A Comparison of Regulatory Implications of Traditional and Exact Two-Stage Dose–Response Models

We compare the regulatory implications of applying the traditional (linearized) and exact two-stage dose–response models to animal carcinogenic data. We analyze dose–response data from six studies, representing five different substances, and we determine the goodness-of-fit of each model as well as the 95% confidence lower limit of the dose corresponding to a target excess risk of 10^–5 (the target risk dose TRD). For the two concave datasets, we find that the exact model gives a substantially better fit to the data than the traditional model, and that the exact model gives a TRD that is an order of magnitude lower than that given by the traditional model. In the other cases, the exact model gives a fit equivalent to or better than the traditional model. We also show that although the exact two-stage model may exhibit dose–response concavity at moderate dose levels, it is always linear or sublinear, and never supralinear, in the low-dose limit. Because regulatory concern is almost always confined to the low-dose region extrapolation, supralinear behavior seems not to be of regulatory concern in the exact two-stage model. Finally, we find that when performing this low-dose extrapolation in cases of dose–response concavity, extrapolating the model fit leads to a more conservative TRD than taking a linear extrapolation from 10% excess risk. We conclude with a set of recommendations.     

Quantitative Assessment of the Risk of Lung Cancer Associated with Occupational Exposure to Refractory Ceramic Fibers

We present the results of a quantitative assessment of the lung cancer risk associated with occupational exposure to refractory ceramic fibers (RCF). The primary sources of data for our risk assessment were two long-term oncogenicity studies in male Fischer rats conducted to assess the potential pathogenic effects associated with prolonged inhalation of RCF. An interesting feature of the data was the availability of the temporal profile of fiber burden in the lungs of experimental animals. Because of this information, we were able to conduct both exposure–response and dose–response analyses. Our risk assessment was conducted within the framework of a biologically based model for carcinogenesis, the two-stage clonal expansion model, which allows for the explicit incorporation of the concepts of initiation and promotion in the analyses. We found that a model positing that RCF was an initiator had the highest likelihood. We proposed an approach based on biological considerations for the extrapolation of risk to humans. This approach requires estimation of human lung burdens for specific exposure scenarios, which we did by using an extension of a model due to Yu. Our approach acknowledges that the risk associated with exposure to RCF depends on exposure to other lung carcinogens. We present estimates of risk in two populations: (1) a population of nonsmokers and (2) an occupational cohort of steelworkers not exposed to coke oven emissions, a mixed population that includes both smokers and nonsmokers.     

A Simulation Study of Quantitative Risk Assessment for Bivariate Continuous Outcomes

The neurotoxic effects of chemical agents are often investigated in controlled studies on rodents, with binary and continuous multiple endpoints routinely collected. One goal is to conduct quantitative risk assessment to determine safe dose levels. Yu and Catalano (2005) describe a method for quantitative risk assessment for bivariate continuous outcomes by extending a univariate method of percentile regression. The model is likelihood based and allows for separate dose‐response models for each outcome while accounting for the bivariate correlation. The approach to benchmark dose (BMD) estimation is analogous to that for quantal data without having to specify arbitrary cutoff values. In this article, we evaluate the behavior of the BMD relative to background rates, sample size, level of bivariate correlation, dose‐response trend, and distributional assumptions. Using simulations, we explore the effects of these factors on the resulting BMD and BMDL distributions. In addition, we illustrate our method with data from a neurotoxicity study of parathion exposure in rats.     

Upper Confidence Limits on Excess Risk for Quantitative Responses

The definition and observation of clear-cut adverse health effects for continuous (quantitative) responses, such as altered body weights or organ weights, are difficult propositions. Thus, methods of risk assessment commonly used for binary (quantal) toxic responses such as cancer are not directly applicable. In this paper, two methods for calculating upper confidence limits on excess risk for quantitative toxic effects are proposed, based on a particular definition of an adverse quantitative response. The methods are illustrated with data from a dose-response study, and their performance is evaluated with a Monte Carlo simulation study.     

