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.     

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.     

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.     

Cryptosporidium Infection Risk: Results of New Dose‐Response Modeling

Cryptosporidium human dose‐response data from seven species/isolates are used to investigate six models of varying complexity that estimate infection probability as a function of dose. Previous models attempt to explicitly account for virulence differences among C. parvum isolates, using three or six species/isolates. Four (two new) models assume species/isolate differences are insignificant and three of these (all but exponential) allow for variable human susceptibility. These three human‐focused models (fractional Poisson, exponential with immunity and beta‐Poisson) are relatively simple yet fit the data significantly better than the more complex isolate‐focused models. Among these three, the one‐parameter fractional Poisson model is the simplest but assumes that all Cryptosporidium oocysts used in the studies were capable of initiating infection. The exponential with immunity model does not require such an assumption and includes the fractional Poisson as a special case. The fractional Poisson model is an upper bound of the exponential with immunity model and applies when all oocysts are capable of initiating infection. The beta Poisson model does not allow an immune human subpopulation; thus infection probability approaches 100% as dose becomes huge. All three of these models predict significantly (>10x) greater risk at the low doses that consumers might receive if exposed through drinking water or other environmental exposure (e.g., 72% vs. 4% infection probability for a one oocyst dose) than previously predicted. This new insight into Cryptosporidium risk suggests additional inactivation and removal via treatment may be needed to meet any specified risk target, such as a suggested 10^?4 annual risk of Cryptosporidium infection.     

Development of Dose‐Response Models to Predict the Relationship for Human Toxoplasma gondii Infection Associated with Meat Consumption

Toxoplasma gondii is a protozoan parasite that is responsible for approximately 24% of deaths attributed to foodborne pathogens in the United States. It is thought that a substantial portion of human T. gondii infections is acquired through the consumption of meats. The dose‐response relationship for human exposures to T. gondii‐infected meat is unknown because no human data are available. The goal of this study was to develop and validate dose‐response models based on animal studies, and to compute scaling factors so that animal‐derived models can predict T. gondii infection in humans. Relevant studies in literature were collected and appropriate studies were selected based on animal species, stage, genotype of T. gondii, and route of infection. Data were pooled and fitted to four sigmoidal‐shaped mathematical models, and model parameters were estimated using maximum likelihood estimation. Data from a mouse study were selected to develop the dose‐response relationship. Exponential and beta‐Poisson models, which predicted similar responses, were selected as reasonable dose‐response models based on their simplicity, biological plausibility, and goodness fit. A confidence interval of the parameter was determined by constructing 10,000 bootstrap samples. Scaling factors were computed by matching the predicted infection cases with the epidemiological data. Mouse‐derived models were validated against data for the dose‐infection relationship in rats. A human dose‐response model was developed as P (d) = 1–exp (–0.0015 × 0.005 × d) or P (d) = 1–(1 + d × 0.003 / 582.414)^?1.479. Both models predict the human response after consuming T. gondii‐infected meats, and provide an enhanced risk characterization in a quantitative microbial risk assessment model for this pathogen.     

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.     

Incorporating Time‐Dose‐Response into Legionella Outbreak Models

A novel method was used to incorporate in vivo host–pathogen dynamics into a new robust outbreak model for legionellosis. Dose‐response and time‐dose‐response (TDR) models were generated for Legionella longbeachae exposure to mice via the intratracheal route using a maximum likelihood estimation approach. The best‐fit TDR model was then incorporated into two L. pneumophila outbreak models: an outbreak that occurred at a spa in Japan, and one that occurred in a Melbourne aquarium. The best‐fit TDR from the murine dosing study was the beta‐Poisson with exponential‐reciprocal dependency model, which had a minimized deviance of 32.9. This model was tested against other incubation distributions in the Japan outbreak, and performed consistently well, with reported deviances ranging from 32 to 35. In the case of the Melbourne outbreak, the exponential model with exponential dependency was tested against non‐time‐dependent distributions to explore the performance of the time‐dependent model with the lowest number of parameters. This model reported low minimized deviances around 8 for the Weibull, gamma, and lognormal exposure distribution cases. This work shows that the incorporation of a time factor into outbreak distributions provides models with acceptable fits that can provide insight into the in vivo dynamics of the host‐pathogen system.     

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.     

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.     

