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.     

Classic Dose‐Response and Time Postinoculation Models for Leptospira

Leptospirosis is a preeminent zoonotic disease concentrated in tropical areas, and prevalent in both industrialized and rural settings. Dose‐response models were generated from 22 data sets reported in 10 different studies. All of the selected studies used rodent subjects, primarily hamsters, with the predominant endpoint as mortality with the challenge strain administered intraperitoneally. Dose‐response models based on a single evaluation postinfection displayed median lethal dose (LD₅₀) estimates that ranged between 1 and 10⁷ leptospirae depending upon the strain's virulence and the period elapsed since the initial exposure inoculation. Twelve of the 22 data sets measured the number of affected subjects daily over an extended period, so dose‐response models with time‐dependent parameters were estimated. Pooling between data sets produced seven common dose‐response models and one time‐dependent model. These pooled common models had data sets with different test subject hosts, and between disparate leptospiral strains tested on identical hosts. Comparative modeling was done with parallel tests to test the effects of a single different variable of either strain or test host and quantify the difference by calculating a dose multiplication factor. Statistical pooling implies that the mechanistic processes of leptospirosis can be represented by the same dose‐response model for different experimental infection tests even though they may involve different host species, routes, and leptospiral strains, although the cause of this pathophysiological phenomenon has not yet been identified.     

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.     

Dose–Response Modeling: Extrapolating From Experimental Data to Real‐World Populations

Dose–response modeling of biological agents has traditionally focused on describing laboratory‐derived experimental data. Limited consideration has been given to understanding those factors that are controlled in a laboratory, but are likely to occur in real‐world scenarios. In this study, a probabilistic framework is developed that extends Brookmeyer's competing‐risks dose–response model to allow for variation in factors such as dose‐dispersion, dose‐deposition, and other within‐host parameters. With data sets drawn from dose–response experiments of inhalational anthrax, plague, and tularemia, we illustrate how for certain cases, there is the potential for overestimation of infection numbers arising from models that consider only the experimental data in isolation.     

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.     

Influenza Infection Risk and Predominate Exposure Route: Uncertainty Analysis

An effective nonpharmaceutical intervention for influenza interrupts an exposure route that contributes significantly to infection risk. Herein, we use uncertainty analysis (point‐interval method) and Monte Carlo simulation to explore the magnitude of infection risk and predominant route of exposure. We utilized a previously published mathematical model of a susceptible person attending a bed‐ridden infectious person. Infection risk is sensitive to the magnitude of virus emission and contact rates. The contribution of droplet spray exposure to infection risk increases with cough frequency, and decreases with virus concentration in cough particles. We consider two infectivity scenarios: greater infectivity of virus deposited in the upper respiratory tract than virus inhaled in respirable aerosols, based on human studies; and equal infectivity in the two locations, based on studies in guinea pigs. Given that virus have equal probability of infection throughout the respiratory tract, the mean overall infection risk is 9.8 × 10^?2 (95th percentile 0.78). However, when virus in the upper respiratory tract is less infectious than inhaled virus, the overall infection risk is several orders of magnitude lower. In this event, inhalation is a significant exposure route. Contact transmission is important in both infectivity scenarios. The presence of virus in only respirable particles increases the mean overall infection risk by 1–3 orders of magnitude, with inhalation contributing ≥ 99% of the infection risk. The analysis indicates that reduction of uncertainties in the concentration of virus in expiratory particles of different sizes, expiratory event frequency, and infectivity at different sites in the respiratory tract will clarify the predominate exposure routes for influenza.     

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.     

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.     

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.     

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.     

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.     

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.     

Development of a Dose‐Response Model for SARS Coronavirus

In order to develop a dose‐response model for SARS coronavirus (SARS‐CoV), the pooled data sets for infection of transgenic mice susceptible to SARS‐CoV and infection of mice with murine hepatitis virus strain 1, which may be a clinically relevant model of SARS, were fit to beta‐Poisson and exponential models with the maximum likelihood method. The exponential model (k= 4.1 × l0²) could describe the dose‐response relationship of the pooled data sets. The beta‐Poisson model did not provide a statistically significant improvement in fit. With the exponential model, the infectivity of SARS‐CoV was calculated and compared with those of other coronaviruses. The does of SARS‐CoV corresponding to 10% and 50% responses (illness) were estimated at 43 and 280 PFU, respectively. Its estimated infectivity was comparable to that of HCoV‐229E, known as an agent of human common cold, and also similar to those of some animal coronaviruses belonging to the same genetic group. Moreover, the exponential model was applied to the analysis of the epidemiological data of SARS outbreak that occurred at an apartment complex in Hong Kong in 2003. The estimated dose of SARS‐CoV for apartment residents during the outbreak, which was back‐calculated from the reported number of cases, ranged from 16 to 160 PFU/person, depending on the floor. The exponential model developed here is the sole dose‐response model for SARS‐CoV at the present and would enable us to understand the possibility for reemergence of SARS.     

