Benchmark Dose Risk Assessment for Formaldehyde Using Airflow Modeling and a Single-Compartment, DNA-Protein Cross-Link Dosimetry Model to Estimate Human Equivalent Doses

Formaldehyde induced squamous-cell carcinomas in the nasal passages of F344 rats in two inhalation bioassays at exposure levels of 6 ppm and above. Increases in rates of cell proliferation were measured by T. M. Monticello and colleagues at exposure levels of 0.7 ppm and above in the same tissues from which tumors arose. A risk assessment for formaldehyde was conducted at the CIIT Centers for Health Research, in collaboration with investigators from Toxicological Excellence in Risk Assessment (TERA) and the U.S. Environmental Protection Agency (U.S. EPA) in 1999. Two methods for dose-response assessment were used: a full biologically based modeling approach and a statistically oriented analysis by benchmark dose (BMD) method. This article presents the later approach, the purpose of which is to combine BMD and pharmacokinetic modeling to estimate human cancer risks from formaldehyde exposure. BMD analysis was used to identify points of departure (exposure levels) for low-dose extrapolation in rats for both tumor and the cell proliferation endpoints. The benchmark concentrations for induced cell proliferation were lower than for tumors. These concentrations were extrapolated to humans using two mechanistic models. One model used computational fluid dynamics (CFD) alone to determine rates of delivery of inhaled formaldehyde to the nasal lining. The second model combined the CFD method with a pharmacokinetic model to predict tissue dose with formaldehyde-induced DNA-protein cross-links (DPX) as a dose metric. Both extrapolation methods gave similar results, and the predicted cancer risk in humans at low exposure levels was found to be similar to that from a risk assessment conducted by the U.S. EPA in 1991. Use of the mechanistically based extrapolation models lends greater certainty to these risk estimates than previous approaches and also identifies the uncertainty in the measured dose-response relationship for cell proliferation at low exposure levels, the dose-response relationship for DPX in monkeys, and the choice between linear and nonlinear methods of extrapolation as key remaining sources of uncertainty.     

A dose-response analysis of skin cancer from inorganic arsenic in drinking water

A study of the prevalence of skin cancer among 40,421 persons consuming arsenic-contaminated drinking water in Taiwan was used for a cancer dose-response assessment of ingested arsenic. The numbers of persons at risk over three dose intervals and four exposure durations were estimated from the data in order to apply the method of maximum likelihood to a multistage-Weibull time/dose-response model. A constant exposure level since birth for each of the exposure categories was assumed. It was found that the cumulative hazard increases as a power of three in age, and is linear or quadratic (with a linear coefficient) in dose. Observations from a smaller epidemiologic survey in Mexico were similar to what would be predicted from the model of the Taiwan data. Assuming that the skin cancer risk from ingested arsenic in the American population would also be similar to the Taiwan population, an American male would have a lifetime risk of developing skin cancer of 1.3 x 10(-3) (3.0 x 10(-3] if exposed to 1 microgram/kg/day for a 76-year lifespan (median lifespan in the U.S.).     

The Beta Poisson Dose-Response Model Is Not a Single-Hit Model

The choice of a dose-response model is decisive for the outcome of quantitative risk assessment. Single-hit models have played a prominent role in dose-response assessment for pathogenic microorganisms, since their introduction. Hit theory models are based on a few simple concepts that are attractive for their clarity and plausibility. These models, in particular the Beta Poisson model, are used for extrapolation of experimental dose-response data to low doses, as are often present in drinking water or food products. Unfortunately, the Beta Poisson model, as it is used throughout the microbial risk literature, is an approximation whose validity is not widely known. The exact functional relation is numerically complex, especially for use in optimization or uncertainty analysis. Here it is shown that although the discrepancy between the Beta Poisson formula and the exact function is not very large for many data sets, the differences are greatest at low doses--the region of interest for many risk applications. Errors may become very large, however, in the results of uncertainty analysis, or when the data contain little low-dose information. One striking property of the exact single-hit model is that it has a maximum risk curve, limiting the upper confidence level of the dose-response relation. This is due to the fact that the risk cannot exceed the probability of exposure, a property that is not retained in the Beta Poisson approximation. This maximum possible response curve is important for uncertainty analysis, and for risk assessment of pathogens with unknown properties.     

