChE activity had larger differences between the acute and repeated treatment paradigms, and showed slightly greater deviations from dose-additivity. Because these treatments utilized larger dosages than anticipated environmental exposures, concern for non-additive effects in humans is minimized. The small magnitude of the deviations from dose-additivity also suggest that in the absence of repeated exposure data, results from an acute study of readily reversible carbamate toxicity can be used to estimate the response to repeated daily exposures.

Statistical design and environmental relevance are important aspects of studies of chemical mixtures, such as pesticides. We used a dose-additivity model to test experimentally the default assumptions of dose additivity for two mixtures of seven N-methylcarbamates (carbaryl, carbofuran, formetanate, methomyl, methiocarb, oxamyl, and propoxur). The best-fitting models were selected for the single-chemical dose-response data and used to develop a combined prediction model, which was then compared with the experimental mixture data. We evaluated behavioral (motor activity) and cholinesterase (ChE)-inhibitory (brain, red blood cells) outcomes at the time of peak acute effects following oral gavage in adult and preweanling (17 days old) Long-Evans male rats. The mixtures varied only in their mixing ratios. In the relative potency mixture, proportions of each carbamate were set at equitoxic component doses. A California environmental mixture was based on the 2005 sales of each carbamate in California. In adult rats, the relative potency mixture showed dose additivity for red blood cell ChE and motor activity, and brain ChE inhibition showed a modest greater-than additive (synergistic) response, but only at a middle dose. In rat pups, the relative potency mixture was either dose-additive (brain ChE inhibition, motor activity) or slightly less-than additive (red blood cell ChE inhibition). On the other hand, at both ages, the environmental mixture showed greater-than additive responses on all three endpoints, with significant deviations from predicted at most to all doses tested. Thus, we observed different interactive properties for different mixing ratios of these chemicals. These approaches for studying pesticide mixtures can improve evaluations of potential toxicity under varying experimental conditions that may mimic human exposures.

There is increasing interest in the use of tiered approaches in risk assessment of mixtures or co-exposures to chemicals for prioritization. One possible screening-level risk assessment approach is the threshold of toxicological concern (TTC). To date, default assumptions of dose or response additivity have been used to characterize the toxicity of chemical mixtures. Before a screening-level approach could be used, it is essential to know whether synergistic interactions can occur at low, environmentally relevant exposure levels. Studies demonstrating synergism in mammalian test systems were identified from the literature, with emphasis on studies performed at doses close to the points of departure (PODs) for individual chemicals. This search identified 90 studies on mixtures. Few included quantitative estimates of low-dose synergy; calculations of the magnitude of interaction were included in only 11 papers. Quantitative methodology varied across studies in terms of the null hypothesis, response measured, POD used to test for synergy, and consideration of the slope of the dose-response curve. It was concluded that consistent approaches should be applied for quantification of synergy, including that synergy be defined in terms of departure from dose additivity; uniform procedures be developed for assessing synergy at low exposures; and the method for determining the POD for calculating synergy be standardized. After evaluation of the six studies that provided useful quantitative estimates of synergy, the magnitude of synergy at low doses did not exceed the levels predicted by additive models by more than a factor of 4.

Risk assessment formulas are often distinguished from dose-response models by being rough but necessary. The evaluation of these rough formulas is described here, using the example of mixture risk assessment. Two conditions make the dose-response part of mixture risk assessment difficult, lack of data on mixture dose-response relationships, and the need to address risk from combinations of chemicals because of public demands and statutory requirements. Consequently, the U.S. Environmental Protection Agency has developed methods for carrying out quantitative dose-response assessment for chemical mixtures that require information only on the toxicity of single chemicals and of chemical pair interactions. These formulas are based on plausible ideas and default parameters but minimal supporting data on whole mixtures. Because of this lack of mixture data, the usual evaluation of accuracy (predicted vs. observed) cannot be performed. Two approaches to the evaluation of such formulas are to consider fundamental biological concepts that support the quantitative formulas (e.g., toxicologic similarity) and to determine how well the proposed method performs under simplifying constraints (e.g., as the toxicologic interactions disappear). These ideas are illustrated using dose addition and two weight-of-evidence formulas for incorporating toxicologic interactions.

