Dose‐Response Modeling for Inhalational Anthrax in Rabbits Following Single or Multiple Exposures

There is a need to advance our ability to characterize the risk of inhalational anthrax following a low‐dose exposure. The exposure scenario most often considered is a single exposure that occurs during an attack. However, long‐term daily low‐dose exposures also represent a realistic exposure scenario, such as what may be encountered by people occupying areas for longer periods. Given this, the objective of the current work was to model two rabbit inhalational anthrax dose‐response data sets. One data set was from single exposures to aerosolized Bacillus anthracis Ames spores. The second data set exposed rabbits repeatedly to aerosols of B. anthracis Ames spores. For the multiple exposure data the cumulative dose (i.e., the sum of the individual daily doses) was used for the model. Lethality was the response for both. Modeling was performed using Benchmark Dose Software evaluating six models: logprobit, loglogistic, Weibull, exponential, gamma, and dichotomous‐Hill. All models produced acceptable fits to either data set. The exponential model was identified as the best fitting model for both data sets. Statistical tests suggested there was no significant difference between the single exposure exponential model results and the multiple exposure exponential model results, which suggests the risk of disease is similar between the two data sets. The dose expected to cause 10% lethality was 15,600 inhaled spores and 18,200 inhaled spores for the single exposure and multiple exposure exponential dose‐response model, respectively, and the 95% lower confidence intervals were 9,800 inhaled spores and 9,200 inhaled spores, respectively.     

Use of Mechanistic Models to Estimate Low-Dose Cancer Risks

The utility of mechanistic models of cancer for predicting cancer risks at low doses is examined. Based upon a general approximation to the dose-response that is valid at low doses, it is shown that at low doses the dose-response predicted by a mechanistic model is a linear combination of the dose-responses for each of the physiological parameters in the model that are affected by exposure. This demonstrates that, unless the mechanistic model provides a theoretical basis for determining the dose-responses for these parameters, the extrapolation of risks to low doses using a mechanistic model is basically "curve fitting," just as is the case when extrapolating using statistical models. This suggests that experiments to generate data for use in mechanistic models should emphasize measuring the dose-response for dose-related parameters as accurately as possible and at the lowest feasible doses.     

Modeling Rabbit Responses to Single and Multiple Aerosol Exposures of Bacillus anthracis Spores

Survival models are developed to predict response and time‐to‐response for mortality in rabbits following exposures to single or multiple aerosol doses of Bacillus anthracis spores. Hazard function models were developed for a multiple‐dose data set to predict the probability of death through specifying functions of dose response and the time between exposure and the time‐to‐death (TTD). Among the models developed, the best‐fitting survival model (baseline model) is an exponential dose–response model with a Weibull TTD distribution. Alternative models assessed use different underlying dose–response functions and use the assumption that, in a multiple‐dose scenario, earlier doses affect the hazard functions of each subsequent dose. In addition, published mechanistic models are analyzed and compared with models developed in this article. None of the alternative models that were assessed provided a statistically significant improvement in fit over the baseline model. The general approach utilizes simple empirical data analysis to develop parsimonious models with limited reliance on mechanistic assumptions. The baseline model predicts TTDs consistent with reported results from three independent high‐dose rabbit data sets. More accurate survival models depend upon future development of dose–response data sets specifically designed to assess potential multiple‐dose effects on response and time‐to‐response. The process used in this article to develop the best‐fitting survival model for exposure of rabbits to multiple aerosol doses of B. anthracis spores should have broad applicability to other host–pathogen systems and dosing schedules because the empirical modeling approach is based upon pathogen‐specific empirically‐derived parameters.     

One-Hit Models of Carcinogenesis: Conservative or Not?

One-hit formulas are widely believed to be "conservative" when used to analyze carcinogenesis bioassays, in the sense that they will rarely underestimate risks of cancer at low exposures. Such formulas are generally applied to the lifetime incidence of cancer at a specific site, with risks estimated from animal data at zero dose (control), and two or more additional doses that are appreciable fractions of a maximum tolerated dose. No empirical study has demonstrated that the one-hit formula is conservative in the sense described. The Carcinogenesis Bioassay Database System contains data on 1212 separate bioassays of 308 chemical substances tested at exactly three evaluable doses. These provided sufficient data to examine 8432 specific combinations of cancer site with sex, species, and chemical. For each of these we fitted a one-hit formula to the zero and maximum dose data points, then examined the relation of the fitted curve to the incidence rate observed at the mid-dose, with and without adjustment for intercurrent mortality. Both underestimates and overestimates of risk at mid-dose occurred substantially more often than expected by chance. We cannot tell whether such underestimates would occur at lower doses, but offer six biological reasons why underestimates might be expected. In a high percentage of animal bioassays, the one-hit formula is not conservative when applied in the usual way to animal data. It remains possible that the one-hit formula may indeed be conservative at sufficiently low doses (below the observational range), but the usual procedure, applied to the usual dose range, can be nonconservative in estimating the slope of the formula at such low doses. Risk assessments for regulation of carcinogens should incorporate some measure of additional uncertainty.     