Hexavalent Chromium and Lung Cancer in the Chromate Industry: A Quantitative Risk Assessment

The purpose of this investigation was to estimate excess lifetime risk of lung cancer death resulting from occupational exposure to hexavalent-chromium-containing dusts and mists. The mortality experience in a previously studied cohort of 2,357 chromate chemical production workers with 122 lung cancer deaths was analyzed with Poisson regression methods. Extensive records of air samples evaluated for water-soluble total hexavalent chromium were available for the entire employment history of this cohort. Six different models of exposure-response for hexavalent chromium were evaluated by comparing deviances and inspection of cubic splines. Smoking (pack-years) imputed from cigarette use at hire was included in the model. Lifetime risks of lung cancer death from exposure to hexavalent chromium (assuming up to 45 years of exposure) were estimated using an actuarial calculation that accounts for competing causes of death. A linear relative rate model gave a good and readily interpretable fit to the data. The estimated rate ratio for 1 mg/m3-yr of cumulative exposure to hexavalent chromium (as CrO3), with a lag of five years, was RR=2.44 (95% CI=1.54-3.83). The excess lifetime risk of lung cancer death from exposure to hexavalent chromium at the current OSHA permissible exposure limit (PEL) (0.10 mg/m3) was estimated to be 255 per 1,000 (95% CI: 109-416). This estimate is comparable to previous estimates by U.S. EPA, California EPA, and OSHA using different occupational data. Our analysis predicts that current occupational standards for hexavalent chromium permit a lifetime excess risk of dying of lung cancer that exceeds 1 in 10, which is consistent with previous risk assessments.     

Improving cancer dose-response characterization by using physiologically based pharmacokinetic modeling: an analysis of pooled data for acrylonitrile-induced brain tumors to assess cancer potency in the rat.

Historically, U.S. regulators have derived cancer slope factors by using applied dose and tumor response data from a single key bioassay or by averaging the cancer slope factors of several key bioassays. Recent changes in U.S. Environmental Protection Agency (EPA) guidelines for cancer risk assessment have acknowledged the value of better use of mechanistic data and better dose-response characterization. However, agency guidelines may benefit from additional considerations presented in this paper. An exploratory study was conducted by using rat brain tumor data for acrylonitrile (AN) to investigate the use of physiologically based pharmacokinetic (PBPK) modeling along with pooling of dose-response data across routes of exposure as a means for improving carcinogen risk assessment methods. In this study, two contrasting assessments were conducted for AN-induced brain tumors in the rat on the basis of (1) the EPA's approach, the dose-response relationship was characterized by using administered dose/concentration for each of the key studies assessed individually; and (2) an analysis of the pooled data, the dose-response relationship was characterized by using PBPK-derived internal dose measures for a combined database of ten bioassays. The cancer potencies predicted for AN by the contrasting assessments are remarkably different (i.e., risk-specific doses differ by as much as two to four orders of magnitude), with the pooled data assessments yielding lower values. This result suggests that current carcinogen risk assessment practices overestimate AN cancer potency. This methodology should be equally applicable to other data-rich chemicals in identifying (1) a useful dose measure, (2) an appropriate dose-response model, (3) an acceptable point of departure, and (4) an appropriate method of extrapolation from the range of observation to the range of prediction when a chemical's mode of action remains uncertain.     

Use of Monte Carlo Simulation for Human Exposure Assessment at a Superfund Site

This work presents a comparison of probabilistic and deterministic health risk estimates based on data from an industrial site in the northeastern United States. The risk assessment considered exposures to volatile solvents by drinking water ingestion and showering. Probability densities used as inputs included concentrations, contact rates, and exposure frequencies; dose-response inputs were single values. Deterministic risk estimates were calculated by the "reasonable maximum exposure" (RME) approach recommended by the EPA Superfund program. The RME non-carcinogenic risk fell between the 90th and the 95th percentile of the probability density; the RME cancer risk fell between the 95th percentile and the maximum. These results suggest that in this case (1) EPA's deterministic RME risk was reasonably protective, (2) results of probabilistic and deterministic calculations were consistent, and (3) commercially available software Monte Carlo software effectively provided multiple risk estimates recommended by recent EPA guidance.     

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.     