A substantial effort has been spent over the past few decades to label toxicologic interaction outcomes as synergistic, antagonistic, or additive. Although useful in influencing the emotions of the public and the press, these labels have contributed fairly little to our understanding of joint toxic action. Part of the difficulty is that their underlying toxicological concepts are only defined for two chemical mixtures, while most environmental and occupational exposures are to mixtures of many more chemicals. Furthermore, the mathematical characterizations of synergism and antagonism are inextricably linked to the prevailing definition of 'no interaction,' instead of some intrinsic toxicological property. For example, the US EPA has selected dose addition as the no-interaction definition for mixture risk assessment, so that synergism would represent toxic effects that exceed those predicted from dose addition. For now, labels such as synergism are useful to regulatory agencies, both for qualitative indications of public health risk as well as numerical decision tools for mixture risk characterization. Efforts to quantify interaction designations for use in risk assessment formulas, however, are highly simplified and carry large uncertainties. Several research directions, such as pharmacokinetic measurements and models, and toxicogenomics, should promote significant improvements by providing multi-component data that will allow biologically based mathematical models of joint toxicity to replace these pairwise interaction labels in mixture risk assessment procedures.

When considered from a public health perspective, the central question regarding chemical mixtures is deceptively simple: Are current approaches to risk assessment for chemical mixtures affording effective (adequate) and efficient (cost-effective) protection for members of our society? Answering this question realistically depends on an understanding of the hierarchical goals of public health (i.e. prevention, intervention, treatment) and an accurate evaluation of the extent to which these goals are being achieved. To allow decision makers to make informed judgments about the health risks of chemical mixtures, adequate scientific knowledge and understanding must be available to support risk assessment activities, which are an integral part of the regulatory decision making process. Designing and implementing relevant research depends on the existence of a feedback loop between researchers and regulators, where the information needs of regulators influence the nature and direction of research and the information and understanding generated by researchers improves the scientific basis for public health decisions. A clear, consistent, commonly accepted taxonomy for describing important mixture-related phenomena is a key factor in creating and maintaining the necessary feedback loop. Ultimately, both researchers and regulators share a common goal with regard to chemical mixtures; improving the state-of-the-science so that we can make informed decisions about protecting public health. A survey of research issues and needs that are crucial to attaining this goal is presented.

The historical approach to assessing health risks of environmental chemicals has been to evaluate them one at a time. In fact, we are exposed every day to a wide variety of chemicals and are increasingly aware of potential health implications. Although considerable progress has been made in the science underlying risk assessments for real-world exposures, implementation has lagged because many practitioners are unaware of methods and tools available to support these analyses. To address this issue, the US Environmental Protection Agency developed a toolbox of cumulative risk resources for contaminated sites, as part of a resource document that was published in 2007. This paper highlights information for nearly 80 resources from the toolbox and provides selected updates, with practical notes for cumulative risk applications. Resources are organized according to the main elements of the assessment process: (1) planning, scoping, and problem formulation; (2) environmental fate and transport; (3) exposure analysis extending to human factors; (4) toxicity analysis; and (5) risk and uncertainty characterization, including presentation of results. In addition to providing online access, plans for the toolbox include addressing nonchemical stressors and applications beyond contaminated sites and further strengthening resource accessibility to support evolving analyses for cumulative risk and sustainable communities.

Mixture risk assessment is often hampered by the lack of dose–response information on the mixture being assessed, forcing reliance on component formulas such as dose addition. We present a four-step approach for evaluating chemical mixture data for consistency with dose addition for use in supporting a component based mixture risk assessment. Following the concepts in the U.S. EPA mixture risk guidance (U.S. EPA, 2000a,b), toxicological interaction for a defined mixture (all components known) is departure from a clearly articulated definition of component additivity. For the common approach of dose additivity, the EPA guidance identifies three desirable characteristics, foremost of which is that the component chemicals are toxicologically similar. The other two characteristics are empirical: the mixture components have toxic potencies that are fixed proportions of each other (throughout the dose range of interest), and the mixture dose term in the dose additive prediction formula, which we call the combined prediction model (CPM), can be represented by a linear combination of the component doses. A consequent property of the proportional toxic potencies is that the component chemicals must share a common dose–response model, where only the dose coefficients depend on the chemical components. A further consequence is that the mixture data must be described by the same mathematical function (“mixture model”) as the components, but with a distinct coefficient for the total mixture dose. The mixture response is predicted from the component dose–response curves by using the dose additive CPM and the prediction is then compared with the observed mixture results. The four steps are to evaluate: (1) toxic proportionality by determining how well the CPM matches the single chemical models regarding mean and variance; (2) fit of the mixture model to the mixture data; (3) agreement between the mixture data and the CPM prediction; and (4) consistency between the CPM and the mixture model. Because there are four evaluations instead of one, some involving many parameters or dose groups, there are more opportunities to reject statistical hypotheses about dose addition, thus statistical adjustment for multiple comparisons is necessary. These four steps contribute different pieces of information about the consistency of the component and mixture data with the two empirical characteristics of dose additivity. We examine this four-step approach in how it can show empirical support for dose addition as a predictor for an untested mixture in a screening level risk assessment. The decision whether to apply dose addition should be based on all four of those evidentiary pieces as well as toxicological understanding of these chemicals and should include interpretations of the numerical and toxicological issues that arise during the evaluation. This approach is demonstrated with neurotoxicity data on carbamate mixtures.