A Distributional Approach to Characterizing Low-Dose Cancer Risk

Since cancer risk at very low doses cannot be directly measured in humans or animals, mathematical extrapolation models and scientific judgment are required. This article demonstrates a probabilistic approach to carcinogen risk assessment that employs probability trees, subjective probabilities, and standard bootstrapping procedures. The probabilistic approach is applied to the carcinogenic risk of formaldehyde in environmental and occupational settings. Sensitivity analyses illustrate conditional estimates of risk for each path in the probability tree. Fundamental mechanistic uncertainties are characterized. A strength of the analysis is the explicit treatment of alternative beliefs about pharmacokinetics and pharmacodynamics. The resulting probability distributions on cancer risk are compared with the point estimates reported by federal agencies. Limitations of the approach are discussed as well as future research directions.     

The Fallacy of Ranking Possible Carcinogen Hazards Using the TD50

Ames et al. have proposed a new model for evaluating carcinogenic hazards in the environment. They advocate ranking possible carcinogens on the basis of the TD50, the estimated dose at which 50% of the test animals would get tumors, and extrapolating that ranking to all other doses. We argue that implicit in this methodology is a simplistic and inappropriate statistical model. All carcinogens are assumed to act similarly and to have dose-response curves of the same shape that differ only in the value of one parameter. We show by counterexample that the rank order of cancer potencies for two chemicals can change over a reasonable range of doses. Ames et al.'s use of these TD50 ranks to compare the hazards from low level exposures to contaminants in our food and environment is wholly inappropriate and inaccurate. Their dismissal of public health concern for environmental exposures, in general, based on these comparisons, is not supported by the data.     

Extrapolation of Carcinogenicity Between Species: Qualitative and Quantitative Factors

Prediction of human cancer risk from the results of rodent bioassays requires two types of extrapolation: a qualitative extrapolation from short-lived rodent species to long-lived humans, and a quantitative extrapolation from near-toxic doses in the bioassay to low-level human exposures. Experimental evidence on the accuracy of prediction between closely related species tested under similar experimental conditions (rats, mice, and hamsters) indicates that: (1) if a chemical is positive in one species, it will be positive in the second species about 75% of the time; however, since about 50% of test chemicals are positive in each species, by chance alone one would expect a predictive value between species of about 50%. (2) If a chemical induces tumors in a particular target organ in one species, it will induce tumors in the same organ in the second species about 50% of the time. Similar predictive values are obtained in an analysis of prediction from humans to rats or from humans to mice for known human carcinogens. Limitations of bioassay data for use in quantitative extrapolation are discussed, including constraints on both estimates of carcinogenic potency and of the dose-response in experiments with only two doses and a control. Quantitative extrapolation should be based on an understanding of mechanisms of carcinogenesis, particularly mitogenic effects that are present at high and not low doses.     

Methodology for Determining the Appropriateness of a Linear Dose‐Response Function

Microbial food safety risk assessment models can often at times be simplified by eliminating the need to integrate a complex dose‐response relationship across a distribution of exposure doses. This is possible if exposure pathways lead to pathogens at exposure that consistently have a small probability of causing illness. In this situation, the probability of illness will follow an approximately linear function of dose. Consequently, the predicted probability of illness per serving across all exposures is linear with respect to the expected value of dose. The majority of dose‐response functions are approximately linear when the dose is low. Nevertheless, what constitutes “low” is dependent on the parameters of the dose‐response function for a particular pathogen. In this study, a method is proposed to determine an upper bound of the exposure distribution for which the use of a linear dose‐response function is acceptable. If this upper bound is substantially larger than the expected value of exposure doses, then a linear approximation for probability of illness is reasonable. If conditions are appropriate for using the linear dose‐response approximation, for example, the expected value for exposure doses is two to three logs₁₀ smaller than the upper bound of the linear portion of the dose‐response function, then predicting the risk‐reducing effectiveness of a proposed policy is trivial. Simple examples illustrate how this approximation can be used to inform policy decisions and improve an analyst's understanding of risk.     

