Dose‐Response Models Incorporating Aerosol Size Dependency for Francisella tularensis

The effect of bioaerosol size was incorporated into predictive dose‐response models for the effects of inhaled aerosols of Francisella tularensis (the causative agent of tularemia) on rhesus monkeys and guinea pigs with bioaerosol diameters ranging between 1.0 and 24 μm. Aerosol‐size‐dependent models were formulated as modification of the exponential and β‐Poisson dose‐response models and model parameters were estimated using maximum likelihood methods and multiple data sets of quantal dose‐response data for which aerosol sizes of inhaled doses were known. Analysis of F. tularensis dose‐response data was best fit by an exponential dose‐response model with a power function including the particle diameter size substituting for the rate parameter k scaling the applied dose. There were differences in the pathogen's aerosol‐size‐dependence equation and models that better represent the observed dose‐response results than the estimate derived from applying the model developed by the International Commission on Radiological Protection (ICRP, 1994) that relies on differential regional lung deposition for human particle exposure.     

A Quantitative Microbial Risk Assessment Model for Legionnaires'' Disease: Animal Model Selection and Dose-Response Modeling

Legionnaires' disease (LD), first reported in 1976, is an atypical pneumonia caused by bacteria of the genus Legionella, and most frequently by L. pneumophila (Lp). Subsequent research on exposure to the organism employed various animal models, and with quantitative microbial risk assessment (QMRA) techniques, the animal model data may provide insights on human dose-response for LD. This article focuses on the rationale for selection of the guinea pig model, comparison of the dose-response model results, comparison of projected low-dose responses for guinea pigs, and risk estimates for humans. Based on both in vivo and in vitro comparisons, the guinea pig (Cavia porcellus) dose-response data were selected for modeling human risk. We completed dose-response modeling for the beta-Poisson (approximate and exact), exponential, probit, logistic, and Weibull models for Lp inhalation, mortality, and infection (end point elevated body temperature) in guinea pigs. For mechanistic reasons, including low-dose exposure probability, further work on human risk estimates for LD employed the exponential and beta-Poisson models. With an exposure of 10 colony-forming units (CFU) (retained dose), the QMRA model predicted a mild infection risk of 0.4 (as evaluated by seroprevalence) and a clinical severity LD case (e.g., hospitalization and supportive care) risk of 0.0009. The calculated rates based on estimated human exposures for outbreaks used for the QMRA model validation are within an order of magnitude of the reported LD rates. These validation results suggest the LD QMRA animal model selection, dose-response modeling, and extension to human risk projections were appropriate.     

Dose‐Response Model of Rocky Mountain Spotted Fever (RMSF) for Human

Rickettsia rickettsii is the causative agent of Rocky Mountain spotted fever (RMSF) and is the prototype bacterium in the spotted fever group of rickettsiae, which is found in North, Central, and South America. The bacterium is gram negative and an obligate intracellular pathogen. The disease is transmitted to humans and vertebrate host through tick bites; however, some cases of aerosol transmission also have been reported. The disease can be difficult to diagnose in the early stages, and without prompt and appropriate treatment, it can be fatal. This article develops dose‐response models of different routes of exposure for RMSF in primates and humans. The beta‐Poisson model provided the best fit to the dose‐response data of aerosol‐exposed rhesus monkeys, and intradermally inoculated humans (morbidity as end point of response). The average 50% infectious dose among (ID₅₀) exposed human population, N₅₀, is 23 organisms with 95% confidence limits of 1 to 89 organisms. Similarly, ID₁₀ and ID₂₀ are 2.2 and 5.0, respectively. Moreover, the data of aerosol‐exposed rhesus monkeys and intradermally inoculated humans could be pooled. This indicates that the dose‐response models fitted to different data sets are not significantly different and can be described by the same relationship.     

On the risk of mortality to primates exposed to anthrax spores.

Current events have heightened the importance of understanding the risks from inhalation exposure to small numbers of spores of Bacillus anthracis. Previously reported data sets have not been fully assessed using current understanding of microbial dose response. This article presents an assessment of the reported primate dose-response data. At low doses, the risk to large populations of low doses of inhaled spores (e.g., < 100) is not insignificant.     