The role of nonchemical stressors in modulating the human health risk associated with chemical exposures is an area of increasing attention. On 9 March 2011, a workshop titled “Approaches for Incorporating Nonchemical Stressors into Cumulative Risk Assessment” took place during the 50th Anniversary Annual Society of Toxicology Meeting in Washington D.C. Objectives of the workshop included describing the current state of the science from various perspectives (i.e., regulatory, exposure, modeling, and risk assessment) and presenting expert opinions on currently available methods for incorporating nonchemical stressors into cumulative risk assessments. Herein, distinct frameworks for characterizing exposure to, joint effects of, and risk associated with chemical and nonchemical stressors are discussed.

Reactions between chemicals used to disinfect drinking water and compounds present in source waters produce chemical mixtures containing hundreds of disinfection byproducts (DBPs). Although the results have been somewhat inconsistent, some epidemiological studies suggest associations may exist between DBP exposures and adverse developmental outcomes. The potencies of individual DBPs in rodent and rabbit developmental bioassays suggest that no individual DBP can account for the relative risk estimates reported in the positive epidemiologic studies, leading to the hypothesis that these outcomes could result from the toxicity of DBP mixtures. As a first step in a mixtures risk assessment for DBP developmental effects, this paper identifies developmentally toxic DBPs and examines data relevant to the mode of action (MOA) for DBP developmental toxicity. We identified 24 developmentally toxic DBPs and four adverse developmental outcomes associated with human DBP exposures: spontaneous abortion, cardiovascular defects, neural tube defects, and low birth weight infancy. A plausible MOA, involving hormonal disruption of pregnancy, is delineated for spontaneous abortion, which some epidemiologic studies associate with total trihalomethane and bromodichloromethane exposures. The DBP data for the other three outcomes were inadequate to define key MOA steps.

There is a need to define exposure-response curves for both Cu excess and deficiency to assist in determining the acceptable range of oral intake. A comprehensive database has been developed where different health outcomes from elevated and deficient Cu intakes were assigned ordinal severity scores to create common measures of response. A generalized linear model for ordinal data was used to estimate the probability of response associated with dose, duration and severity. The model can account for differences in animal species, the exposure medium (drinking water and feed), age, sex, and solubility. Using this model, an optimal intake level of 2.6 mg Cu/d was determined. This value is higher than the current U.S. recommended dietary intake (RDI; 0.9 mg/d) that protects against toxicity from Cu deficiency. It is also lower than the current tolerable upper intake level (UL; 10 mg/d) that protects against toxicity from Cu excess. Compared to traditional risk assessment approaches, categorical regression can provide risk managers with more information, including a range of intake levels associated with different levels of severity and probability of response. To weigh the relative harms of deficiency and excess, it is important that the results be interpreted along with the available information on the nature of the responses that were assigned to each severity score.