Bayesian Development of a Dose‐Response Model for Aspergillus fumigatus and Invasive Aspergillosis

Invasive aspergillosis (IA) is a major cause of mortality in immunocompromized hosts, most often consecutive to the inhalation of spores of Aspergillus. However, the relationship between Aspergillus concentration in the air and probability of IA is not quantitatively known. In this study, this relationship was examined in a murine model of IA. Immunosuppressed Balb/c mice were exposed for 60 minutes at day 0 to an aerosol of A. fumigatus spores (Af293 strain). At day 10, IA was assessed in mice by quantitative culture of the lungs and galactomannan dosage. Fifteen separate nebulizations with varying spore concentrations were performed. Rates of IA ranged from 0% to 100% according to spore concentrations. The dose‐response relationship between probability of infection and spore exposure was approximated using the exponential model and the more flexible beta‐Poisson model. Prior distributions of the parameters of the models were proposed then updated with data in a Bayesian framework. Both models yielded close median dose‐responses of the posterior distributions for the main parameter of the model, but with different dispersions, either when the exposure dose was the concentration in the nebulized suspension or was the estimated quantity of spores inhaled by a mouse during the experiment. The median quantity of inhaled spores that infected 50% of mice was estimated at 1.8 × 10⁴ and 3.2 × 10⁴ viable spores in the exponential and beta‐Poisson models, respectively. This study provides dose‐response parameters for quantitative assessment of the relationship between airborne exposure to the reference A. fumigatus strain and probability of IA in immunocompromized hosts.     

QMRA for Drinking Water: 2. The Effect of Pathogen Clustering in Single‐Hit Dose‐Response Models

Spatial and/or temporal clustering of pathogens will invalidate the commonly used assumption of Poisson‐distributed pathogen counts (doses) in quantitative microbial risk assessment. In this work, the theoretically predicted effect of spatial clustering in conventional “single‐hit” dose‐response models is investigated by employing the stuttering Poisson distribution, a very general family of count distributions that naturally models pathogen clustering and contains the Poisson and negative binomial distributions as special cases. The analysis is facilitated by formulating the dose‐response models in terms of probability generating functions. It is shown formally that the theoretical single‐hit risk obtained with a stuttering Poisson distribution is lower than that obtained with a Poisson distribution, assuming identical mean doses. A similar result holds for mixed Poisson distributions. Numerical examples indicate that the theoretical single‐hit risk is fairly insensitive to moderate clustering, though the effect tends to be more pronounced for low mean doses. Furthermore, using Jensen's inequality, an upper bound on risk is derived that tends to better approximate the exact theoretical single‐hit risk for highly overdispersed dose distributions. The bound holds with any dose distribution (characterized by its mean and zero inflation index) and any conditional dose‐response model that is concave in the dose variable. Its application is exemplified with published data from Norovirus feeding trials, for which some of the administered doses were prepared from an inoculum of aggregated viruses. The potential implications of clustering for dose‐response assessment as well as practical risk characterization are discussed.     

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.     

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.     

A Generalized QMRA Beta‐Poisson Dose‐Response Model

Quantitative microbial risk assessment (QMRA) is widely accepted for characterizing the microbial risks associated with food, water, and wastewater. Single‐hit dose‐response models are the most commonly used dose‐response models in QMRA. Denoting as the probability of infection at a given mean dose d, a three‐parameter generalized QMRA beta‐Poisson dose‐response model, , is proposed in which the minimum number of organisms required for causing infection, K_min, is not fixed, but a random variable following a geometric distribution with parameter . The single‐hit beta‐Poisson model, , is a special case of the generalized model with K_min = 1 (which implies ). The generalized beta‐Poisson model is based on a conceptual model with greater detail in the dose‐response mechanism. Since a maximum likelihood solution is not easily available, a likelihood‐free approximate Bayesian computation (ABC) algorithm is employed for parameter estimation. By fitting the generalized model to four experimental data sets from the literature, this study reveals that the posterior median estimates produced fall short of meeting the required condition of = 1 for single‐hit assumption. However, three out of four data sets fitted by the generalized models could not achieve an improvement in goodness of fit. These combined results imply that, at least in some cases, a single‐hit assumption for characterizing the dose‐response process may not be appropriate, but that the more complex models may be difficult to support especially if the sample size is small. The three‐parameter generalized model provides a possibility to investigate the mechanism of a dose‐response process in greater detail than is possible under a single‐hit model.     

Fractional Poisson—A Simple Dose‐Response Model for Human Norovirus

This study utilizes old and new Norovirus (NoV) human challenge data to model the dose‐response relationship for human NoV infection. The combined data set is used to update estimates from a previously published beta‐Poisson dose‐response model that includes parameters for virus aggregation and for a beta‐distribution that describes variable susceptibility among hosts. The quality of the beta‐Poisson model is examined and a simpler model is proposed. The new model (fractional Poisson) characterizes hosts as either perfectly susceptible or perfectly immune, requiring a single parameter (the fraction of perfectly susceptible hosts) in place of the two‐parameter beta‐distribution. A second parameter is included to account for virus aggregation in the same fashion as it is added to the beta‐Poisson model. Infection probability is simply the product of the probability of nonzero exposure (at least one virus or aggregate is ingested) and the fraction of susceptible hosts. The model is computationally simple and appears to be well suited to the data from the NoV human challenge studies. The model's deviance is similar to that of the beta‐Poisson, but with one parameter, rather than two. As a result, the Akaike information criterion favors the fractional Poisson over the beta‐Poisson model. At low, environmentally relevant exposure levels (<100), estimation error is small for the fractional Poisson model; however, caution is advised because no subjects were challenged at such a low dose. New low‐dose data would be of great value to further clarify the NoV dose‐response relationship and to support improved risk assessment for environmentally relevant exposures.     

