Dose-Response Models for Inhalation of Bacillus anthracis Spores: Interspecies Comparisons

Because experiments with Bacillus anthracis are costly and dangerous, the scientific, public health, and engineering communities are served by thorough collation and analysis of experiments reported in the open literature. This study identifies available dose-response data from the open literature for inhalation exposure to B. anthracis and, via dose-response modeling, characterizes the response of nonhuman animal models to challenges. Two studies involving four data sets amenable to dose-response modeling were found in the literature: two data sets of response of guinea pigs to intranasal dosing with the Vollum and ATCC-6605 strains, one set of responses of rhesus monkeys to aerosol exposure to the Vollum strain, and one data set of guinea pig response to aerosol exposure to the Vollum strain. None of the data sets exhibited overdispersion and all but one were best fit by an exponential dose-response model. The beta-Poisson dose-response model provided the best fit to the remaining data set. As indicated in prior studies, the response to aerosol challenges is a strong function of aerosol diameter. For guinea pigs, the LD₅₀ increases with aerosol size for aerosols at and above 4.5 μm. For both rhesus monkeys and guinea pigs there is about a 15-fold increase in LD₅₀ when aerosol size is increased from 1 μm to 12 μm. Future experimental research and dose-response modeling should be performed to quantify differences in responses of subpopulations to B. anthracis and to generate data allowing development of interspecies correction factors.     

Time-Dose-Response Models for Microbial Risk Assessment

While microbial risk assessment (MRA) has been used for over 25 years, traditional dose-response analysis has only predicted the overall risk of adverse consequences from exposure to a given dose. An important issue for consequence assessment from bioterrorist and other microbiological exposure is the distribution of cases over time due to the initial exposure. In this study, the classical exponential and beta-Poisson dose-response models were modified to include exponential-power dependency of time post inoculation (TPI) or its simplified form, exponential-reciprocal dependency of TPI, to quantify the time of onset of an effect presumably associated with the kinetics of in vivo bacterial growth. Using the maximum likelihood estimation approach, the resulting time-dose-response models were found capable of providing statistically acceptable fits to all tested pooled animal survival dose-response data. These new models can consequently describe the development of animal infectious response over time and represent observed responses fairly accurately. This is the first study showing that a time-dose-response model can be developed for describing infections initiated by various pathogens. It provides an advanced approach for future MRA frameworks.     

Ebola Virus Dose Response Model for Aerosolized Exposures: Insights from Primate Data

This study develops dose–response models for Ebolavirus using previously published data sets from the open literature. Two such articles were identified in which three different species of nonhuman primates were challenged by aerosolized Ebolavirus in order to study pathology and clinical disease progression. Dose groups were combined and pooled across each study in order to facilitate modeling. The endpoint of each experiment was death. The exponential and exact beta-Poisson models were fit to the data using maximum likelihood estimation. The exact beta-Poisson was deemed the recommended model because it more closely approximated the probability of response at low doses though both models provided a good fit. Although transmission is generally considered to be dominated by person-to-person contact, aerosolization is a possible route of exposure. If possible, this route of exposure could be particularly concerning for persons in occupational roles managing contaminated liquid wastes from patients being treated for Ebola infection and the wastewater community responsible for disinfection. Therefore, this study produces a necessary mathematical relationship between exposure dose and risk of death for the inhalation route of exposure that can support quantitative microbial risk assessment aimed at informing risk mitigation strategies including personal protection policies against occupational exposures.     

Development and application of a dose–response model for Elizabethkingia spp

Elizabethkingia spp. are common environmental pathogens responsible for infections in more vulnerable populations. Although the exposure routes of concern are not well understood, some hospital-associated outbreaks have indicated possible waterborne transmission. In order to facilitate quantitative microbial risk assessment (QMRA) for Elizabethkingia spp., this study fit dose–response models to frog and mice datasets that evaluated intramuscular and intraperitoneal exposure to Elizabethkingia spp. The frog datasets could be pooled, and the exact beta-Poisson model was the best fitting model with optimized parameters α  = 0.52 and β = 86,351. Using the exact beta-Poisson model, the dose of Elizabethkingia miricola resulting in a 50% morbidity response (LD₅₀) was estimated to be approximately 237,000 CFU. The model developed herein was used to estimate the probability of infection for a hospital patient under a modeled exposure scenario involving a contaminated medical device and reported Elizabethkingia spp. concentrations isolated from hospital sinks after an outbreak. The median exposure dose was approximately 3 CFU/insertion event, and the corresponding median risk of infection was 3.4E-05. The median risk estimated in this case study was lower than the 3% attack rate observed in a previous outbreak, however, there are noted gaps pertaining to the possible concentrations of Elizabethkingia spp. in tap water and the most likely exposure routes. This is the first dose–response model developed for Elizabethkingia spp. thus enabling future risk assessments to help determine levels of risk and potential effective risk management strategies.     