Previous risk assessment reviews analyzed the potential for dietary acrylamide to increase breast cancer risk. Here, we critically review acrylamide animal bioassay data on mammary tumors for human relevance. We applied a systematic evaluation using reasonable standards of scientific certainty and a systematic weight of evidence (WOE) approach to evaluate several hypothesized modes of action (MOA), including (1) genotoxicity related to glycidamide formation and oxidative stress, (2) endocrine effects due to age-related hyperprolactinemia or secondary to neurotoxicity, and (3) epigenetic effects. We conclude that the appropriate approach for low-dose extrapolation of the rat mammary tumors can be narrowed to two options: (1) linear low-dose extrapolation (i.e., based on a MOA of mutagenicity from direct DNA interaction) from a point of departure (POD) for the combined incidence of adenomas and adenocarcinomas, since these tumor types are related; or (2) non-linear extrapolation, using uncertainty factors to estimate a Reference Dose (RfD) from a POD for tumor promotion derived using the combined fibroadenoma, adenoma and adenocarcinoma data. Non-linear extrapolation is used in the latter approach because these combined tumor types are unlikely to be exclusively caused by mutagenicity. Comparison of the WOE for each alternative MOA indicates that a non-linear approach (option 2) is more appropriate for evaluation of acrylamide-induced mammary tumors; a linear approach (option 1) is shown for comparison.

Humans are exposed daily to multiple chemicals, including incidental exposures to complex chemical mixtures released into the environment and to combinations of chemicals that already co-exist in the environment because of previous releases from various sources. Exposures to chemical mixtures can occur through multiple pathways and across multiple routes. In this paper, we propose an iterative approach for assessing exposures to environmental chemical mixtures; it is similar to single-chemical approaches. Our approach encompasses two elements of the Risk Assessment Paradigm: Problem Formulation and Exposure Assessment. Multiple phases of the assessment occur in each element of the paradigm. During Problem Formulation, analysts identify and characterize the source(s) of the chemical mixture, ensure that dose–response and exposure assessment measures are concordant, and develop a preliminary evaluation of the mixture's fate. During Exposure Assessment, analysts evaluate the fate of the chemicals comprising the mixture using appropriate models and measurement data, characterize the exposure scenario, and estimate human exposure to the mixture. We also describe the utility of grouping the chemicals to be analyzed based on both physical–chemical properties and an understanding of environmental fate. In the article, we also highlight the need for understanding of changes in the mixture composition in the environment due to differential transport, differential degradation, and differential partitioning to other media. The Results section describes the application of the method to various chemical mixtures, highlighting issues associated with assessing exposures to chemical mixtures in the environment.

This article is reproduced from the previous edition, volume 3, pp 120–123, © 2005, Elsevier Inc.

A PBPK model for 2,4-D was developed that involves flow-limited pH trapping modified to consider tissue binding, binding to plasma, and high-dose inhibition of urinary excretion. The PBPK model provides reasonable estimates of the kinetics of 2,4-D in rats as well as in humans, providing a common metric for expressing risk. The risk characterization for 2,4-D based on the PBPK model is consistent with that based on standard risk assessment methods, except that the apparent variability in the risk characterization is reduced. The model demonstrates that non-linear pharmacokinetics and inhibition of urinary excretion would not be expected in occupational exposures. This case study suggests that preliminary PBPK models could be developed for numerous pesticides based on commonly available data. If properly validated with well-designed worker exposure studies, such models may be useful in more complete assessments of risks to workers as well as members of the general public.

Project-level research strategies at the U.S. Environmental Protection Agency regarding chemical mixtures are impacted by administrative priorities, public interests, expert opinions, scientific advances, regulatory needs, and legislative actions, influencing the setting of priorities and goals. Perhaps, the most significant influence on conducting chemical mixtures research is the passage of laws requiring the EPA to investigate the potential toxicity of various mixtures, specifically the Comprehensive Environmental Response, Compensation, and Liability Act of 1980, the Food Quality Protection Act of 1996, and the Safe Drinking Water Act Amendments of 1996. Scarce resources are allocated to broadly defined issues for consideration by teams of scientists, who design and implement specific projects. Because resources are limited, projects may have several goals, e.g., filling specific data gaps to support a regulation and, simultaneously, producing data to evaluate a risk assessment method. Research areas of emphasis are shaped by risk assessment needs, data gap uncertainties, and experimental design considerations. This paper discusses factors shaping EPA research strategies for chemical mixtures and presents an example of efficient research planning to investigate potential toxicity from exposure to drinking water disinfection by-products.