Evaluating the Potential for a Helicobacter pylori Drinking Water Guideline

Helicobacter pylori is a microaerophilic, gram‐negative bacterium that is linked to adverse health effects including ulcers and gastrointestinal cancers. The goal of this analysis is to develop the necessary inputs for a quantitative microbial risk assessment (QMRA) needed to develop a potential guideline for drinking water at the point of ingestion (e.g., a maximum contaminant level, or MCL) that would be protective of human health to an acceptable level of risk while considering sources of uncertainty. Using infection and gastric cancer as two discrete endpoints, and calculating dose‐response relationships from experimental data on humans and monkeys, we perform both a forward and reverse risk assessment to determine the risk from current reported surface water concentrations of H. pylori and an acceptable concentration of H. pylori at the point of ingestion. This approach represents a synthesis of available information on human exposure to H. pylori via drinking water. A lifetime risk of cancer model suggests that a MCL be set at <1 organism/L given a 5‐log removal treatment because we cannot exclude the possibility that current levels of H. pylori in environmental source waters pose a potential public health risk. Research gaps include pathogen occurrence in source and finished water, treatment removal rates, and determination of H. pylori risks from other water sources such as groundwater and recreational water.     

A Quantitative Estimate of Leukemia Mortality Associated with Occupational Exposure to Benzene3

In 1980, the U.S. Supreme Court vacated a revised occupational standard for benzene, stating that the Occupational Safety and Health Administration (OSHA) had failed to demonstrate that significant health risks existed under the current standard. This decision has been interpreted by OSHA as requiring the consideration of quantitative risk assessments, whenever possible, in the development of regulations for occupational carcinogens. In light of this decision, the available epidemiologic evidence was used to generate a quantitative risk assessment for benzene. Uncertainties regarding the levels and lengths of benzene exposure for the studied cohorts were incorporated into the analysis. Based on the one-hit model, the assessment indicates that a working lifetime exposure to benzene at the current permissible exposure level (10 ppm) poses a substantial excess risk of death from leukemia. This report discusses the calculation of the risk estimates, the basis for relying on certain assumptions, and the inherent limitations of using epidemiologic studies to quantify cancer risks.     

What to Do at Low Doses: A Bounding Approach for Economic Analysis

To quantify the health benefits of environmental policies, economists generally require estimates of the reduced probability of illness or death. For policies that reduce exposure to carcinogenic substances, these estimates traditionally have been obtained through the linear extrapolation of experimental dose-response data to low-exposure scenarios as described in the U.S. Environmental Protection Agency's Guidelines for Carcinogen Risk Assessment (1986). In response to evolving scientific knowledge, EPA proposed revisions to the guidelines in 1996. Under the proposed revisions, dose-response relationships would not be estimated for carcinogens thought to exhibit nonlinear modes of action. Such a change in cancer-risk assessment methods and outputs will likely have serious consequences for how benefit-cost analyses of policies aimed at reducing cancer risks are conducted. Any tendency for reduced quantification of effects in environmental risk assessments, such as those contemplated in the revisions to EPA's cancer-risk assessment guidelines, impedes the ability of economic analysts to respond to increasing calls for benefit-cost analysis. This article examines the implications for benefit-cost analysis of carcinogenic exposures of the proposed changes to the 1986 Guidelines and proposes an approach for bounding dose-response relationships when no biologically based models are available. In spite of the more limited quantitative information provided in a carcinogen risk assessment under the proposed revisions to the guidelines, we argue that reasonable bounds on dose-response relationships can be estimated for low-level exposures to nonlinear carcinogens. This approach yields estimates of reduced illness for use in a benefit-cost analysis while incorporating evidence of nonlinearities in the dose-response relationship. As an illustration, the bounding approach is applied to the case of chloroform exposure.     

Assessing Cancer Risks from Short-Term Exposures in Children

For the vast majority of chemicals that have cancer potency estimates on IRIS, the underlying database is deficient with respect to early-life exposures. This data gap has prevented derivation of cancer potency factors that are relevant to this time period, and so assessments may not fully address children's risks. This article provides a review of juvenile animal bioassay data in comparison to adult animal data for a broad array of carcinogens. This comparison indicates that short-term exposures in early life are likely to yield a greater tumor response than short-term exposures in adults, but similar tumor response when compared to long-term exposures in adults. This evidence is brought into a risk assessment context by proposing an approach that: (1) does not prorate children's exposures over the entire life span or mix them with exposures that occur at other ages; (2) applies the cancer slope factor from adult animal or human epidemiology studies to the children's exposure dose to calculate the cancer risk associated with the early-life period; and (3) adds the cancer risk for young children to that for older children/adults to yield a total lifetime cancer risk. The proposed approach allows for the unique exposure and pharmacokinetic factors associated with young children to be fully weighted in the cancer risk assessment. It is very similar to the approach currently used by U.S. EPA for vinyl chloride. The current analysis finds that the database of early life and adult cancer bioassays supports extension of this approach from vinyl chloride to other carcinogens of diverse mode of action. This approach should be enhanced by early-life data specific to the particular carcinogen under analysis whenever possible.     