Quantal Risk Assessment Database: A Database for Exploring Patterns in Quantal Dose‐Response Data in Risk Assessment and its Application to Develop Priors for Bayesian Dose‐Response Analysis

Quantitative risk assessments for physical, chemical, biological, occupational, or environmental agents rely on scientific studies to support their conclusions. These studies often include relatively few observations, and, as a result, models used to characterize the risk may include large amounts of uncertainty. The motivation, development, and assessment of new methods for risk assessment is facilitated by the availability of a set of experimental studies that span a range of dose‐response patterns that are observed in practice. We describe construction of such a historical database focusing on quantal data in chemical risk assessment, and we employ this database to develop priors in Bayesian analyses. The database is assembled from a variety of existing toxicological data sources and contains 733 separate quantal dose‐response data sets. As an illustration of the database's use, prior distributions for individual model parameters in Bayesian dose‐response analysis are constructed. Results indicate that including prior information based on curated historical data in quantitative risk assessments may help stabilize eventual point estimates, producing dose‐response functions that are more stable and precisely estimated. These in turn produce potency estimates that share the same benefit. We are confident that quantitative risk analysts will find many other applications and issues to explore using this database.     

Calculation of Benchmark Doses from Continuous Data

A benchmark dose (BMD) is the dose of a substance that corresponds to a prescribed increase in the response (called the benchmark response or BMR) of a health effect. A statistical lower bound on the benchmark dose (BMDL) has been proposed as a replacement for the no-observed-adverse-effect-level (NOAEL) in setting acceptable human exposure levels. A method is developed in this paper for calculating BMDs and BMDLs from continuous data in a manner that is consistent with those calculated from quantal data. The method involves defining an abnormal response, either directly by specifying a cutoff x₀ that separates continuous responses into normal and abnormal categories, or indirectly by specifying the proportion P₀ of abnormal responses expected among unexposed subjects. The method does not involve actually dichotomizing individual continuous responses into quantal responses, and in certain cases can be applied to continuous data in summarized form (e.g., means and standard deviations of continuous responses among subjects in discrete dose groups). In addition to specifying the BMR and either x₀ or P₀ , the method requires specification of the distribution of continuous responses, including specification of the dose-response θ(d) for a measure of central tendency. A method is illustrated for selecting θ(d) to make the probability of an abnormal response any desired dose-response function. This enables the same dose-response model (Weibull, log-logistic, etc.) to be used for the probability of an abnormal response, regardless of whether the underlying data are continuous or quantal. Whenever the continuous responses are normally distributed with standard deviation σ (independent of dose), the method is equivalent to defining the BMD as the dose corresponding to a prescribed change in the mean response relative to σ.     

Assessing Overall Risk in Reproductive Experiments

Toxicologists are often interested in assessing the joint effect of an exposure on multiple reproductive endpoints, including early loss, fetal death, and malformation. Exposures that occur prior to mating or extremely early in development can adversely affect the number of implantation sites or fetuses that form within each dam and may even prevent pregnancy. A simple approach for assessing overall adverse effects in such studies is to consider fetuses or implants that fail to develop due to exposure as missing data. The missing data can be imputed, and standard methods for the analysis of quantal response data can then be used for quantitative risk assessment or testing. In this article, a new bias-corrected imputation procedure is proposed and evaluated. The procedure is straightforward to implement in standard statistical packages and has excellent operating characteristics when used in combination with a marginal model fit with generalized estimating equations. The methods are applied to data from a reproductive toxicity study of Nitrofurazone conducted by the National Toxicology Program.     

Model Selection and Estimation with Quantal‐Response Data in Benchmark Risk Assessment

This article describes several approaches for estimating the benchmark dose (BMD) in a risk assessment study with quantal dose‐response data and when there are competing model classes for the dose‐response function. Strategies involving a two‐step approach, a model‐averaging approach, a focused‐inference approach, and a nonparametric approach based on a PAVA‐based estimator of the dose‐response function are described and compared. Attention is raised to the perils involved in data “double‐dipping” and the need to adjust for the model‐selection stage in the estimation procedure. Simulation results are presented comparing the performance of five model selectors and eight BMD estimators. An illustration using a real quantal‐response data set from a carcinogenecity study is provided.     