Reassessing Benzene Cancer Risks Using Internal Doses

Human cancer risks from benzene exposure have previously been estimated by regulatory agencies based primarily on epidemiological data, with supporting evidence provided by animal bioassay data. This paper reexamines the animal-based risk assessments for benzene using physiologically-based pharmacokinetic (PBPK) models of benzene metabolism in animals and humans. It demonstrates that internal doses (interpreted as total benzene metabolites formed) from oral gavage experiments in mice are well predicted by a PBPK model developed by Travis et al. Both the data and the model outputs can also be accurately described by the simple nonlinear regression model total metabolites = 76.4x/(80.75 + x), where x = administered dose in mg/kg/day. Thus, PBPK modeling validates the use of such nonlinear regression models, previously used by Bailer and Hoel. An important finding is that refitting the linearized multistage (LMS) model family to internal doses and observed responses changes the maximum-likelihood estimate (MLE) dose-response curve for mice from linear-quadratic to cubic, leading to low-dose risk estimates smaller than in previous risk assessments. This is consistent with the conclusion for mice from the Bailer and Hoel analysis. An innovation in this paper is estimation of internal doses for humans based on a PBPK model (and the regression model approximating it) rather than on interspecies dose conversions. Estimates of human risks at low doses are reduced by the use of internal dose estimates when the estimates are obtained from a PBPK model, in contrast to Bailer and Hoel's findings based on interspecies dose conversion. Sensitivity analyses and comparisons with epidemiological data and risk models suggest that our finding of a nonlinear MLE dose-response curve at low doses is robust to changes in assumptions and more consistent with epidemiological data than earlier risk models.     

Evaluation of Inhaled Versus Deposited Dose Using the Exponential Dose‐Response Model for Inhalational Anthrax in Nonhuman Primate,Rabbit, and Guinea Pig

The application of the exponential model is extended by the inclusion of new nonhuman primate (NHP), rabbit, and guinea pig dose‐lethality data for inhalation anthrax. Because deposition is a critical step in the initiation of inhalation anthrax, inhaled doses may not provide the most accurate cross‐species comparison. For this reason, species‐specific deposition factors were derived to translate inhaled dose to deposited dose. Four NHP, three rabbit, and two guinea pig data sets were utilized. Results from species‐specific pooling analysis suggested all four NHP data sets could be pooled into a single NHP data set, which was also true for the rabbit and guinea pig data sets. The three species‐specific pooled data sets could not be combined into a single generic mammalian data set. For inhaled dose, NHPs were the most sensitive (relative lowest LD₅₀) species and rabbits the least. Improved inhaled LD₅₀s proposed for use in risk assessment are 50,600, 102,600, and 70,800 inhaled spores for NHP, rabbit, and guinea pig, respectively. Lung deposition factors were estimated for each species using published deposition data from Bacillus spore exposures, particle deposition studies, and computer modeling. Deposition was estimated at 22%, 9%, and 30% of the inhaled dose for NHP, rabbit, and guinea pig, respectively. When the inhaled dose was adjusted to reflect deposited dose, the rabbit animal model appears the most sensitive with the guinea pig the least sensitive species.     

Comparison of Six Dose-Response Models for Use with Food-Borne Pathogens

Food-related illness in the United States is estimated to affect over six million people per year and cost the economy several billion dollars. These illnesses and costs could be reduced if minimum infectious doses were established and used as the basis of regulations and monitoring. However, standard methodologies for dose-response assessment are not yet formulated for microbial risk assessment. The objective of this study was to compare dose-response models for food-borne pathogens and determine which models were most appropriate for a range of pathogens. The statistical models proposed in the literature and chosen for comparison purposes were log-normal, log-logistic, exponential, -Poisson and Weibull-Gamma. These were fit to four data sets also taken from published literature, Shigella flexneri, Shigella dysenteriae,Campylobacter jejuni, and Salmonella typhosa, using the method of maximum likelihood. The Weibull-gamma, the only model with three parameters, was also the only model capable of fitting all the data sets examined using the maximum likelihood estimation for comparisons. Infectious doses were also calculated using each model. Within any given data set, the infectious dose estimated to affect one percent of the population ranged from one order of magnitude to as much as nine orders of magnitude, illustrating the differences in extrapolation of the dose response models. More data are needed to compare models and examine extrapolation from high to low doses for food-borne pathogens.     

