Characterizing Risk for Cumulative Risk Assessments

In assessing environmental health risks, the risk characterization step synthesizes information gathered in evaluating exposures to stressors together with dose–response relationships, characteristics of the exposed population, and external environmental conditions. This article summarizes key steps of a cumulative risk assessment (CRA) followed by a discussion of considerations for characterizing cumulative risks. Cumulative risk characterizations differ considerably from single chemical‐ or single source‐based risk characterization. CRAs typically focus on a specific population instead of a pollutant or pollutant source and should include an evaluation of all relevant sources contributing to the exposures in the population and other factors that influence dose–response relationships. Second, CRAs may include influential environmental and population‐specific conditions, involving multiple chemical and nonchemical stressors. Third, a CRA could examine multiple health effects, reflecting joint toxicity and the potential for toxicological interactions. Fourth, the complexities often necessitate simplifying methods, including judgment‐based and semi‐quantitative indices that collapse disparate data into numerical scores. Fifth, because of the higher dimensionality and potentially large number of interactions, information needed to quantify risk is typically incomplete, necessitating an uncertainty analysis. Three approaches that could be used for characterizing risks in a CRA are presented: the multiroute hazard index, stressor grouping by exposure and toxicity, and indices for screening multiple factors and conditions. Other key roles of the risk characterization in CRAs are also described, mainly the translational aspect of including a characterization summary for lay readers (in addition to the technical analysis), and placing the results in the context of the likely risk‐based decisions.     

Reproductive and Developmental Risks from Ethylene Oxide: A Probabilistic Characterization of Possible Regulatory Thresholds

Ethylene oxide is a gas produced in large quantities in the United States that is used primarily as a chemical intermediate in the production of ethylene glycol, propylene glycol, non-ionic surfactants, ethanolamines, glycol ethers, and other chemicals. It has been well established that ethylene oxide can induce cancer, genetic, reproductive and developmental, and acute health effects in animals. The U.S. Environmental Protection Agency is currently developing both a cancer potency factor and a reference concentration (RfC) for ethylene oxide. This study used the rich database on the reproductive and developmental effects of ethylene oxide to develop a probabilistic characterization of possible regulatory thresholds for ethylene oxide. This analysis was based on the standard regulatory approach for noncancer risk assessment, but involved several innovative elements, such as: (1) the use of advanced statistical methods to account for correlations in developmental outcomes among littermates and allow for simultaneous control of covariates (such as litter size); (2) the application of a probabilistic approach for characterizing the uncertainty in extrapolating the animal results to humans; and (3) the use of a quantitative approach to account for the variation in heterogeneity among the human population. This article presents several classes of results, including: (1) probabilistic characterizations of ED10s for two quantal reproductive outcomes-resorption and fetal death, (2) probabilistic characterizations of one developmental outcome-the dose expected to yield a 5% reduction in fetal (or pup) weight, (3) estimates of the RfCs that would result from using these values in the standard regulatory approach for noncancer risk assessment, and (4) a probabilistic characterization of the level of ethylene oxide exposure that would be expected to yield a 1/1,000 increase in the risk of reproductive or developmental outcomes in exposed human populations.     

An ecological risk assessment for chlorpyrifos in an agriculturally dominated tributary of the San Joaquin River.

