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.     

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.     

Relative Contributions of Four Exposure Pathways to Influenza Infection Risk

The relative contribution of four influenza virus exposure pathways—(1) virus-contaminated hand contact with facial membranes, (2) inhalation of respirable cough particles, (3) inhalation of inspirable cough particles, and (4) spray of cough droplets onto facial membranes—must be quantified to determine the potential efficacy of nonpharmaceutical interventions of transmission. We used a mathematical model to estimate the relative contributions of the four pathways to infection risk in the context of a person attending a bed-ridden family member ill with influenza. Considering the uncertainties in the sparse human subject influenza dose-response data, we assumed alternative ratios of 3,200:1 and 1:1 for the infectivity of inhaled respirable virus to intranasally instilled virus. For the 3,200:1 ratio, pathways (1), (2), and (4) contribute substantially to influenza risk: at a virus saliva concentration of 10⁶ mL⁻¹, pathways (1), (2), (3), and (4) contribute, respectively, 31%, 17%, 0.52%, and 52% of the infection risk. With increasing virus concentrations, pathway (2) increases in importance, while pathway (4) decreases in importance. In contrast, for the 1:1 infectivity ratio, pathway (1) is the most important overall: at a virus saliva concentration of 10⁶ mL⁻¹, pathways (1), (2), (3), and (4) contribute, respectively, 93%, 0.037%, 3.3%, and 3.7% of the infection risk. With increasing virus concentrations, pathway (3) increases in importance, while pathway (4) decreases in importance. Given the sparse knowledge concerning influenza dose and infectivity via different exposure pathways, nonpharmaceutical interventions for influenza should simultaneously address potential exposure via hand contact to the face, inhalation, and droplet spray.     

Effects of Surface Material,Ventilation, and Human Behavior on Indirect Contact Transmission Risk of Respiratory Infection

Infectious particles can be deposited on surfaces. Susceptible persons who contacted these contaminated surfaces may transfer the pathogens to their mucous membranes via hands, leading to a risk of respiratory infection. The exposure and infection risk contributed by this transmission route depend on indoor surface material, ventilation, and human behavior. In this study, quantitative infection risk assessments were used to compare the significances of these factors. The risks of three pathogens, influenza A virus, respiratory syncytial virus (RSV), and rhinovirus, in an aircraft cabin and in a hospital ward were assessed. Results showed that reducing the contact rate is relatively more effective than increasing the ventilation rate to lower the infection risk. Nonfabric surface materials were found to be much more favorable in the indirect contact transmission for RSV and rhinovirus than fabric surface materials. In the cases considered in this study, halving the ventilation rate and doubling the hand contact rate to surfaces and the hand contact rate to mucous membranes would increase the risk by 3.7–16.2%, 34.4–94.2%, and 24.1–117.7%, respectively. Contacting contaminated nonfabric surfaces may pose an indirect contact risk up to three orders of magnitude higher than that of contacting contaminated fabric surfaces. These findings provide more consideration for infection control and building environmental design.     

Validation and Application of Models to Predict Facemask Influenza Contamination in Healthcare Settings

Facemasks are part of the hierarchy of interventions used to reduce the transmission of respiratory pathogens by providing a barrier. Two types of facemasks used by healthcare workers are N95 filtering facepiece respirators (FFRs) and surgical masks (SMs). These can become contaminated with respiratory pathogens during use, thus serving as potential sources for transmission. However, because of the lack of field studies, the hazard associated with pathogen‐exposed facemasks is unknown. A mathematical model was used to calculate the potential influenza contamination of facemasks from aerosol sources in various exposure scenarios. The aerosol model was validated with data from previous laboratory studies using facemasks mounted on headforms in a simulated healthcare room. The model was then used to estimate facemask contamination levels in three scenarios generated with input parameters from the literature. A second model estimated facemask contamination from a cough. It was determined that contamination levels from a single cough (≈19 viruses) were much less than likely levels from aerosols (4,473 viruses on FFRs and 3,476 viruses on SMs). For aerosol contamination, a range of input values from the literature resulted in wide variation in estimated facemask contamination levels (13–202,549 viruses), depending on the values selected. Overall, these models and estimates for facemask contamination levels can be used to inform infection control practice and research related to the development of better facemasks, to characterize airborne contamination levels, and to assist in assessment of risk from reaerosolization and fomite transfer because of handling and reuse of contaminated facemasks.     