Animal and Human Dose‐Response Models for Brucella Species

Human Brucellosis is one of the most common zoonotic diseases worldwide. Disease transmission often occurs through the handling of domestic livestock, as well as ingestion of unpasteurized milk and cheese, but can have enhanced infectivity if aerosolized. Because there is no human vaccine available, rising concerns about the threat of Brucellosis to human health and its inclusion in the Center for Disease Control's Category B Bioterrorism/Select Agent List make a better understanding of the dose‐response relationship of this microbe necessary. Through an extensive peer‐reviewed literature search, candidate dose‐response data were appraised so as to surpass certain standards for quality. The statistical programming language, “R,” was used to compute the maximum likelihood estimation to fit two models, the exponential and the approximate beta‐Poisson (widely used for quantitative risk assessment) to dose‐response data. Dose‐response models were generated for prevalent species of Brucella: Br. suis, Br. melitensis, and Br. abortus. Dose‐response models were created for aerosolized Br. suis exposure to guinea pigs from pooled studies. A parallel model for guinea pigs inoculated through both aerosol and subcutaneous routes with Br. melitensis showed that the median infectious dose corresponded to a 30 colony‐forming units (CFU) dose of Br. suis, much less than the N₅₀ dose of about 94 CFU for Br. melitensis organisms. When Br. melitensis was tested subcutaneously on mice, the N₅₀ dose was higher, 1,840 CFU. A dose‐response model was constructed from pooled data for mice, rhesus macaques, and humans inoculated through three routes (subcutaneously/aerosol/intradermally) with Br. melitensis.     

On the Relationship Between Carcinogenicity and Acute Toxicity

Parodi et al. ⁽¹⁾ and Zeise et al. ⁽²⁾ found a surprising statistical correlation (or association) between acute toxicity and carcinogenic potency. In order to shed light on the questions of whether or not it is a causal correlation, and whether or not it is a statistical or tautological artifact, we have compared the correlations for the NCI/NTP data set with those for chemicals not in this set. Carcinogenic potencies were taken from the Gold et al. database. We find a weak correlation with an average value of TD₅₀/LD₅₀= 0.04 for the non-NCI data set, compared with TD₅₀/LD₅₀= 0.15 for the NCI data set. We conclude that it is not easy to distinguish types of carcinogens on the basis of whether or not they are acutely toxic.     

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.     

Development of an Interspecies Nested Dose‐Response Model for Mycobacterium avium subspecies paratuberculosis

Mycobacterium avium subspecies paratuberculosis (MAP) causes chronic inflammation of the intestines in humans, ruminants, and other species. It is the causative agent of Johne's disease in cattle, and has been implicated as the causative agent of Crohn's disease in humans. To date, no quantitative microbial risk assessment (QMRA) for MAP utilizing a dose‐response function exists. The objective of this study is to develop a nested dose‐response model for infection from oral exposure to MAP utilizing data from the peer‐reviewed literature. Four studies amenable to dose‐response modeling were identified in the literature search and optimized to the one‐parameter exponential or two‐parameter beta‐Poisson dose‐response models. A nesting analysis was performed on all permutations of the candidate data sets to determine the acceptability of pooling data sets across host species. Three of four data sets exhibited goodness of fit to at least one model. All three data sets exhibited good fit to the beta‐Poisson model, and one data set exhibited goodness of fit, and best fit, to the exponential model. Two data sets were successfully nested using the beta‐Poisson model with parameters α = 0.0978 and N₅₀ = 2.70 × 10² CFU. These data sets were derived from sheep and red deer host species, indicating successful interspecies nesting, and demonstrate the highly infective nature of MAP. The nested dose‐response model described should be used for future QMRA research regarding oral exposure to MAP.     

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.     

Calculation of Benchmark Doses from Continuous Data

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

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.     

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.     

A Parametric Model for Detecting Hormetic Effects in Developmental Toxicity Studies

Hormetic effects have been observed at low exposure levels based on the dose-response pattern of data from developmental toxicity studies. This indicates that there might actually be a reduced risk of exhibiting toxic effects at low exposure levels. Hormesis implies the existence of a threshold dose level and there are dose-response models that include parameters that account for the threshold. We propose a function that introduces a parameter to account for hormesis. This function is a subset of the set of all functions that could represent a hormetic dose-response relationship at low exposure levels to toxic agents. We characterize the overall dose-response relationship with a piecewise function that consists of a hormetic u-shape curve at low dose levels and a logistic curve at high dose levels. We apply our model to a data set from an experiment conducted at the National Toxicology Program (NTP). We also use the beta-binomial distribution to model the litter response data. It can be seen by observing the structure of these data that current experimental designs for developmental studies employ a limited number of dose groups. These designs may not be satisfactory when the goal is to illustrate the existence of hormesis. In particular, increasing the number of low-level doses improves the power for detecting hormetic effects. Therefore, we also provide the results of simulations that were done to characterize the power of current designs in detecting hormesis and to demonstrate how this power can be improved upon by altering these designs with the addition of only a few low exposure levels.     

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.     

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.     