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.     

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.     

Why Reduced-Form Regression Models of Health Effects Versus Exposures Should Not Replace QRA: Livestock Production and Infant Mortality as an Example

Do pollution emissions from livestock operations increase infant mortality rate (IMR)? A recent regression analysis of changes in IMR against changes in aggregate “animal units” (a weighted sum of cattle, pig, and poultry numbers) over time, for counties throughout the United States, suggested the provocative conclusion that they do: “[A] doubling of production leads to a 7.4% increase in infant mortality.” Yet, we find that regressing IMR changes against changes in specific components of “animal units” (cattle, pigs, and broilers) at the state level reveals statistically significant negative associations between changes in livestock production (especially, cattle production) and changes in IMR. We conclude that statistical associations between livestock variables and IMR variables are very sensitive to modeling choices (e.g., selection of explanatory variables, and use of specific animal types vs. aggregate “animal units). Such associations, whether positive or negative, do not warrant causal interpretation. We suggest that standard methods of quantitative risk assessment (QRA), including emissions release (source) models, fate and transport modeling, exposure assessment, and dose-response modeling, really are important—and indeed, perhaps, essential—for drawing valid causal inferences about health effects of exposures to guide sound, well-informed public health risk management policy. Reduced-form regression models, which skip most or all of these steps, can only quantify statistical associations (which may be due to model specification, variable selection, residual confounding, or other noncausal factors). Sound risk management requires the extra work needed to identify and model valid causal relations.     

Quantitative Cancer Risk Estimation for Formaldehyde

Of primary concern are irreversible effects, such as cancer induction, that formaldehyde exposure could have on human health. Dose-response data from human exposure situations would provide the most solid foundation for risk assessment, avoiding problematic extrapolations from the health effects seen in nonhuman species. However, epidemiologic studies of human formaldehyde exposure have provided little definitive information regarding dose-response. Reliance must consequently be placed on laboratory animal evidence. An impressive array of data points to significantly nonlinear relationships between rodent tumor incidence and administered dose, and between target tissue dose and administered dose (the latter for both rodents and Rhesus monkeys) following exposure to formaldehyde by inhalation. Disproportionately less formaldehyde binds covalently to the DNA of nasal respiratory epithelium at low than at high airborne concentrations. Use of this internal measure of delivered dose in analyses of rodent bioassay nasal tumor response yields multistage model estimates of low-dose risk, both point and upper bound, that are lower than equivalent estimates based upon airborne formaldehyde concentration. In addition, risk estimates obtained for Rhesus monkeys appear at least 10-fold lower than corresponding estimates for identically exposed Fischer-344 rats.     

Model Averaging Using Fractional Polynomials to Estimate a Safe Level of Exposure

Quantitative risk assessment involves the determination of a safe level of exposure. Recent techniques use the estimated dose-response curve to estimate such a safe dose level. Although such methods have attractive features, a low-dose extrapolation is highly dependent on the model choice. Fractional polynomials, basically being a set of (generalized) linear models, are a nice extension of classical polynomials, providing the necessary flexibility to estimate the dose-response curve. Typically, one selects the best-fitting model in this set of polynomials and proceeds as if no model selection were carried out. We show that model averaging using a set of fractional polynomials reduces bias and has better precision in estimating a safe level of exposure (say, the benchmark dose), as compared to an estimator from the selected best model. To estimate a lower limit of this benchmark dose, an approximation of the variance of the model-averaged estimator, as proposed by Burnham and Anderson, can be used. However, this is a conservative method, often resulting in unrealistically low safe doses. Therefore, a bootstrap-based method to more accurately estimate the variance of the model averaged parameter is proposed.     

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.     

Benchmark Analysis: Shopping with Proper Confidence

We discuss the issue of using benchmark doses for quantifying (excess) risk associated with exposure to environmental hazards. The paradigm of low-dose risk estimation in dose-response modeling is used as the primary application scenario. Emphasis is placed on making simultaneous inferences on benchmark doses when data are in the form of proportions, although the concepts translate easily to other forms of outcome data.     