Evaluation of the Influenza Risk Reduction from Antimicrobial Spray Application on Porous Surfaces

Antimicrobial spray products are used by millions of people around the world for cleaning and disinfection of commonly touched surfaces. Influenza A is a pathogen of major concern, leading to up to 49,000 deaths and 114,000 hospitalizations per year in the United States alone. One of the recognized routes of transmission for influenza A is by transfer of viruses from surfaces to hands and subsequently to mucous membranes. Therefore, routine cleaning and disinfection of surfaces is an important part of the environmental management of influenza A. While the emphasis is generally on spraying hard surfaces and laundering cloth and linens with high temperature machine drying, not all surfaces can be treated in this manner. The quantitative microbial risk assessment (QMRA) approach was used to develop a stochastic risk model for estimating the risk of infection from indirect contact with porous fomite with and without surface treatment with an antimicrobial spray. The data collected from laboratory analysis combined with the risk model show that influenza A infection risk can be lowered by four logs after using an antimicrobial spray on a porous surface. Median risk associated with a single touch to a contaminated fabric was estimated to be 1.25 × 10⁻⁴ for the untreated surface, and 3.6 × 10⁻⁸ for the treated surface as a base case assumption. This single touch scenario was used to develop a generalizable model for estimating risks and comparing scenarios with and without treatment to more realistic multiple touch scenarios over time periods and with contact rates previously reported in the literature. The results of this study and understanding of product efficacy on risk reduction inform and broaden the range of risk management strategies for influenza A by demonstrating effective risk reduction associated with treating nonporous fomites that cannot be laundered at high temperatures.     

Model Uncertainty and Model Averaging in the Estimation of Infectious Doses for Microbial Pathogens

Food‐borne infection is caused by intake of foods or beverages contaminated with microbial pathogens. Dose‐response modeling is used to estimate exposure levels of pathogens associated with specific risks of infection or illness. When a single dose‐response model is used and confidence limits on infectious doses are calculated, only data uncertainty is captured. We propose a method to estimate the lower confidence limit on an infectious dose by including model uncertainty and separating it from data uncertainty. The infectious dose is estimated by a weighted average of effective dose estimates from a set of dose‐response models via a Kullback information criterion. The confidence interval for the infectious dose is constructed by the delta method, where data uncertainty is addressed by a bootstrap method. To evaluate the actual coverage probabilities of the lower confidence limit, a Monte Carlo simulation study is conducted under sublinear, linear, and superlinear dose‐response shapes that can be commonly found in real data sets. Our model‐averaging method achieves coverage close to nominal in almost all cases, thus providing a useful and efficient tool for accurate calculation of lower confidence limits on infectious doses.     

Construction of a Dose–Illness Relationship via Modeling Morbidity and Application to Risk Assessment of Wastewater Reuse

A disease burden (DB) evaluation for environmental pathogens is generally performed using disability‐adjusted life years with the aim of providing a quantitative assessment of the health hazard caused by pathogens. A critical step in the preparation for this evaluation is the estimation of morbidity between exposure and disease occurrence. In this study, the method of a traditional dose–response analysis was first reviewed, and then a combination of the theoretical basis of a “single‐hit” and an “infection‐illness” model was performed by incorporating two critical factors: the “infective coefficient” and “infection duration.” This allowed a dose–morbidity model to be built for direct use in DB calculations. In addition, human experimental data for typical intestinal pathogens were obtained for model validation, and the results indicated that the model was well fitted and could be further used for morbidity estimation. On this basis, a real case of a water reuse project was selected for model application, and the morbidity as well as the DB caused by intestinal pathogens during water reuse was evaluated. The results show that the DB attributed to Enteroviruses was significant, while that for enteric bacteria was negligible. Therefore, water treatment technology should be further improved to reduce the exposure risk of Enteroviruses . Since road flushing was identified as the major exposure route, human contact with reclaimed water through this pathway should be limited. The methodology proposed for model construction not only makes up for missing data of morbidity during risk evaluation, but is also necessary to quantify the maximum possible DB.     