Single-species toxicity testing of ambient water samples and national-scale probabilistic risk assessment have implicated the organophosphorous (OP) insecticide chlorpyrifos (O, O-diethyl O-(3,5,6-trichloro-2-pyridyl)-phosphorothioate) as a potential chemical stressor of aquatic organisms residing in the lower San Joaquin River basin. This site-specific aquatic ecological risk assessment was conducted to determine the probability of adverse effects occurring from exposure to chlorpyrifos in an agriculturally dominated tributary of the San Joaquin River and to assess the ecological significance of such effects. Assessment endpoints were fish population persistence and invertebrate community productivity. Daily chemical measurements collected over a period of one year were analyzed temporally for frequency, duration, and spacing between events for acute and chronic exposure episodes. Effects thresholds for fish and freshwater lotic invertebrates were determined from single-species laboratory toxicity tests. Potential risk was characterized by the degree of overlap of distributions of exposure events and effects, with consideration given to additive toxicity of other OP insecticides, recovery periods, and duration of chronic exposure (> or = 21 d). Ecological significance was determined by analysis of fish assemblage dietary and reproductive habits in relation to the surrogate invertebrate taxa judged at risk. Results of analysis indicated no direct effects on fish, and indirect effects on fish through elimination of invertebrate food items were considered unlikely. Biological survey information will be necessary to address uncertainty in this risk conclusion, especially as it relates to the benthic invertebrate community. Results of this site-specific risk analysis suggest that fish population persistence and invertebrate community productivity were not adversely affected by measured chlorpyrifos residues during a year-long monitoring period.     

Integration of Probabilistic Exposure Assessment and Probabilistic Hazard Characterization

A method is proposed for integrated probabilistic risk assessment where exposure assessment and hazard characterization are both included in a probabilistic way. The aim is to specify the probability that a random individual from a defined (sub)population will have an exposure high enough to cause a particular health effect of a predefined magnitude, the critical effect size ( CES ). The exposure level that results in exactly that CES in a particular person is that person's individual critical effect dose ( ICED ). Individuals in a population typically show variation, both in their individual exposure ( IEXP ) and in their ICED . Both the variation in IEXP and the variation in ICED are quantified in the form of probability distributions. Assuming independence between both distributions, they are combined (by Monte Carlo) into a distribution of the individual margin of exposure ( IMoE ). The proportion of the IMoE distribution below unity is the probability of critical exposure ( PoCE ) in the particular (sub)population. Uncertainties involved in the overall risk assessment (i.e., both regarding exposure and effect assessment) are quantified using Monte Carlo and bootstrap methods. This results in an uncertainty distribution for any statistic of interest, such as the probability of critical exposure ( PoCE ). The method is illustrated based on data for the case of dietary exposure to the organophosphate acephate. We present plots that concisely summarize the probabilistic results, retaining the distinction between variability and uncertainty. We show how the relative contributions from the various sources of uncertainty involved may be quantified.     

Improving Risk Assessment Calculations for Traditional Foods Through Collaborative Research with First Nations Communities

As industrial development is increasing near northern Canadian communities, human health risk assessments (HHRA) are conducted to assess the predicted magnitude of impacts of chemical emissions on human health. One exposure pathway assessed for First Nations communities is the consumption of traditional plants, such as muskeg tea (Labrador tea) (Ledum/Rhododendron groenlandicum) and mint (Mentha arvensis). These plants are used to make tea and are not typically consumed in their raw form. Traditional practices were used to harvest muskeg tea leaves and mint leaves by two First Nations communities in northern Alberta, Canada. Under the direction of community elders, community youth collected and dried plants to make tea. Soil, plant, and tea decoction samples were analyzed for inorganic elements using inductively coupled plasma‐mass spectrometry. Concentrations of inorganic elements in the tea decoctions were orders of magnitude lower than in the vegetation (e.g., manganese 0.107 mg/L in tea, 753 mg/kg in leaves). For barium, the practice of assessing ingestion of raw vegetation would have resulted in a hazard quotient (HQ) greater than the benchmark of 0.2. Using measured tea concentrations it was determined that exposure would result in risk estimates orders of magnitude below the HQ benchmark of 0.2 (HQ = 0.0049 and 0.017 for muskeg and mint tea, respectively). An HHRA calculating exposure to tea vegetation through direct ingestion of the leaves may overestimate risk. The results emphasize that food preparation methods must be considered when conducting an HHRA. This study illustrates how collaboration between Western scientists and First Nations communities can add greater clarity to risk assessments.     