Drinking water disinfection has effectively eliminated much of the morbidity and mortality associated with waterborne infectious diseases in the United States. Various disinfection processes, however, produce certain types and amounts of disinfection by-products (DBPs), including trihalomethanes (THM), haloacetic acids, haloacetonitriles, and bromate, among others. Human health risks from the ubiquitous exposure to complex mixtures of DBPs are of concern because existing epidemiologic and toxicologic studies suggest the existence of systemic or carcinogenic effects. Researchers from several organizations have developed a multiple-purpose design approach to this problem that combines efficient laboratory experimental designs with statistical models to provide data on critical research issues (e.g., estimation of human health risk from low-level DBP exposures, evaluation of additivity assumptions as useful for risk characterization, estimation of health risks from different drinking water treatment options). A series of THM experiments have been designed to study embryonic development, mortality and cancer in Japanese medaka (Oryzias latipes) and liver and kidney endpoints in female CD-1 mice. The studies are to provide dose-response data for specific mixtures of the 4 THMs, for the single chemicals, and for binary combinations. The dose-levels and mixing ratios for these experiments were selected to be useful for development and refinement of three different statistical methods: testing for departures from dose-additivity; development of an interactions-based hazard index; and use of proportional-response addition as a risk characterization method. Preliminary results suggest that dose-additivity is a reasonable risk assessment assumption for DBPs. The future of mixtures research will depend on such collaborative efforts that maximize the use of resources and focus on issues of high relevance to the risk assessment of human health.

Humans are typically exposed to low doses of combinations of chemicals rather than to one or two chemicals at a time, yet most of the available toxicity data provide information on single chemicals or binary pairs, rather than on whole mixtures. The use of existing interactions study data for the quantitative risk assessment of chemical mixtures is problematic. These studies generally lack the necessary statistical characterizations to be useful in quantitative risk assessment procedures. The U.S. EPA developed guidelines for risk assessment for chemical mixtures in 1986 and is currently in the process of making revisions. Significant advances have been made in both the theoretical development and application of procedures such as dose addition, response addition, toxicity equivalence factors, comparative potency and interactions data characterizations. Details on the current revisions to the guidelines are given, along with information on the research efforts that have influenced these revisions or that represent future directions in chemical mixtures risk assessment.

The excess cancer risk that might result from exposure to a mixture of chemical carcinogens usually is estimated with data from experiments conducted on individual chemicals. An upper bound on the total excess risk is estimated commonly by summing individual upper bound risk estimates. The degree to which this approach might overstate the true risk associated with the mixture has not been evaluated previously. This paper reports the results of a Monte Carlo simulation study on the degree of reduction in conservation that might be achieved using alternative methods for calculating mixture upper bounds. An unexpected finding is that for chemicals that exhibit strongly linear dose-response relationships, the summing of multistage-model-based upper bounds on excess risk can be anti-conservative, that is, it can provide less than the nominal 100(1-alpha)% coverage.

This paper presents a method for identifying and assessing the significance of interaction patterns among various chemicals and chemical classes of importance to regulatory toxicologists. To this end, efforts were made to assemble and evaluate experimental data on toxicologically significant interactions, to use this information to characterize the consistency of toxicological interactions, and to define classes of compounds that display similar toxicological interactions. The motivation for this effort is to be able to propose hypotheses, which can be validated by experimentation, on how 2 or more chemicals will interact.

This paper describes two general methods for estimating ADIs that circumvent some of the limitations inherent in current approaches. The first method is based on a graphic presentation of toxicity data and is also shown to be useful for estimating acceptable intakes for durations of toxicant exposure other than the entire lifetime. The second method uses dose-response or dose-effect data to calculate lower CLs on the dose rate associated with specified response or effect levels. These approaches should lead to firmer, better established ADIs through increased use of the entire spectrum of toxicity data.

The general solution of a Markov model for first-order kinetics is developed as a sum of independent, multinomially distributed random processes. Fluctuations in the mean and variance functions are discussed and shown to be unrelated in time during the early phase of the reaction. Numerical examples are presented for two- and three-component systems.

Predictions of human health risk for single chemicals are often based on animal studies and hence require some sort of adjustment for species differences in toxic susceptibility. In the past, either the animal dose has been divided by an uncertainty factor or the dose has been transformed by a mathematical model into a human equivalent dose. A generalization of the allometric model previously used for carcinogens, the so-called "surface area model, " is investigated here for use with graded severity response data for noncarcinogenic systemic toxicity. Statistical methods for estimating one of the model's parameters, the power of body weight, are proposed and tested on simulated and actual toxicity data. Early results indicate reasonable accuracy if data are available for a large number of dose groups.