Dose Response Models For Infectious Gastroenteritis

When pathogenic microorganisms enter the human body via ingestion with food or drinking water, they encounter a system of barriers mounted by the host. In order to reach parts of the intestinal tract that are suitable for growth and attachment, each of the barriers must be overcome successfully. The present view on infection states that at least one of the ingested pathogens must survive to start colonization. This is the basis for dose response models, used for quantitative risk assessment. In this paper, the usefulness of the Beta Poisson model for multiple barriers is corroborated. Infection is associated with the presence of elevated numbers of reproducing pathogens in the intestinal tract. This does not necessarily imply illness symptoms: when intestinal microorganisms engage in damaging activities, this may lead to illness symptoms. At the same time, these activities probably elicit defensive measures from the host, promoting the removal of pathogens and terminating infection. The duration of the period of colonization reflects the balance between the colonization potential of pathogens and the strength of host defenses. Starting from the assumption that during infection the host has a certain hazard of becoming ill, a simple dose response relation for acute gastroenteritis is developed. With the use of literature data from volunteer experiments, we show that examples can be found for three possible alternatives: an increase in the probability of illness with increasing dose, a decrease with higher doses, and a probability of illness (given infection) independent of the ingested dose. These alternatives may reflect different modes of interaction between pathogens and host.     

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.     

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.     

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.     

Sensitivity and Uncertainty Studies of the CRAC2 Computer Code

We have studied the sensitivity of health impacts from nuclear reactor accidents, as predicted by the CRAC2 computer code, to the following sources of uncertainty: (1) the model for plume rise, (2) the model for wet deposition, (3) the meteorological bin-sampling procedure for selecting weather sequences with rain, (4) the dose conversion factors for inhalation as affected by uncertainties in the particle size of the carrier aerosol and the clearance rates of radionuclides from the respiratory tract, (5) the weathering half-time for external ground-surface exposure, and (6) the transfer coefficients for terrestrial foodchain pathways. Predicted health impacts usually showed little sensitivity to use of an alternative plume-rise model or a modified rain-bin structure in bin-sampling. Health impacts often were quite sensitive to use of an alternative wet-deposition model in single-trial runs with rain during plume passage, but were less sensitive to the model in bin-sampling runs. Uncertainties in the inhalation dose conversion factors had important effects on early injuries in single-trial runs. Latent cancer fatalities were moderately sensitive to uncertainties in the weathering half-time for ground-surface exposure, but showed little sensitivity to the transfer coefficients for terrestrial foodchain pathways. Sensitivities of CRAC2 predictions to uncertainties in the models and parameters also depended on the magnitude of the source term, and some of the effects on early health effects were comparable to those that were due only to selection of different sets of weather sequences in bin-sampling.     

A Risk Assessment Scheme of Infection Transmission Indoors Incorporating the Impact of Resuspension

A new risk assessment scheme was developed to quantify the impact of resuspension to infection transmission indoors. Airborne and surface pathogenic particle concentration models including the effect of two major resuspension scenarios (airflow‐induced particle resuspension [AIPR] and walking‐induced particle resuspension [WIPR]) were derived based on two‐compartment mass balance models and validated against experimental data found in the literature. The inhalation exposure to pathogenic particles was estimated using the derived airborne concentration model, and subsequently incorporated into a dose‐response model to assess the infection risk. Using the proposed risk assessment scheme, the influences of resuspension towards indoor infection transmission were examined by two hypothetical case studies. In the case of AIPR, the infection risk increased from 0 to 0.54 during 0–0.5 hours and from 0.54 to 0.57 during 0.5–4 hours. In the case of WIPR, the infection risk increased from 0 to 0.87 during 0–0.5 hours and from 0.87 to 1 during 0.5–4 hours. Sensitivity analysis was conducted based on the design‐of‐experiments method and showed that the factors that are related to the inspiratory rate of viable pathogens and pathogen virulence have the most significant effect on the infection probability under the occurrence of AIPR and WIPR. The risk assessment scheme could serve as an effective tool for the risk assessment of infection transmission indoors.     