Empirical Scaling of Single Oral Lethal Doses Across Mammalian Species Based on a Large Database

The scaling of administered doses to achieve equal degrees of toxic effect in different species has been relatively poorly examined for noncancer toxicity, either empirically or theoretically. We investigate empirical patterns in the correspondence of single oral dose LD, values across several mammalian species for a large number of chemicals based on data reported in the RTECSQ database maintained by the National Institute for Occupational Safety and Health. We find a good correspondence of LD, values across species when the dose levels are expressed in terms of mgadministered per kg of body mass. Our findings contrast with earlier analyses that support scaling doses by the 3/4-power of body mass to achieve equal subacute toxicity of antineoplastic agents. We suggest that, especially for severe toxicity, single- and repeated-dosing regimes may have different cross-species scaling properties, as they may depend on standing levels of defenses and rate of regeneration of defenses, respectively.     

Addressing Nonlinearity in the Exposure-Response Relationship for a Genotoxic Carcinogen: Cancer Potency Estimates for Ethylene Oxide

Ethylene oxide (EO) has been identified as a carcinogen in laboratory animals. Although the precise mechanism of action is not known, tumors in animals exposed to EO are presumed to result from its genotoxicity. The overall weight of evidence for carcinogenicity from a large body of epidemiological data in the published literature remains limited. There is some evidence for an association between EO exposure and lympho/hematopoietic cancer mortality. Of these cancers, the evidence provided by two large cohorts with the longest follow-up is most consistent for leukemia. Together with what is known about human leukemia and EO at the molecular level, there is a body of evidence that supports a plausible mode of action for EO as a potential leukemogen. Based on a consideration of the mode of action, the events leading from EO exposure to the development of leukemia (and therefore risk) are expected to be proportional to the square of the dose. In support of this hypothesis, a quadratic dose-response model provided the best overall fit to the epidemiology data in the range of observation. Cancer dose-response assessments based on human and animal data are presented using three different assumptions for extrapolating to low doses: (1) risk is linearly proportionate to dose; (2) there is no appreciable risk at low doses (margin-of-exposure or reference dose approach); and (3) risk below the point of departure continues to be proportionate to the square of the dose. The weight of evidence for EO supports the use of a nonlinear assessment. Therefore, exposures to concentrations below 37 microg/m3 are not likely to pose an appreciable risk of leukemia in human populations. However, if quantitative estimates of risk at low doses are desired and the mode of action for EO is considered, these risks are best quantified using the quadratic estimates of cancer potency, which are approximately 3.2- to 32-fold lower, using alternative points of departure, than the linear estimates of cancer potency for EO. An approach is described for linking the selection of an appropriate point of departure to the confidence in the proposed mode of action. Despite high confidence in the proposed mode of action, a small linear component for the dose-response relationship at low concentrations cannot be ruled out conclusively. Accordingly, a unit risk value of 4.5 x 10(-8) (microg/m3)(-1) was derived for EO, with a range of unit risk values of 1.4 x 10(-8) to 1.4 x 10(-7) (microg/m3)(-1) reflecting the uncertainty associated with a theoretical linear term at low concentrations.     

One Agency's Use of Risk Assessment and Risk Communication1

Few organizations have the courage to evaluate their own use of risk assessment (identifying hazards and estimating their probability and magnitude) and risk communication (interacting with internal and external stakeholder groups about risks). The USDA Animal and Plant Health Inspection Service (APHIS) wants to enhance its overall risk analysis process for managing a wide range of risks to animals, plants, and human health. We gathered survey data for a baseline of APHIS professionals’ understanding and use of risk assessment and risk communication. APHIS professionals spend a surprisingly large share of their time communicating about risks. They perceive that risk estimates influence decisions, but that risk estimates should have more influence. Respondents reported little opposition to APHIS risk management decisions, and little use of channels such as USDA Extension Service for disseminating risk messages. Substantial variance across responses is explained mostly by differences in the roles of the 11 work units (now 10) within the agency. Location also contributes to the variance. Demographic variables seem less important.     

Expert Scientific Judgment and Cancer Risk Assessment: A Pilot Study of Pharmacokinetic Data

When high-dose tumor data are extrapolated to low doses, it is typically assumed that the dose of a carcinogen delivered to target cells is proportional to the dose administered to test animals, even at exposure levels below the experimental range. Since pharmacokinetic data are becoming available that in some cases question the validity of this assumption, risk assessors must decide whether to maintain the standard assumption. A pilot study of formaldehyde is reported that was undertaken to demonstrate how expert scientific judgment can help guide a controversial risk assessment where pharmacokinetic data are considered inconclusive. Eight experts on pharmacokinetic data were selected by a formal procedure, and each was interviewed personally using a structured interview protocol. The results suggest that expert scientific opinion is polarized in this case, a situation that risk assessors can respond to with a range of risk characterizations considered biologically plausible by the experts. Convergence of expert opinion is likely in this case of several specific research strategies ar executed in a competent fashion. Elicitation of expert scientific judgment is a promising vehicle for evaluating the quality of pharmacokinetic data, expressing uncertainty in risk assessment, and fashioning a research agenda that offers possible forging of scientific consensus.     