Model Uncertainty and Risk Estimation for Experimental Studies of Quantal Responses

Experimental animal studies often serve as the basis for predicting risk of adverse responses in humans exposed to occupational hazards. A statistical model is applied to exposure-response data and this fitted model may be used to obtain estimates of the exposure associated with a specified level of adverse response. Unfortunately, a number of different statistical models are candidates for fitting the data and may result in wide ranging estimates of risk. Bayesian model averaging (BMA) offers a strategy for addressing uncertainty in the selection of statistical models when generating risk estimates. This strategy is illustrated with two examples: applying the multistage model to cancer responses and a second example where different quantal models are fit to kidney lesion data. BMA provides excess risk estimates or benchmark dose estimates that reflects model uncertainty.     

Benchmark Dose Analysis via Nonparametric Regression Modeling

Estimation of benchmark doses (BMDs) in quantitative risk assessment traditionally is based upon parametric dose‐response modeling. It is a well‐known concern, however, that if the chosen parametric model is uncertain and/or misspecified, inaccurate and possibly unsafe low‐dose inferences can result. We describe a nonparametric approach for estimating BMDs with quantal‐response data based on an isotonic regression method, and also study use of corresponding, nonparametric, bootstrap‐based confidence limits for the BMD. We explore the confidence limits’ small‐sample properties via a simulation study, and illustrate the calculations with an example from cancer risk assessment. It is seen that this nonparametric approach can provide a useful alternative for BMD estimation when faced with the problem of parametric model uncertainty.     

Characterizing Dose-Response I: Critical Assessment of the Benchmark Dose Concept

We present a critical assessment of the benchmark dose (BMD) method introduced by Crump⁽¹⁾ as an alternative method for setting a characteristic dose level for toxicant risk assessment. The no-observed-adverse-effect-level (NOAEL) method has been criticized because it does not use all of the data and because the characteristic dose level obtained depends on the dose levels and the statistical precision (sample sizes) of the study design. Defining the BMD in terms of a confidence bound on a point estimate results in a characteristic dose that also varies with the statistical precision and still depends on the study dose levels.⁽²⁾ Indiscriminate choice of benchmark response level may result in a BMD that reflects little about the dose-response behavior available from using all of the data. Another concern is that the definition of the BMD for the quantal response case is different for the continuous response case. Specifically, defining the BMD for continuous data using a ratio of increased effect divided by the background response results in an arbitrary dependence on the natural background for the endpoint being studied, making comparison among endpoints less meaningful and standards more arbitrary. We define a modified benchmark dose as a point estimate using the ratio of increased effect divided by the full adverse response range which enables consistent placement of the benchmark response level and provides a BMD with a more consistent relationship to the dose-response curve shape.     

Hormesis: A Highly Generalizable and Reproducible Phenomenon With Important Implications for Risk Assessment

From a comprehensive search of the literature, the hormesis phenomenon was found to occur over a wide range of chemicals, taxonomic groups, and endpoints. By use of computer searches and extensive cross-referencing, nearly 3000 potentially relevant articles were identified. Evidence of chemical and radiation hormesis was judged to have occurred in approximately 1000 of these by use of a priori criteria. These criteria included study design features (e.g., number of doses, dose range), dose–response relationship, statistical analysis, and reproducibility of results. Numerous biological endpoints were assessed, with growth responses the most prevalent, followed by metabolic effects, reproductive responses, longevity, and cancer. Hormetic responses were generally observed to be of limited magnitude with an average maximum stimulation of 30 to 60 percent over that of the controls. This maximum usually occurred 4- to 5-fold below the NOAEL for a particular endpoint. The present analysis suggests that hormesis is a reproducible and generalizable biological phenomenon and is a fundamental component of many, if not most, dose–response relationships. The relatively infrequent observation of hormesis in the literature is believed to be due primarily to experimental design considerations, especially with respect to the number and range of doses and endpoint selection. Because of regulatory considerations, most toxicologic studies have been carried out at high doses above the low-dose region where the hormesis phenomenon occurs.     