Comparison of Contact Site Cancer Potency Across Dose Routes: Case Study with Epichlorohydrin*

Risk assessment for airborne carcinogens is often limited by a lack of inhalation bioassay data. While extrapolation from oral-based cancer potency factors may be possible for some agents, this is not considered feasible for contact site carcinogens. The change in contact sites (oral: g.i. tract; inhalation: respiratory tract) when switching dose routes leads to possible differences in tissue sensitivity as well as chemical delivery. This research evaluates the feasibility to extrapolate across dose routes for a contact site carcinogen through a case study with epichlorohydrin (EPI). EPI cancer potency at contact sites is compared across three bioassays involving different dose routes (gavage, drinking water, inhalation) through the use of dosimetry models to adjust for EPI delivery to contact sites. Results indicate a large disparity (two orders of magnitude) in potency across the three routes of administration when expressed as the externally applied dose. However, when expressed as peak delivered dose, inhalation and oral potency estimates are similar and overall, the three potency estimates are within a factor of seven. The results suggest that contact site response to EPI is more dependent upon the rate than the route of delivery, with peak concentration the best way to extrapolate across dose routes. These results cannot be projected to other carcinogens without further study.     

Heterogeneity: A Major Factor Influencing Microbial Exposure and Risk Assessment

Microbial risk assessment is dependent on several biological and environmental factors that affect both the exposure characteristics to the biological agents and the mechanisms of pathogenicity involved in the pathogen‐host relationship. Many exposure assessment studies still focus on the location parameters of the probability distribution representing the concentration of the pathogens and/or toxin. However, the mean or median by themselves are insufficient to evaluate the adverse effects that are associated with a given level of exposure. Therefore, the effects on the risk of disease of a number of factors, including the shape parameters characterizing the distribution patterns of the pathogen in their environment, were investigated. The statistical models, which were developed to provide a better understanding of the factors influencing the risk, highlight the role of heterogeneity and its consequences on the commonly used risk assessment paradigm. Indeed, the heterogeneity characterizing the spatial and temporal distribution of the pathogen and/or the toxin contained in the water or food consumed is shown to be a major factor that may influence the magnitude of the risk dramatically. In general, the risk diminishes with higher levels of heterogeneity. This scheme is totally inverted in the presence of a threshold in the dose‐response relationship, since heterogeneity will then have a tremendous impact, namely, by magnifying the risk when the mean concentration of pathogens is below the threshold. Moreover, the approach of this article may be useful for risk ranking analysis, regarding different exposure conditions, and may also lead to improved water and food quality guidelines.     

Risk of Legionellosis in residential areas around farms irrigating with municipal wastewater

The conservation of freshwater is of both global and national importance, and in the United States, agriculture is one of the largest consumers of this resource. Reduction of the strain farming puts on local surface or groundwater is vital for ensuring resilience in the face of climate change, and one possible option is to irrigate with a combination of freshwater and reclaimed water from municipal wastewater treatment facilities. However, this wastewater can contain pathogens that are harmful to human health, such as Legionella pneumophila, which is a bacterium that can survive aerosolization and airborne transportation and cause severe pneumonia when inhaled. To assess an individual adult's risk of infection with L. pneumophila from a single exposure to agricultural spray irrigation, a quantitative microbial risk assessment was conducted for a scenario of spray irrigation in central Illinois, for the growing seasons in 2017, 2018, and 2019. The assessment found that the mean risk of infection for a single exposure exceeded the safety threshold of 10^–6 infections/exposure up to 1 km from a low-pressure irrigator and up to 2 km from a high-pressure irrigator, although no median risk exceeded the threshold for any distance or irrigator pressure. These findings suggest that spray irrigation with treated municipal wastewater could be a viable option for reducing freshwater consumption in Midwest farming, as long as irrigation on windy days is avoided and close proximity to the active irrigator is limited.     