Physiological Daily Inhalation Rates for Health Risk Assessment in Overweight/Obese Children,Adults, and Elderly

Physiological daily inhalation rates reported in our previous study for normal‐weight subjects 2.6–96 years old were compared to inhalation data determined in free‐living overweight/obese individuals (n = 661) aged 5–96 years. Inhalation rates were also calculated in normal‐weight (n = 408), overweight (n = 225), and obese classes 1, 2, and 3 adults (n = 134) aged 20–96 years. These inhalation values were based on published indirect calorimetry measurements (n = 1,069) and disappearance rates of oral doses of water isotopes (i.e., ²H₂O and H₂¹⁸O) monitored by gas isotope ratio mass spectrometry usually in urine samples for an aggregate period of over 16,000 days. Ventilatory equivalents for overweight/obese subjects at rest and during their aggregate daytime activities (28.99 ± 6.03 L to 34.82 ± 8.22 L of air inhaled/L of oxygen consumed; mean ±  SD) were determined and used for calculations of inhalation rates. The interindividual variability factor calculated as the ratio of the highest 99th percentile to the lowest 1st percentile of daily inhalation rates is higher for absolute data expressed in m³/day (26.7) compared to those of data in m³/kg‐day (12.2) and m³/m²‐day (5.9). Higher absolute rates generally found in overweight/obese individuals compared to their normal‐weight counterparts suggest higher intakes of air pollutants (in μg/day) for the former compared to the latter during identical exposure concentrations and conditions. Highest absolute mean (24.57 m³/day) and 99th percentile (55.55 m³/day) values were found in obese class 2 adults. They inhale on average 8.21 m³ more air per day than normal‐weight adults.     

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.     

Modeling the Dose Response Relationship of Waterborne Acanthamoeba

This study developed dose response models for determining the probability of eye or central nervous system infections from previously conducted studies using different strains of Acanthamoeba spp. The data were a result of animal experiments using mice and rats exposed corneally and intranasally to the pathogens. The corneal inoculations of Acanthamoeba isolate Ac 118 included varied amounts of Corynebacterium xerosis and were best fit by the exponential model. Virulence increased with higher levels of C. xerosis. The Acanthamoeba culbertsoni intranasal study with death as an endpoint of response was best fit by the beta‐Poisson model. The HN‐3 strain of A. castellanii was studied with an intranasal exposure and three different endpoints of response. For all three studies, the exponential model was the best fit. A model based on pooling data sets of the intranasal exposure and death endpoint resulted in an LD₅₀ of 19,357 amebae. The dose response models developed in this study are an important step towards characterizing the risk associated with free‐living amoeba like Acanthamoeba in drinking water distribution systems. Understanding the human health risk posed by free‐living amoeba will allow for quantitative microbial risk assessments that support building design decisions to minimize opportunities for pathogen growth and survival.     

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.     

Radon as a Tracer of Lung Changes Induced by Smoking

After smoking, exposure to radon and its progeny is the second leading cause of lung cancer. The probability of inducing lung carcinomas by inhaled radon progeny depends on the deposited radiation dose, and is significantly affected by physiological and morphometric changes induced by smoking. Due to irritation of the airways, the inhalation of cigarette smoke leads to the hyperproduction of mucus. Two concurrent processes occur: on one hand, increased production of mucus protects the target cells against radiation damage; on the other hand, in the case of long-term smokers, a chronic lung obstruction develops, causing an increase in the radiation dose to the lungs. Depending on the duration and intensity of smoking, these processes contribute to the final radiation dose with different weights. The primary objective of this study was to investigate to what extent these smoke-induced changes can modify the resulting absorbed dose of inhaled radon progeny relative to healthy nonsmokers. Since the bronchial dose depends on the degree of lung tissue damage, we have used this dose as a tool for detecting the effects of smoking on the lung epithelium. In other words, the biological effect of radon served as a tracer of changes induced by smoking.     

Daily Inhalation Rate and Time‐Activity/Location Pattern in Japanese Preschool Children

Lack of data on daily inhalation rate and activity of children has been an issue in health risk assessment of air pollutants. This study aimed to obtain the daily inhalation rate and intensity and frequency of physical activity in relation to the environment in Japanese preschool children. Children aged four–six years (n= 138) in the suburbs of Tokyo participated in this study, which involved three days' continuous monitoring of physical activity using a tri‐axial accelerometer and parent's completion of a time/location diary during daily life. The estimated three‐day mean daily inhalation rate (body temperature, pressure, saturated with water vapor) was 9.9 ± 1.6 m³/day (0.52 ± 0.09 m³/kg/day). The current daily inhalation rate value of 0.580 m³/kg/day proposed for use in health risk assessment in Japan is confirmed to be valid to calculate central value of inhaled dose of air pollutants in five‐ to six‐year‐old children. However, the 95th percentile daily inhalation rate of 0.83 m³/kg/day based on measurement for five‐year‐old children is recommended to be used to provide an upper bound estimate of exposure that ensure the protection of all five‐ to six‐year‐old children from the health risk of air pollutants. Children spent the majority of their time in sedentary and light level of physical activity (LPA) when indoors, while 85% of their time when outdoors was spent in LPA and moderate‐to‐vigorous physical activity. The results suggest the need to consider variability of minute respiratory ventilation rate according to the environment for more refined short‐term health risk assessment.