A Case Study Comparing Static and Spatially Explicit Ecological Exposure Analysis Methods

Exposure to chemical contaminants must be estimated when performing ecological risk assessments. A previous article proposed a habitat area and quality conditioned population exposure estimator, E[HQ]P, and described an individual-based, random walk, Monte Carlo model (SE3M) to facilitate calculation of E[HQ]P. In this article, E[HQ]P was compared with exposure estimates from a baseline risk assessment that evaluated mink and great blue heron exposure to fluoride at a federal Superfund site. Calculation of E[HQ]P took into consideration a receptor's forage area, movement behavior, population size, and the areal extent and quality of suitable habitat. The baseline assessment used four methods that did (total and unit Tier 2) and did not (total and unit Tier 1) consider habitat area or quality; where "total" included all exposure units on site and "unit" only a given exposure unit. Total Tier 1 estimates were consistently higher than E[HQ]P (e.g., 169.1 mg/kg x d versus 21.6 mg/kg x d). Risk managers using total Tier 1 results for decision making would be unlikely to underestimate exposure; however, implementability of correspondingly lower remedial objectives could be challenging. Unit Tier 1 estimates were higher (e.g., 96.5 mg/kg x d versus 61.6 mg/kg x d) or lower (e.g., 3.5 mg/kg x d versus 51.1 mg/kg x d) than E[HQ]P depending on variations in landscape features. Total Tier 2 and E[HQ]P estimates were similar (e.g., 20.7 mg/kg x d versus 21.6 mg/kg x d) when an ecologically questionable average exposure was assumed. Unit Tier 2 estimates were consistently well below E[HQ]P (e.g., 17.8 mg/kg x d versus 61.6 mg/kg x d) when an average exposure was not assumed. Risk managers using unit Tier 1 or 2 results could be basing their decisions on potentially large underestimates of exposure. By forgoing average exposure assumptions, and explicitly addressing landscape heterogeneity, SE3M appears capable of yielding exposure estimates that are not as potentially misleading to risk managers as those produced with traditional averaging methods.     

A Bayesian Semiparametric Model for Radiation Dose‐Response Estimation

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

Risk Characterization for Nanotechnology

Nanotechnology is a broad term that encompasses materials, structures, or processes that utilize engineered nanomaterials, which can be defined as materials intentionally designed to have one or more dimensions between 1 and 100 nm. Historically, risk characterization has been viewed as the final phase of a risk assessment process that integrates hazard identification, dose‐response assessment, and exposure assessment. The novelty and diversity of materials, structures, and tools that are covered by above‐defined “nanotechnology” raise substantial methodological issues and pose significant challenges for each of these phases of risk assessment. These issues and challenges culminate in the risk characterization phase of the risk assessment process, and this article discusses several of these key issues and approaches to developing risk characterization results and their implications for risk management decision making that are specific to nanotechnology.     

Exposure Assessment for Pesticide Intake from Multiple Food Products: A Bayesian Latent‐Variable Approach

Pesticide risk assessment for food products involves combining information from consumption and concentration data sets to estimate a distribution for the pesticide intake in a human population. Using this distribution one can obtain probabilities of individuals exceeding specified levels of pesticide intake. In this article, we present a probabilistic, Bayesian approach to modeling the daily consumptions of the pesticide Iprodione though multiple food products. Modeling data on food consumption and pesticide concentration poses a variety of problems, such as the large proportions of consumptions and concentrations that are recorded as zero, and correlation between the consumptions of different foods. We consider daily food consumption data from the Netherlands National Food Consumption Survey and concentration data collected by the Netherlands Ministry of Agriculture. We develop a multivariate latent‐Gaussian model for the consumption data that allows for correlated intakes between products. For the concentration data, we propose a univariate latent‐t model. We then combine predicted consumptions and concentrations from these models to obtain a distribution for individual daily Iprodione exposure. The latent‐variable models allow for both skewness and large numbers of zeros in the consumption and concentration data. The use of a probabilistic approach is intended to yield more robust estimates of high percentiles of the exposure distribution than an empirical approach. Bayesian inference is used to facilitate the treatment of data with a complex structure.     