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.     

Comparison of the Cancer Risk of Methylene Chloride Predicted from Animal Bioassay Data with the Epidemiologic Evidence

Methylene chloride has been shown to be a lung and liver carcinogen in the mouse; yet, the current epidemiologic data show no adverse health effects associated with chronic exposure to this compound. Hearne et al. have compared the results of a large mortality study on occupational exposure to methylene chloride to the human risk predictions based on the rodent bioassay to point out the inconsistency between the animal toxicologic and human epidemiologic data. The maximum number of lung and liver cancers predicted due to methylene chloride exposure based on the rodent bioassay data was 24 compared to 14 deaths from these cancers actually observed in the Hearne et al. epidemiology study. We assess the minimum risk detectable by the human study in order to calculate the upperbound potency of methylene chloride and compare it to the potency derived from the bioassay data. Results from the epidemiology study imply an upperbound potency of 1.5 x 10(-2) per ppm, compared to 1.4 x 10(-2) per ppm calculated using the most conservative analysis of the animal data. We conclude that the negative epidemiology study of Hearne et al. is not sufficiently powerful to show that the risk is inconsistent with the human risk estimated by modeling the rodent bioassay data. Specifically, the doses to which the workers were exposed, the population studied, and the latency period were not adequate to determine that the risks are outside the bounds of the risk estimates predicted by low-dose modeling of the animal data.     

Inferring an Augmented Bayesian Network to Confront a Complex Quantitative Microbial Risk Assessment Model with Durability Studies: Application to Bacillus Cereus on a Courgette Purée Production Chain

The Monte Carlo (MC) simulation approach is traditionally used in food safety risk assessment to study quantitative microbial risk assessment (QMRA) models. When experimental data are available, performing Bayesian inference is a good alternative approach that allows backward calculation in a stochastic QMRA model to update the experts’ knowledge about the microbial dynamics of a given food‐borne pathogen. In this article, we propose a complex example where Bayesian inference is applied to a high‐dimensional second‐order QMRA model. The case study is a farm‐to‐fork QMRA model considering genetic diversity of Bacillus cereus in a cooked, pasteurized, and chilled courgette purée. Experimental data are Bacillus cereus concentrations measured in packages of courgette purées stored at different time‐temperature profiles after pasteurization. To perform a Bayesian inference, we first built an augmented Bayesian network by linking a second‐order QMRA model to the available contamination data. We then ran a Markov chain Monte Carlo (MCMC) algorithm to update all the unknown concentrations and unknown quantities of the augmented model. About 25% of the prior beliefs are strongly updated, leading to a reduction in uncertainty. Some updates interestingly question the QMRA model.     

NUSAP Method for Evaluating the Data Quality in a Quantitative Microbial Risk Assessment Model for Salmonella in the Pork Production Chain

The numeral unit spread assessment pedigree (NUSAP) system was implemented to evaluate the quality of input parameters in a quantitative microbial risk assessment (QMRA) model for Salmonella spp. in minced pork meat. The input parameters were grouped according to four successive exposure pathways: (1) primary production (2) transport, holding, and slaughterhouse, (3) postprocessing, distribution, and storage, and (4) preparation and consumption. An inventory of 101 potential input parameters was used for building the QMRA model. The characteristics of each parameter were defined using a standardized procedure to assess (1) the source of information, (2) the sampling methodology and sample size, and (3) the distributional properties of the estimate. Each parameter was scored by a panel of experts using a pedigree matrix containing four criteria (proxy, empirical basis, method, and validation) to assess the quality, and this was graphically represented by means of kite diagrams. The parameters obtained significantly lower scores for the validation criterion as compared with the other criteria. Overall strengths of parameters related to the primary production module were significantly stronger compared to the other modules (the transport, holding, and slaughterhouse module, the processing, distribution, and storage module, and the preparation and consumption module). The pedigree assessment contributed to select 20 parameters, which were subsequently introduced in the QMRA model. The NUSAP methodology and kite diagrams are objective tools to discuss and visualize the quality of the parameters in a structured way. These two tools can be used in the selection procedure of input parameters for a QMRA, and can lead to a more transparent quality assurance in the QMRA.     