Methods and Rationale for Derivation of a Reference Dose for Methylmercury by the U.S. EPA

In 2001, the U.S. Environmental Protection Agency derived a reference dose (RfD) for methylmercury, which is a daily intake that is likely to be without appreciable risk of deleterious effects during a lifetime. This derivation used a series of benchmark dose (BMD) analyses provided by a National Research Council (NRC) panel convened to assess the health effects of methylmercury. Analyses were performed for a number of endpoints from three large longitudinal cohort studies of the neuropsychological consequences of in utero exposure to methylmercury: the Faroe Islands, Seychelles Islands, and New Zealand studies. Adverse effects were identified in the Faroe Islands and New Zealand studies, but not in the Seychelles Islands. The NRC also performed an integrative analysis of all three studies. The EPA applied a total uncertainty factor (UF) of 10 for intrahuman toxicokinetic and toxicodynamic variability and uncertainty. Dose conversion from cord blood mercury concentrations to maternal methylmercury intake was performed using a one-compartment model. Derivation of potential RfDs from a number of endpoints from the Faroe Islands study converged on 0.1 microg/kg/day, as did the integrative analysis of all three studies. EPA identified several areas for which further information or analyses is needed. Perhaps the most immediately relevant is the ratio of cord:maternal blood mercury concentration, as well as the variability around this ratio. EPA assumed in its dose conversion that the ratio was 1.0; however, available data suggest it is perhaps 1.5-2.0. Verification of a deviation from unity presumably would be translated directly into comparable reduction in the RfD. Other areas that EPA identified as significant areas requiring further attention are cardiovascular consequences of methylmercury exposure and delayed neurotoxicity during aging as a result of previous developmental or adult exposure.     

Ethylene Oxide Cancer Risk Assessment Based on Epidemiological Data: Application of Revised Regulatory Guidelines

Ethylene oxide (EO) research has significantly increased since the 1980s, when regulatory risk assessments were last completed on the basis of the animal cancer chronic bioassays. In tandem with the new scientific understanding, there have been evolutionary changes in regulatory risk assessment guidelines, that encourage flexibility and greater use of scientific information. The results of an updated meta-analysis of the findings from 10 unique EO study cohorts from five countries, including nearly 33,000 workers, and over 800 cancers are presented, indicating that EO does not cause increased risk of cancers overall or of brain, stomach or pancreatic cancers. The findings for leukemia and non-Hodgkin's lymphoma (NHL) are inconclusive. Two studies with the requisite attributes of size, individual exposure estimates and follow up are the basis for dose-response modeling and added lifetime risk predictions under environmental and occupational exposure scenarios and a variety of plausible alternative assumptions. A point of departure analysis, with various margins of exposure, is also illustrated using human data. The two datasets produce remarkably similar leukemia added risk predictions, orders of magnitude lower than prior animal-based predictions under conservative, default assumptions, with risks on the order of 1 × 10^–6 or lower for exposures in the low ppb range. Inconsistent results for lymphoid tumors, a non-standard grouping using histologic information from death certificates, are discussed. This assessment demonstrates the applicability of the current risk assessment paradigm to epidemiological data.     

Dose-Response and Risk Assessment of Airborne Hexavalent Chromium and Lung Cancer Mortality

This study evaluates the dose-response relationship for inhalation exposure to hexavalent chromium [Cr(VI)] and lung cancer mortality for workers of a chromate production facility, and provides estimates of the carcinogenic potency. The data were analyzed using relative risk and additive risk dose-response models implemented with both Poisson and Cox regression. Potential confounding by birth cohort and smoking prevalence were also assessed. Lifetime cumulative exposure and highest monthly exposure were the dose metrics evaluated. The estimated lifetime additional risk of lung cancer mortality associated with 45 years of occupational exposure to 1 microg/m3 Cr(VI) (occupational exposure unit risk) was 0.00205 (90%CI: 0.00134, 0.00291) for the relative risk model and 0.00216 (90%CI: 0.00143, 0.00302) for the additive risk model assuming a linear dose response for cumulative exposure with a five-year lag. Extrapolating these findings to a continuous (e.g., environmental) exposure scenario yielded an environmental unit risk of 0.00978 (90%CI: 0.00640, 0.0138) for the relative risk model [e.g., a cancer slope factor of 34 (mg/kg-day)-1] and 0.0125 (90%CI: 0.00833, 0.0175) for the additive risk model. The relative risk model is preferred because it is more consistent with the expected trend for lung cancer risk with age. Based on statistical tests for exposure-related trend, there was no statistically significant increased lung cancer risk below lifetime cumulative occupational exposures of 1.0 mg-yr/m3, and no excess risk for workers whose highest average monthly exposure did not exceed the current Permissible Exposure Limit (52 microg/m3). It is acknowledged that this study had limited power to detect increases at these low exposure levels. These cancer potency estimates are comparable to those developed by U.S. regulatory agencies and should be useful for assessing the potential cancer hazard associated with inhaled Cr(VI).     