A Bayesian Semiparametric Model for Radiation Dose‐Response Estimation

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

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.     

Phthalate Exposure Through Food and Consumers' Risk Perception of Chemicals in Food

Phthalates have been detected in various types of retail foods. Consumers' exposure to phthalates is common. Consumers are concerned about chemicals in food. Our aim was to investigate the relationships between consumers' exposure to phthalates through food, consumers' interest in a natural and healthy diet, risk perception of food chemicals, and consumers' diet patterns. We collected data through a mail survey in the adult Swiss-German population ( N  = 1,200). We modeled exposure to di(2-ethylhexyl) phthalate (DEHP), dibutyl phthalate (DBP), benzyl butyl phthalate (BBP), and diethyl phthalate (DEP) based on a food frequency questionnaire and phthalate concentrations reported from food surveys. Using rating scales, we assessed risk perceptions of chemicals in food and interest in a natural and healthy diet. Higher risk perceptions and higher natural and healthy diet interest were associated with higher daily doses of DEHP, BBP, and DEP. No health risk from phthalates in food was identified for the vast majority of the population. Four consumers' diet clusters were discerned, with differences in phthalate exposure, risk perceptions, and interest in a natural and healthy diet. This study shows that even those consumers who express strong interest in natural food and low acceptance of food chemicals, and who try to make respective food choices, are exposed to contaminants such as phthalates.     

Interspecies Extrapolation: A Reexamination of Acute Toxicity Data

We reanalyze the acute toxicity data on cancer chemotherapeutic agents compiled by Freireich et al.(1) and Schein et al.(2) to derive coefficients of the allometric equation for scaling toxic doses across species (toxic dose = a.[body weight]b). In doing so, we extend the analysis of Travis and White (Risk Analysis, 1988, 8, 119-125) by addressing uncertainties inherent in the analysis and by including the hamster data, previously not used. Through Monte Carlo sampling, we specifically account for measurement errors when deriving confidence intervals and testing hypotheses. Two hypotheses are considered: first, that the allometric scaling power (b) varies for chemicals of the type studied; second, that the same scaling power, or "scaling law," holds for all chemicals in the data set. Following the first hypothesis, in 95% of the cases the allometric power of body weight falls in the range from 0.42-0.97, with a population mean of 0.74. Assuming the second hypothesis to be true-that the same scaling law is followed for all chemicals-the maximum likelihood estimate of the scaling power is 0.74; confidence bounds on the mean depend on the size of measurement error assumed. Under a "best case" analysis, 95% confidence bounds on the mean are 0.71 and 0.77, similar to the results reported by Travis and White. For alternative assumptions regarding measurement error, the confidence intervals are larger and include 0.67, but not 1.00. Although a scaling power of about 0.75 provides the best fit to the data as a whole, a scaling power of 0.67, corresponding to scaling per unit surface area, is not rejected when the nonhomogeneity of variances is taken into account. Hence, both surface area and 0.75 power scaling are consistent with the Freireich et al. and Schein et al. data sets. To illustrate the potential impact of overestimating the scaling power, we compare reported human MTDs to values extrapolated from mouse LD10s.     

A Risk Analysis for Airborne Pathogens with Low Infectious Doses: Application to Respirator Selection Against Coccidioides immitis Spores

Probability models incorporating a deterministic versus stochastic infectious dose are described for estimating infection risk due to airborne pathogens that infect at low doses. Such pathogens can be occupational hazards or candidate agents for bioterrorism. Inputs include parameters for the infectious dose model, distribution parameters for ambient pathogen concentrations, the breathing rate, the duration of an exposure period, the anticipated number of exposure periods, and, if a respirator device is used, distribution parameters for respirator penetration values. Application of the models is illustrated with a hypothetical scenario involving exposure to Coccidioides immitis, a fungus present in soil in areas of the southwestern United States Inhaling C. immitis spores causes a respiratory tract infection and is a recognized occupational hazard in jobs involving soil dust exposure in endemic areas An uncertainty analysis is applied to risk estimation in the context of selecting respiratory protection with a desired degree of efficacy.