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.     

Listeria monocytogenes Dose Response Revisited—Incorporating Adjustments for Variability in Strain Virulence and Host Susceptibility

Evaluations of Listeria monocytogenes dose‐response relationships are crucially important for risk assessment and risk management, but are complicated by considerable variability across population subgroups and L. monocytogenes strains. Despite difficulties associated with the collection of adequate data from outbreak investigations or sporadic cases, the limitations of currently available animal models, and the inability to conduct human volunteer studies, some of the available data now allow refinements of the well‐established exponential L. monocytogenes dose response to more adequately represent extremely susceptible population subgroups and highly virulent L. monocytogenes strains. Here, a model incorporating adjustments for variability in L. monocytogenes strain virulence and host susceptibility was derived for 11 population subgroups with similar underlying comorbidities using data from multiple sources, including human surveillance and food survey data. In light of the unique inherent properties of L. monocytogenes dose response, a lognormal‐Poisson dose‐response model was chosen, and proved able to reconcile dose‐response relationships developed based on surveillance data with outbreak data. This model was compared to a classical beta‐Poisson dose‐response model, which was insufficiently flexible for modeling the specific case of L. monocytogenes dose‐response relationships, especially in outbreak situations. Overall, the modeling results suggest that most listeriosis cases are linked to the ingestion of food contaminated with medium to high concentrations of L. monocytogenes. While additional data are needed to refine the derived model and to better characterize and quantify the variability in L. monocytogenes strain virulence and individual host susceptibility, the framework derived here represents a promising approach to more adequately characterize the risk of listeriosis in highly susceptible population subgroups.     

Statistical Approach to Identify Threshold and Point of Departure in Dose–Response Data

The study presents an integrated, rigorous statistical approach to define the likelihood of a threshold and point of departure (POD) based on dose–response data using nested family of bent‐hyperbola models. The family includes four models: the full bent‐hyperbola model, which allows for transition between two linear regiments with various levels of smoothness; a bent‐hyperbola model reduced to a spline model, where the transition is fixed to a knot; a bent‐hyperbola model with a restricted negative asymptote slope of zero, named hockey‐stick with arc (HS‐Arc); and spline model reduced further to a hockey‐stick type model (HS), where the first linear segment has a slope of zero. A likelihood‐ratio test is used to discriminate between the models and determine if the more flexible versions of the model provide better or significantly better fit than a hockey‐stick type model. The full bent‐hyperbola model can accommodate both threshold and nonthreshold behavior, can take on concave up and concave down shapes with various levels of curvature, can approximate the biochemically relevant Michaelis–Menten model, and even be reduced to a straight line. Therefore, with the use of this model, the presence or absence of a threshold may even become irrelevant and the best fit of the full bent‐hyperbola model be used to characterize the dose–response behavior and risk levels, with no need for mode of action (MOA) information. Point of departure (POD), characterized by exposure level at which some predetermined response is reached, can be defined using the full model or one of the better fitting reduced models.     

A Quantitative Microbiological Risk Assessment for Campylobacter in Petting Zoos

The significance of petting zoos for transmission of Campylobacter to humans and the effect of interventions were estimated. A stochastic QMRA model simulating a child or adult visiting a Dutch petting zoo was built. The model describes the transmission of Campylobacter in animal feces from the various animal species, fences, and the playground to ingestion by visitors through touching these so‐called carriers and subsequently touching their lips. Extensive field and laboratory research was done to fulfill data needs. Fecal contamination on all carriers was measured by swabbing in 10 petting zoos, using Escherichia coli as an indicator. Carrier‐hand and hand‐lip touching frequencies were estimated by, in total, 13 days of observations of visitors by two observers at two petting zoos. The transmission from carrier to hand and from hand to lip by touching was measured using preapplied cow feces to which E. coli WG5 was added as an indicator. Via a Beta‐Poisson dose‐response function, the number of Campylobacter cases for the whole of the Netherlands (16 million population) in a year was estimated at 187 and 52 for children and adults, respectively, so 239 in total. This is significantly lower than previous QMRA results on chicken fillet and drinking water consumption. Scenarios of 90% reduction of the contamination (meant to mimic cleaning) of all fences and just goat fences reduces the number of cases by 82% and 75%, respectively. The model can easily be adapted for other fecally transmitted pathogens.     

Nonparametric Bayesian Methods for Benchmark Dose Estimation

The article proposes and investigates the performance of two Bayesian nonparametric estimation procedures in the context of benchmark dose estimation in toxicological animal experiments. The methodology is illustrated using several existing animal dose‐response data sets and is compared with traditional parametric methods available in standard benchmark dose estimation software (BMDS), as well as with a published model‐averaging approach and a frequentist nonparametric approach. These comparisons together with simulation studies suggest that the nonparametric methods provide a lot of flexibility in terms of model fit and can be a very useful tool in benchmark dose estimation studies, especially when standard parametric models fail to fit to the data adequately.