Quantitative Risk Assessment for Developmental Neurotoxic Effects

Developmental neurotoxicity concerns the adverse health effects of exogenous agents acting on neurodevelopment. Because human brain development is a delicate process involving many cellular events, the developing fetus is rather susceptible to compounds that can alter the structure and function of the brain. Today, there is clear evidence that early exposure to many neurotoxicants can severely damage the developing nervous system. Although in recent years, there has been much attention given to model development and risk assessment procedures for developmental toxicants, the area of developmental neurotoxicity has been largely ignored. Here, we consider the problem of risk estimation for developmental neurotoxicants from animal bioassay data. Since most responses from developmental neurotoxicity experiments are nonquantal in nature, an adverse health effect will be defined as a response that occurs with very small probability in unexposed animals. Using a two-stage hierarchical normal dose-response model, upper confidence limits on the excess risk due to a given level of added exposure are derived. Equivalently, the model is used to obtain lower confidence limits on dose for a small negligible level of risk. Our method is based on the asymptotic distribution of the likelihood ratio statistic (cf. Crump, 1995). An example is used to provide further illustration.     

Cancer Risk Estimation of Genotoxic Chemicals Based on Target Dose and a Multiplicative Model

A mechanistic model and associated procedures are proposed for cancer risk assessment of genotoxic chemicals. As previously shown for ionizing radiation, a linear multiplicative model was found to be compatible with published experimental data for ethylene oxide, acrylamide, and butadiene. The validity of this model was anticipated in view of the multiplicative interaction of mutation with inherited and acquired growth-promoting conditions. Concurrent analysis led to rejection of an additive model (i.e. the model commonly applied for cancer risk assessment). A reanalysis of data for radiogenic cancer in mouse, dog and man shows that the relative risk coefficient is approximately the same (0.4 to 0.5 percent per rad) for tumours induced in the three species.Doses in vivo, defined as the time-integrated concentrations of ultimate mutagens, expressed in millimol × kg^–1 × h (mMh) are, like radiation doses given in Gy or rad, proportional to frequencies of potentially mutagenic events. The radiation dose equivalents of chemical doses are, calculated by multiplying chemical doses (in mMh) with the relative genotoxic potencies (in rad × mMh^–1) determined in vitro. In this way the relative cancer incidence increments in rats and mice exposed to ethylene oxide were shown to be about 0.4 percent per rad-equivalent, in agreement with the data for radiogenic cancer.Our analyses suggest that values of the relative risk coefficients for genotoxic chemicals are independent of species and that relative cancer risks determined in animal tests apply also to humans. If reliable animal test data are not available, cancer risks may be estimated by the relative potency. In both cases exposure dose/target dose relationships, the latter via macromolecule adducts, should be determined.     

Issues in Qualitative and Quantitative Risk Analysis for Developmental Toxicology1

The qualitative and quantitative evaluation of risk in developmental toxicology has been discussed in several recent publications.(^1–3) A number of issues still are to be resolved in this area. The qualitative evaluation and interpretation of end points in developmental toxicology depends on an understanding of the biological events leading to the end points observed, the relationships among end points, and their relationship to dose and to maternal toxicity. The interpretation of these end points is also affected by the statistical power of the experiments used for detecting the various end points observed. The quantitative risk assessment attempts to estimate human risk for developmental toxicity as a function of dose. The current approach is to apply safety (uncertainty) factors to die no observed effect level (NOEL). An alternative presented and discussed here is to model the experimental data and apply a safety factor to an estimated risk level to achieve an “acceptable” level of risk. In cases where the dose-response curves upward, this approach provides a conservative estimate of risk. This procedure does not preclude the existence of a threshold dose. More research is needed to develop appropriate dose-response models that can provide better estimates for low-dose extrapolation of developmental effects.     