Comparative Probabilistic Assessment of Occupational Pesticide Exposures Based on Regulatory Assessments

Implementation of probabilistic analyses in exposure assessment can provide valuable insight into the risks of those at the extremes of population distributions, including more vulnerable or sensitive subgroups. Incorporation of these analyses into current regulatory methods for occupational pesticide exposure is enabled by the exposure data sets and associated data currently used in the risk assessment approach of the Environmental Protection Agency (EPA). Monte Carlo simulations were performed on exposure measurements from the Agricultural Handler Exposure Database and the Pesticide Handler Exposure Database along with data from the Exposure Factors Handbook and other sources to calculate exposure rates for three different neurotoxic compounds (azinphos methyl, acetamiprid, emamectin benzoate) across four pesticide‐handling scenarios. Probabilistic estimates of doses were compared with the no observable effect levels used in the EPA occupational risk assessments. Some percentage of workers were predicted to exceed the level of concern for all three compounds: 54% for azinphos methyl, 5% for acetamiprid, and 20% for emamectin benzoate. This finding has implications for pesticide risk assessment and offers an alternative procedure that may be more protective of those at the extremes of exposure than the current approach.     

Perception of Climate Risk among Rural Farmers in Vietnam: Consistency within Households and with the Empirical Record

Rural farmers in Vietnamese communes perceive climate risk and potential impacts on livelihood within a complex context that may influence individual and household decisions. In a primary survey of 1,145 residents of the Thach Ha district of Ha Tinh province, we gathered data regarding perception about stability in climate, potential risks to livelihood, demographic characteristics, orientation toward risk, and interest in expanding economic activity. Temporal analysis of meteorological and economic indicator data forms an empirical basis for comparison with human perception. We ask the basic question: Are rural farmers’ perceptions of climate consistent with the historical record and reproducible within households? We find that respondents do perceive climate anomalies, with some anchoring on recent extreme events as revealed by climate observational data, and further that spouses disproportionately share perceptions relative to randomly simulated pairings. To put climate‐related risk perception in a larger context, we examine patterns across a range of risks to livelihood faced by farmers (livestock disease, pests, markets, health), using dimension reduction techniques. We find that our respondents distinguish among potential causes of low economic productivity, with substantial emphasis on climate‐related impacts. They do not express uniform concern across risks, but rather average patterns reveal common modes and distinguish climate concern. Still, among those expressing concern about climate‐related risks to livelihood we do not find an association with expressed intention to pursue changes in economic activity as a risk management response.     

Bayesian Hierarchical Structure for Quantifying Population Variability to Inform Probabilistic Health Risk Assessments

Human variability is a very important factor considered in human health risk assessment for protecting sensitive populations from chemical exposure. Traditionally, to account for this variability, an interhuman uncertainty factor is applied to lower the exposure limit. However, using a fixed uncertainty factor rather than probabilistically accounting for human variability can hardly support probabilistic risk assessment advocated by a number of researchers; new methods are needed to probabilistically quantify human population variability. We propose a Bayesian hierarchical model to quantify variability among different populations. This approach jointly characterizes the distribution of risk at background exposure and the sensitivity of response to exposure, which are commonly represented by model parameters. We demonstrate, through both an application to real data and a simulation study, that using the proposed hierarchical structure adequately characterizes variability across different populations.     

Building a Human Health Risk Assessment Ontology (RsO): A Proposed Framework

Over the last decade the health and environmental research communities have made significant progress in collecting and improving access to genomic, toxicology, exposure, health, and disease data useful to health risk assessment. One of the barriers to applying these growing volumes of information in fields such as risk assessment is the lack of informatics tools to organize, curate, and evaluate thousands of journal publications and hundreds of databases to provide new insights on relationships among exposure, hazard, and disease burden. Many fields are developing ontologies as a way of organizing and analyzing large amounts of complex information from multiple scientific disciplines. Ontologies include a vocabulary of terms and concepts with defined logical relationships to each other. Building from the recently published exposure ontology and other relevant health and environmental ontologies, this article proposes an ontology for health risk assessment (RsO) that provides a structural framework for organizing risk assessment information and methods. The RsO is anchored by eight major concepts that were either identified by exploratory curations of the risk literature or the exposure‐ontology working group as key for describing the risk assessment domain. These concepts are: (1) stressor, (2) receptor, (3) outcome, (4) exposure event, (5) dose‐response approach, (6) dose‐response metric, (7) uncertainty, and (8) measure of risk. We illustrate the utility of these concepts for the RsO with example curations of published risk assessments for ionizing radiation, arsenic in drinking water, and persistent pollutants in salmon.     