An Analytical Framework for Relating Dose, Risk, and Incidence: An Application to Occupational Tuberculosis Infection

An adverse health impact is often treated as a binary variable (response vs. no response), in which case the risk of response is defined as a monotonically increasing function R of the dose received D. For a population of size N , specifying the forms of R(D) and of the probability density function (pdf) for D allows determination of the pdf for risk, and computation of the mean and variance of the distribution of incidence, where the latter parameters are denoted E[S _N] and Var[ S _N], respectively. The distribution of S _N describes uncertainty in the future incidence value. Given variability in dose (and risk) among population members, the distribution of incidence is Poisson-binomial. However, depending on the value of E[S _N], the distribution of incidence is adequately approximated by a Poisson distribution with parameter μ= E[S _N], or by a normal distribution with mean and variance equal to E[S _N] and Var[ S _N]. The general analytical framework is applied to occupational infection by Mycobacterium tuberculosis (M. tb). Tuberculosis is transmitted by inhalation of 1–5 μm particles carrying viable M. tb bacilli. Infection risk has traditionally been modeled by the expression: R(D) = 1 – exp(– D ), where D is the expected number of bacilli that deposit in the pulmonary region. This model assumes that the infectious dose is one bacillus. The beta pdf and the gamma pdf are shown to be reasonable and especially convenient forms for modeling the distribution of the expected cumulative dose across a large healthcare worker cohort. Use of the the analytical framework is illustrated by estimating the efficacy of different respiratory protective devices in reducing healthcare worker infection risk.     

Risk of Fetal Mortality After Exposure to Listeria monocytogenes Based on Dose-Response Data from Pregnant Guinea Pigs and Primates

One‐third of the annual cases of listeriosis in the United States occur during pregnancy and can lead to miscarriage or stillbirth, premature delivery, or infection of the newborn. Previous risk assessments completed by the Food and Drug Administration/the Food Safety Inspection Service of the U.S. Department of Agriculture/the Centers for Disease Control and Prevention (FDA/USDA/CDC)^{( 1 )} and Food and Agricultural Organization/the World Health Organization (FAO/WHO)^{( 2 )} were based on dose‐response data from mice. Recent animal studies using nonhuman primates^{( 3 , 4 )} and guinea pigs^{( 5 )} have both estimated LD₅₀s of approximately 10⁷ Listeria monocytogenes colony forming units (cfu). The FAO/WHO^{( 2 )} estimated a human LD₅₀ of 1.9 × 10⁶ cfu based on data from a pregnant woman consuming contaminated soft cheese. We reevaluated risk based on dose‐response curves from pregnant rhesus monkeys and guinea pigs. Using standard risk assessment methodology including hazard identification, exposure assessment, hazard characterization, and risk characterization, risk was calculated based on the new dose‐response information. To compare models, we looked at mortality rate per serving at predicted doses ranging from 10^?4 to 10¹² L. monocytogenes cfu. Based on a serving of 10⁶ L. monocytogenes cfu, the primate model predicts a death rate of 5.9 × 10^?1 compared to the FDA/USDA/CDC (fig. IV‐12)^{( 1 )} predicted rate of 1.3 × 10^?7. Based on the guinea pig and primate models, the mortality rate calculated by the FDA/USDA/CDC^{( 1 )} is underestimated for this susceptible population.     

Cardiac Sensitization Thresholds of Halon Replacement Chemicals Predicted in Humans by Physiologically-Based Pharmacokinetic Modeling

Human exposure to halons and halon replacement chemicals is often regulated on the basis of cardiac sensitization potential. The dose-response data obtained from animal testing are used to determine the no observable adverse effect level (NOAEL) and lowest observable adverse effect level (LOAEL) values. This approach alone does not provide the information necessary to evaluate the cardiac sensitization potential for the chemical of interest under a variety of exposure concentrations and durations. In order to provide a tool for decision-makers and regulators tasked with setting exposure guidelines for halon replacement chemicals, a quantitative approach was established which allowed exposures to be assessed in terms of the chemical concentrations in blood during the exposure. A physiologically-based pharmacokinetic (PBPK) model was used to simulate blood concentrations of Halon 1301 (bromotrifluoromethane, CF₃Br), HFC-125 (pentafluoroethane, CHF₂CF₃), HFC-227ea (heptafluoropropane, CF₃CHFCF₃), HCFC-123 (dichlorotrifluoroethane, CHCl₂CF₃), and CF₃I (trifluoroiodomethane) during inhalation exposures. This work demonstrates a quantitative approach for use in linking chemical inhalation exposures to the levels of chemical in blood achieved during the exposure.     

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.