Benzene Inhalation by Parts Washers: New Estimates Based on Measures of Occupational Exposure to Solvent Coaromatics

Questions persist regarding assessment of workers’ exposures to products containing low levels of benzene, such as mineral spirit solvent (MSS). This study summarizes previously unpublished data for parts‐washing activities, and evaluates potential daily and lifetime cumulative benzene exposures incurred by workers who used historical and current formulations of a recycled mineral spirits solvent in manual parts washers. Measured benzene concentrations in historical samples from parts‐washing operations were frequently below analytical detection limits. To better assess benzene exposure among these workers, air‐to‐solvent concentration ratios measured for toluene, ethylbenzene, and xylenes (TEX) were used to predict those for benzene based on a statistical model, conditional on physical‐chemical theory supported by new thermodynamic calculations of TEX and benzene activity coefficients in a modeled MSS‐type solvent. Using probabilistic methods, the distributions of benzene concentrations were then combined with distributions of other exposure parameters to estimate eight‐hour time‐weighted average (TWA) exposure concentration distributions and corresponding daily respiratory dose distributions for workers using these solvents in parts washers. The estimated 50th (95th) percentile of the daily respiratory dose and corresponding eight‐hour TWA air concentration for workers performing parts washing are 0.079 (0.77) mg and 0.0030 (0.028) parts per million by volume (ppm) for historical solvent, and 0.020 (0.20) mg and 0.00078 (0.0075) ppm for current solvent, respectively. Both 95th percentile eight‐hour TWA respiratory exposure estimates for solvent formulations are less than 10% of the current Occupational Safety and Health Administration permissible exposure limit of 1.0 ppm for benzene.     

Annual Burden of Occupationally‐Acquired Influenza Infections in Hospitals and Emergency Departments in the United States

Infections among health‐care personnel (HCP) occur as a result of providing care to patients with infectious diseases, but surveillance is limited to a few diseases. The objective of this study is to determine the annual number of influenza infections acquired by HCP as a result of occupational exposures to influenza patients in hospitals and emergency departments (EDs) in the United States. A risk analysis approach was taken. A compartmental model was used to estimate the influenza dose received in a single exposure, and a dose–response function applied to calculate the probability of infection. A three‐step algorithm tabulated the total number of influenza infections based on: the total number of occupational exposures (tabulated in previous work), the total number of HCP with occupational exposures, and the probability of infection in an occupational exposure. Estimated influenza infections were highly dependent upon the dose–response function. Given current compliance with infection control precautions, we estimated 151,300 and 34,150 influenza infections annually with two dose–response functions (annual incidence proportions of 9.3% and 2.1%, respectively). Greater reductions in infectious were achieved by full compliance with vaccination and IC precautions than with patient isolation. The burden of occupationally‐acquired influenza among HCP in hospitals and EDs in the United States is not trivial, and can be reduced through improved compliance with vaccination and preventive measures, including engineering and administrative controls.     

Bayesian Quantile Impairment Threshold Benchmark Dose Estimation for Continuous Endpoints

Quantitative risk assessment often begins with an estimate of the exposure or dose associated with a particular risk level from which exposure levels posing low risk to populations can be extrapolated. For continuous exposures, this value, the benchmark dose, is often defined by a specified increase (or decrease) from the median or mean response at no exposure. This method of calculating the benchmark dose does not take into account the response distribution and, consequently, cannot be interpreted based upon probability statements of the target population. We investigate quantile regression as an alternative to the use of the median or mean regression. By defining the dose–response quantile relationship and an impairment threshold, we specify a benchmark dose as the dose associated with a specified probability that the population will have a response equal to or more extreme than the specified impairment threshold. In addition, in an effort to minimize model uncertainty, we use Bayesian monotonic semiparametric regression to define the exposure–response quantile relationship, which gives the model flexibility to estimate the quantal dose–response function. We describe this methodology and apply it to both epidemiology and toxicology data.