Development of a Unit Risk Factor for 1,3-Butadiene Based on an Updated Carcinogenic Toxicity Assessment

The Texas Commission on Environmental Quality (TCEQ) has developed an inhalation unit risk factor (URF) for 1,3-butadiene based on leukemia mortality in an updated epidemiological study on styrene-butadiene rubber production workers conducted by researchers at the University of Alabama at Birmingham. Exposure estimates were updated and an exposure estimate validation study as well as dose-response modeling were conducted by these researchers. This information was not available to the U.S. Environmental Protection Agency when it prepared its health assessment of 1,3-butadiene in 2002. An extensive analysis conducted by TCEQ discusses dose-response modeling, estimating risk for the general population from occupational workers, estimating risk for potentially sensitive subpopulations, effect of occupational exposure estimation error, and use of mortality rates to predict incidence. The URF is 5.0 × 10⁻⁷ per μg/m³ or 1.1 × 10⁻⁶ per ppb and is based on a Cox regression dose-response model using restricted continuous data with age as a covariate, and a linear low-dose extrapolation default approach using the 95% lower confidence limit as the point of departure. Age-dependent adjustment factors were applied to account for possible increased susceptibility for early life exposure. The air concentration at 1 in 100,000 excess leukemia mortality, the no-significant-risk level, is 20 μg/m³ (9.1 ppb), which is slightly lower than the TCEQ chronic reference value of 33 μg/m³ (15 ppb) protective of ovarian atrophy. These values will be used to evaluate ambient air monitoring data so the general public is protected against adverse health effects from chronic exposure to 1,3-butadiene.     

Significance of Exposure Assessment to Analysis of Cancer Risk from Inorganic Arsenic in Drinking Water in Taiwan

The primary source of evidence that inorganic arsenic in drinking water is associated with increased mortality from cancer at internal sites (bladder, liver, lung, and other organs) is a large ecologic study conducted in regions of Southwest Taiwan endemic to Blackfoot disease. The dose-response patterns for lung, liver, and bladder cancers display a nonlinear dose-response relationship with arsenic exposure. The data do not appear suitable, however, for the more refined task of dose-response assessment, particularly for inference of risk at the low arsenic concentrations found in some U.S. water supplies. The problem lies in variable arsenic concentrations between the wells within a village, largely due to a mix of shallow wells and deep artesian wells, and in having only one well test for 24 (40%) of the 60 villages. The current analysis identifies 14 villages where the exposure appears most questionable, based on criteria described in the text. The exposure values were then changed for seven of the villages, from the median well test being used as a default to some other point in the village's range of well tests that would contribute to smoothing the appearance of a dose-response curve. The remaining seven villages, six of which had only one well test, were deleted as outliers. The resultant dose-response patterns showed no evidence of excess risk below arsenic concentrations of 0.1 mg/l. Of course, that outcome is dependent on manipulation of the data, as described. Inclusion of the seven deleted villages would make estimates of risk much higher at low doses. In those seven villages, the cancer mortality rates are significantly high for their exposure levels, suggesting that their exposure values may be too low or that other etiological factors need to be taken into account.     

A Trichloroethylene Risk Assessment Using a Monte Carlo Analysis of Parameter Uncertainty in Conjunction with Physiologically-Based Pharmacokinetic Modeling