Health Risk Assessment of a Modern Municipal Waste Incinerator

During the modernization of the municipal waste incinerator (MWI, maximum capacity of 180,000 tons per year) of Metropolitan Grenoble (405,000 inhabitants), in France, a risk assessment was conducted, based on four tracer pollutants: two volatile organic compounds (benzene and 1, 1, 1 trichloroethane) and two heavy metals (nickel and cadmium, measured in particles). A Gaussian plume dispersion model, applied to maximum emissions measured at the MWI stacks, was used to estimate the distribution of these pollutants in the atmosphere throughout the metropolitan area. A random sample telephone survey (570 subjects) gathered data on time-activity patterns, according to demographic characteristics of the population. Life-long exposure was assessed as a time-weighted average of ambient air concentrations. Inhalation alone was considered because, in the Grenoble urban setting, other routes of exposure are not likely. A Monte Carlo simulation was used to describe probability distributions of exposures and risks. The median of the life-long personal exposures distribution to MWI benzene was 3.2·10^–5 g/m³ (20th and 80th percentiles = 1.5·10^–5 and 6.5·10^–5 g/m³), yielding a 2.6·10^–10 carcinogenic risk (1.2·10^–10–5.4·10^–10). For nickel, the corresponding life-time exposure and cancer risk were 1.8·10^–4 g/m³ (0.9.10^–4 – 3.6·10^–4 g/m³) and 8.6·10^–8 (4.3·10^–8–17.3·10^–8); for cadmium they were respectively 8.3·10^–6 g/m³ (4.0·10^–6–17.6·10^–6) and 1.5·10^–8 (7.2·10^–9–3.1·10^–8). Inhalation exposure to cadmium emitted by the MWI represented less than 1% of the WHO Air Quality Guideline (5 ng/m³), while there was a margin of exposure of more than 10⁹ between the NOAEL (150 ppm) and exposure estimates to trichloroethane. Neither dioxins nor mercury, a volatile metal, were measured. This could lessen the attributable life-long risks estimated. The minute (VOCs and cadmium) to moderate (nickel) exposure and risk estimates are in accord with other studies on modern MWIs meeting recent emission regulations, however.     

Bayesian Quantile Impairment Threshold Benchmark Dose Estimation for Continuous Endpoints

Quantitative risk assessment often begins with an estimate of the exposure or dose associated with a particular risk level from which exposure levels posing low risk to populations can be extrapolated. For continuous exposures, this value, the benchmark dose, is often defined by a specified increase (or decrease) from the median or mean response at no exposure. This method of calculating the benchmark dose does not take into account the response distribution and, consequently, cannot be interpreted based upon probability statements of the target population. We investigate quantile regression as an alternative to the use of the median or mean regression. By defining the dose–response quantile relationship and an impairment threshold, we specify a benchmark dose as the dose associated with a specified probability that the population will have a response equal to or more extreme than the specified impairment threshold. In addition, in an effort to minimize model uncertainty, we use Bayesian monotonic semiparametric regression to define the exposure–response quantile relationship, which gives the model flexibility to estimate the quantal dose–response function. We describe this methodology and apply it to both epidemiology and toxicology data.     

Influence of Distribution of Animals between Dose Groups on Estimated Benchmark Dose and Animal Distress for Quantal Responses

Increasingly, dose‐response data are being evaluated with the benchmark dose (BMD) approach rather than by the less precise no‐observed‐adverse‐effect‐level (NOAEL) approach. However, the basis for designing animal experiments, using equally sized dose groups, is still primed for the NOAEL approach. The major objective here was to assess the impact of using dose groups of unequal size on both the quality of the BMD and overall animal distress. We examined study designs with a total number of 200 animals distributed in four dose groups employing quantal data generated by Monte Carlo simulations. Placing more animals at doses close to the targeted BMD provided an estimate of BMD that was slightly better than the standard design with equally sized dose groups. In situations involving a clear dose‐response, this translates into fewer animals receiving high doses and thus less overall animal distress. Accordingly, in connection with risk and safety assessment, animal distress can potentially be reduced by distributing the animals appropriately between dose groups without decreasing the quality of the information obtained.     