Peak Exposures in Epidemiologic Studies and Cancer Risks: Considerations for Regulatory Risk Assessment

We review approaches for characterizing “peak” exposures in epidemiologic studies and methods for incorporating peak exposure metrics in dose–response assessments that contribute to risk assessment. The focus was on potential etiologic relations between environmental chemical exposures and cancer risks. We searched the epidemiologic literature on environmental chemicals classified as carcinogens in which cancer risks were described in relation to “peak” exposures. These articles were evaluated to identify some of the challenges associated with defining and describing cancer risks in relation to peak exposures. We found that definitions of peak exposure varied considerably across studies. Of nine chemical agents included in our review of peak exposure, six had epidemiologic data used by the U.S. Environmental Protection Agency (US EPA) in dose–response assessments to derive inhalation unit risk values. These were benzene, formaldehyde, styrene, trichloroethylene, acrylonitrile, and ethylene oxide. All derived unit risks relied on cumulative exposure for dose–response estimation and none, to our knowledge, considered peak exposure metrics. This is not surprising, given the historical linear no‐threshold default model (generally based on cumulative exposure) used in regulatory risk assessments. With newly proposed US EPA rule language, fuller consideration of alternative exposure and dose–response metrics will be supported. “Peak” exposure has not been consistently defined and rarely has been evaluated in epidemiologic studies of cancer risks. We recommend developing uniform definitions of “peak” exposure to facilitate fuller evaluation of dose response for environmental chemicals and cancer risks, especially where mechanistic understanding indicates that the dose response is unlikely linear and that short‐term high‐intensity exposures increase risk.     

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.     

Probabilistic Framework for the Estimation of the Adult and Child Toxicokinetic Intraspecies Uncertainty Factors

Human health risk assessments use point values to develop risk estimates and thus impart a deterministic character to risk, which, by definition, is a probability phenomenon. The risk estimates are calculated based on individuals and then, using uncertainty factors (UFs), are extrapolated to the population that is characterized by variability. Regulatory agencies have recommended the quantification of the impact of variability in risk assessments through the application of probabilistic methods. In the present study, a framework that deals with the quantitative analysis of uncertainty (U) and variability (V) in target tissue dose in the population was developed by applying probabilistic analysis to physiologically-based toxicokinetic models. The mechanistic parameters that determine kinetics were described with probability density functions (PDFs). Since each PDF depicts the frequency of occurrence of all expected values of each parameter in the population, the combined effects of multiple sources of U/V were accounted for in the estimated distribution of tissue dose in the population, and a unified (adult and child) intraspecies toxicokinetic uncertainty factor UFH-TK was determined. The results show that the proposed framework accounts effectively for U/V in population toxicokinetics. The ratio of the 95th percentile to the 50th percentile of the annual average concentration of the chemical at the target tissue organ (i.e., the UFH-TK) varies with age. The ratio is equivalent to a unified intraspecies toxicokinetic UF, and it is one of the UFs by which the NOAEL can be divided to obtain the RfC/RfD. The 10-fold intraspecies UF is intended to account for uncertainty and variability in toxicokinetics (3.2x) and toxicodynamics (3.2x). This article deals exclusively with toxicokinetic component of UF. The framework provides an alternative to the default methodology and is advantageous in that the evaluation of toxicokinetic variability is based on the distribution of the effective target tissue dose, rather than applied dose. It allows for the replacement of the default adult and children intraspecies UF with toxicokinetic data-derived values and provides accurate chemical-specific estimates for their magnitude. It shows that proper application of probability and toxicokinetic theories can reduce uncertainties when establishing exposure limits for specific compounds and provide better assurance that established limits are adequately protective. It contributes to the development of a probabilistic noncancer risk assessment framework and will ultimately lead to the unification of cancer and noncancer risk assessment methodologies.     