A Monte Carlo simulation is incorporated into a risk assessment for trichloroethylene (TCE) using physiologically-based pharmacokinetic (PBPK) modeling coupled with the linearized multistage model to derive human carcinogenic risk extrapolations. The Monte Carlo technique incorporates physiological parameter variability to produce a statistically derived range of risk estimates which quantifies specific uncertainties associated with PBPK risk assessment approaches. Both inhalation and ingestion exposure routes are addressed. Simulated exposure scenarios were consistent with those used by the Environmental Protection Agency (EPA) in their TCE risk assessment. Mean values of physiological parameters were gathered from the literature for both mice (carcinogenic bioassay subjects) and for humans. Realistic physiological value distributions were assumed using existing data on variability. Mouse cancer bioassay data were correlated to total TCE metabolized and area-under-the-curve (blood concentration) trichloroacetic acid (TCA) as determined by a mouse PBPK model. These internal dose metrics were used in a linearized multistage model analysis to determine dose metric values corresponding to 10^-6 lifetime excess cancer risk. Using a human PBPK model, these metabolized doses were then extrapolated to equivalent human exposures (inhalation and ingestion). The Monte Carlo iterations with varying mouse and human physiological parameters produced a range of human exposure concentrations producing a 10^-6 risk.     

Does EPA Underestimate Cancer Risks by Ignoring Susceptibility Differences?

A 2009 report of the National Research Council (NRC) recommended that the U.S. Environmental Protection Agency (EPA) increase its estimates of increased cancer risk from exposure to environmental agents by ～7‐fold, due to an approximate ～25‐fold typical ratio between the median and upper 95th percentile persons’ cancer sensitivity assuming approximately lognormally distributed sensitivities. EPA inaction on this issue has raised concerns that cancer risks to environmentally exposed populations remain systematically underestimated. This concern is unwarranted, however, because EPA point estimates of cancer risk have always pertained to the average, not the median, person in each modeled exposure group. Nevertheless, EPA has yet to explain clearly how its risk characterization and risk management policies concerning individual risks from environmental chemical carcinogens do appropriately address broad variability in human cancer susceptibility that has been a focus of two major NRC reports to EPA concerning its risk assessment methods.     

Bootstrap Estimation of Benchmark Doses and Confidence Limits with Clustered Quantal Data

The benchmark dose (BMD) is an exposure level that would induce a small risk increase (BMR level) above the background. The BMD approach to deriving a reference dose for risk assessment of noncancer effects is advantageous in that the estimate of BMD is not restricted to experimental doses and utilizes most available dose-response information. To quantify statistical uncertainty of a BMD estimate, we often calculate and report its lower confidence limit (i.e., BMDL), and may even consider it as a more conservative alternative to BMD itself. Computation of BMDL may involve normal confidence limits to BMD in conjunction with the delta method. Therefore, factors, such as small sample size and nonlinearity in model parameters, can affect the performance of the delta method BMDL, and alternative methods are useful. In this article, we propose a bootstrap method to estimate BMDL utilizing a scheme that consists of a resampling of residuals after model fitting and a one-step formula for parameter estimation. We illustrate the method with clustered binary data from developmental toxicity experiments. Our analysis shows that with moderately elevated dose-response data, the distribution of BMD estimator tends to be left-skewed and bootstrap BMDL s are smaller than the delta method BMDL s on average, hence quantifying risk more conservatively. Statistically, the bootstrap BMDL quantifies the uncertainty of the true BMD more honestly than the delta method BMDL as its coverage probability is closer to the nominal level than that of delta method BMDL. We find that BMD and BMDL estimates are generally insensitive to model choices provided that the models fit the data comparably well near the region of BMD. Our analysis also suggests that, in the presence of a significant and moderately strong dose-response relationship, the developmental toxicity experiments under the standard protocol support dose-response assessment at 5% BMR for BMD and 95% confidence level for BMDL.     

Exploring the Uncertainties in Cancer Risk Assessment Using the Integrated Probabilistic Risk Assessment (IPRA) Approach

Current methods for cancer risk assessment result in single values, without any quantitative information on the uncertainties in these values. Therefore, single risk values could easily be overinterpreted. In this study, we discuss a full probabilistic cancer risk assessment approach in which all the generally recognized uncertainties in both exposure and hazard assessment are quantitatively characterized and probabilistically evaluated, resulting in a confidence interval for the final risk estimate. The methodology is applied to three example chemicals (aflatoxin, N‐nitrosodimethylamine, and methyleugenol). These examples illustrate that the uncertainty in a cancer risk estimate may be huge, making single value estimates of cancer risk meaningless. Further, a risk based on linear extrapolation tends to be lower than the upper 95% confidence limit of a probabilistic risk estimate, and in that sense it is not conservative. Our conceptual analysis showed that there are two possible basic approaches for cancer risk assessment, depending on the interpretation of the dose‐incidence data measured in animals. However, it remains unclear which of the two interpretations is the more adequate one, adding an additional uncertainty to the already huge confidence intervals for cancer risk estimates.