Reproductive and Developmental Risks from Ethylene Oxide: A Probabilistic Characterization of Possible Regulatory Thresholds

Ethylene oxide is a gas produced in large quantities in the United States that is used primarily as a chemical intermediate in the production of ethylene glycol, propylene glycol, non-ionic surfactants, ethanolamines, glycol ethers, and other chemicals. It has been well established that ethylene oxide can induce cancer, genetic, reproductive and developmental, and acute health effects in animals. The U.S. Environmental Protection Agency is currently developing both a cancer potency factor and a reference concentration (RfC) for ethylene oxide. This study used the rich database on the reproductive and developmental effects of ethylene oxide to develop a probabilistic characterization of possible regulatory thresholds for ethylene oxide. This analysis was based on the standard regulatory approach for noncancer risk assessment, but involved several innovative elements, such as: (1) the use of advanced statistical methods to account for correlations in developmental outcomes among littermates and allow for simultaneous control of covariates (such as litter size); (2) the application of a probabilistic approach for characterizing the uncertainty in extrapolating the animal results to humans; and (3) the use of a quantitative approach to account for the variation in heterogeneity among the human population. This article presents several classes of results, including: (1) probabilistic characterizations of ED10s for two quantal reproductive outcomes-resorption and fetal death, (2) probabilistic characterizations of one developmental outcome-the dose expected to yield a 5% reduction in fetal (or pup) weight, (3) estimates of the RfCs that would result from using these values in the standard regulatory approach for noncancer risk assessment, and (4) a probabilistic characterization of the level of ethylene oxide exposure that would be expected to yield a 1/1,000 increase in the risk of reproductive or developmental outcomes in exposed human populations.     

A Health Risk Benchmark for the Neurologic Effects of Styrene: Comparison with NOAEL/LOAEL Approach

Benchmark dose (BMD) analysis was used to estimate an inhalation benchmark concentration for styrene neurotoxicity. Quantal data on neuropsychologic test results from styrene-exposed workers [Mutti et al. (1984). American Journal of Industrial Medicine, 5, 275-286] were used to quantify neurotoxicity, defined as the percent of tested workers who responded abnormally to > or = 1, > or = 2, or > or = 3 out of a battery of eight tests. Exposure was based on previously published results on mean urinary mandelic- and phenylglyoxylic acid levels in the workers, converted to air styrene levels (15, 44, 74, or 115 ppm). Nonstyrene-exposed workers from the same region served as a control group. Maximum-likelihood estimates (MLEs) and BMDs at 5 and 10% response levels of the exposed population were obtained from log-normal analysis of the quantal data. The highest MLE was 9 ppm (BMD = 4 ppm) styrene and represents abnormal responses to > or = 3 tests by 10% of the exposed population. The most health-protective MLE was 2 ppm styrene (BMD = 0.3 ppm) and represents abnormal responses to > or = 1 test by 5% of the exposed population. A no observed adverse effect level/lowest observed adverse effect level (NOAEL/LOAEL) analysis of the same quantal data showed workers in all styrene exposure groups responded abnormally to > or = 1, > or = 2, or > or = 3 tests, compared to controls, and the LOAEL was 15 ppm. A comparison of the BMD and NOAEL/LOAEL analyses suggests that at air styrene levels below the LOAEL, a segment of the worker population may be adversely affected. The benchmark approach will be useful for styrene noncancer risk assessment purposes by providing a more accurate estimate of potential risk that should, in turn, help to reduce the uncertainty that is a common problem in setting exposure levels.