Multi‐Exposure Pathway Model to Compare Escherichia coli O157 Risks and Interventions

The relative contributions of exposure pathways associated with cattle‐manure‐borne Escherichia coli O157:H7 on public health have yet to be fully characterized. A stochastic, quantitative microbial risk assessment (QMRA) model was developed to describe a hypothetical cattle farm in order to compare the relative importance of five routes of exposure, including aquatic recreation downstream of the farm, consumption of contaminated ground beef processed with limited interventions, consumption of leafy greens, direct animal contact, and the recreational use of a cattle pasture. To accommodate diverse environmental and hydrological pathways, existing QMRAs were integrated with novel and simplistic climate and field‐level submodels. The model indicated that direct animal contact presents the greatest risk of illness per exposure event during the high pathogen shedding period. However, when accounting for the frequency of exposure, using a high‐risk exposure‐receptor profile, consumption of ground beef was associated with the greatest risk of illness. Additionally, the model was used to evaluate the efficacy of hypothetical interventions affecting one or more exposure routes; concurrent evaluation of multiple routes allowed for the assessment of the combined effect of preharvest interventions across exposure pathways—which may have been previously underestimated—as well as the assessment of the effect of additional downstream interventions. This analysis represents a step towards a full evaluation of the risks associated with multiple exposure pathways; future incorporation of variability associated with environmental parameters and human behaviors would allow for a comprehensive assessment of the relative contribution of exposure pathways at the population level.     

Advice to Risk Assessors Modeling Viral Health Risk Associated with Household Graywater

Quantitative microbial risk assessment (QMRA) is a valuable tool that can be used to predict the risk associated with human exposure to specific microbial contaminants in water sources. The transparency inherent in the QMRA process benefits discussions between multidisciplinary teams because members of such teams have different expertise and their confidence in the risk assessment output will depend upon whether they regard the selected input data and assumptions as being suitable and/or plausible. Selection of input data requires knowledge of the availability of appropriate data sets, the limitations of using a particular data set, and the logic of using alternative approaches. In performing QMRA modeling and in the absence of directly relevant data, compromises must be made. One such compromise made is to use available Escherichia coli data and apply a ratio of enteric viruses to indicator E. coli in wastewater obtained from prior studies to estimate the concentration of enteric viruses in other wastewater types/sources. In this article, we have provided an argument for why we do not recommend the use of a pathogen to E. coli ratio to estimate virus concentrations in single household graywater and additionally suggested circumstances in which use of such a ratio may be justified.     

The Impact of Consumer Phase Models in Microbial Risk Analysis

In quantitative microbiological risk assessment (QMRA), the consumer phase model (CPM) describes the part of the food chain between purchase of the food product at retail and exposure. Construction of a CPM is complicated by the large variation in consumer food handling practices and a limited availability of data. Therefore, several subjective (simplifying) assumptions have to be made when a CPM is constructed, but with a single CPM their impact on the QMRA results is unclear. We therefore compared the performance of eight published CPMs for Campylobacter in broiler meat in an example of a QMRA, where all the CPMs were analyzed using one single input distribution of concentrations at retail, and the same dose‐response relationship. It was found that, between CPMs, there may be a considerable difference in the estimated probability of illness per serving. However, the estimated relative risk reductions are less different for scenarios modeling the implementation of control measures. For control measures affecting the Campylobacter prevalence, the relative risk is proportional irrespective of the CPM used. However, for control measures affecting the concentration the CPMs show some difference in the estimated relative risk. This difference is largest for scenarios where the aim is to remove the highly contaminated portion from human exposure. Given these results, we conclude that for many purposes it is not necessary to develop a new detailed CPM for each new QMRA. However, more observational data on consumer food handling practices and their impact on microbial transfer and survival are needed to generalize this conclusion.     

Modeling Fetal Death and Malformation in Developmental Toxicity Studies

We review approaches to dose-response modeling and risk assessment for binary data from developmental toxicity studies. In particular, we focus on jointly modeling fetal death and malformation and use a continuation ratio formulation of the multinomial distribution to provide a model for risk. Generalized estimating equations are used to account for clustering of animals within litters. The fitted model is then used to calculate doses corresponding to a specified level of excess risk. Two methods of arriving at a lower confidence limit or Benchmark dose are illustrated and compared. We also discuss models based on single binary end points and compare our approach to a binary analysis of whether or not the animal was 'affected' (either dead or malformed). The models are illustrated using data from four developmental toxicity studies in EG, DEHP, TGDM, and DYME conducted through the National Toxicology Program.