Wildfire Risk Transmission in the Colorado Front Range,USA

Wildfires are a global phenomenon that in some circumstances can result in human casualties, economic loss, and ecosystem service degradation. In this article we spatially identify wildfire risk transmission pathways and locate the areas of highest exposure of human populations to wildland fires under severe, but not uncommon, weather events. We quantify varying levels of exposure in terms of population potentially affected and tie the exposure back to the spatial source of the risk for the Front Range of Colorado, USA. We use probabilistic fire simulation modeling to address where fire ignitions are most likely to cause the highest impact to human communities, and to explore the role that various landowners play in that transmission of risk. Our results indicated that, given an ignition and the right fire weather conditions, large areas along the Front Range in Colorado could be exposed to wildfires with high potential to impact human populations, and that overall private ignitions have the potential to impact more people than federal ignitions. These results can be used to identify high‐priority areas for wildfire risk mitigation using various mitigation tools.     

A Tiered Approach for Risk‐Benefit Assessment of Foods

Risk‐benefit analyses are introduced as a new paradigm for old problems. However, in many cases it is not always necessary to perform a full comprehensive and expensive quantitative risk‐benefit assessment to solve the problem, nor is it always possible, given the lack of required date. The choice to continue from a more qualitative to a full quantitative risk‐benefit assessment can be made using a tiered approach. In this article, this tiered approach for risk‐benefit assessment will be addressed using a decision tree. The tiered approach described uses the same four steps as the risk assessment paradigm: hazard and benefit identification, hazard and benefit characterization, exposure assessment, and risk‐benefit characterization, albeit in a different order. For the purpose of this approach, the exposure assessment has been moved upward and the dose‐response modeling (part of hazard and benefit characterization) is moved to a later stage. The decision tree includes several stop moments, depending on the situation where the gathered information is sufficient to answer the initial risk‐benefit question. The approach has been tested for two food ingredients. The decision tree presented in this article is useful to assist on a case‐by‐case basis a risk‐benefit assessor and policymaker in making informed choices when to stop or continue with a risk‐benefit assessment.     

Harnessing the Theoretical Foundations of the Exponential and Beta‐Poisson Dose‐Response Models to Quantify Parameter Uncertainty Using Markov Chain Monte Carlo

Dose‐response models are the essential link between exposure assessment and computed risk values in quantitative microbial risk assessment, yet the uncertainty that is inherent to computed risks because the dose‐response model parameters are estimated using limited epidemiological data is rarely quantified. Second‐order risk characterization approaches incorporating uncertainty in dose‐response model parameters can provide more complete information to decisionmakers by separating variability and uncertainty to quantify the uncertainty in computed risks. Therefore, the objective of this work is to develop procedures to sample from posterior distributions describing uncertainty in the parameters of exponential and beta‐Poisson dose‐response models using Bayes's theorem and Markov Chain Monte Carlo (in OpenBUGS). The theoretical origins of the beta‐Poisson dose‐response model are used to identify a decomposed version of the model that enables Bayesian analysis without the need to evaluate Kummer confluent hypergeometric functions. Herein, it is also established that the beta distribution in the beta‐Poisson dose‐response model cannot address variation among individual pathogens, criteria to validate use of the conventional approximation to the beta‐Poisson model are proposed, and simple algorithms to evaluate actual beta‐Poisson probabilities of infection are investigated. The developed MCMC procedures are applied to analysis of a case study data set, and it is demonstrated that an important region of the posterior distribution of the beta‐Poisson dose‐response model parameters is attributable to the absence of low‐dose data. This region includes beta‐Poisson models for which the conventional approximation is especially invalid and in which many beta distributions have an extreme shape with questionable plausibility.