beta-Poisson Dose-response Model Research Articles

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.

A quantitative risk assessment model for Vibrio parahaemolyticus in raw oysters in Sao Paulo State, Brazil

A risk assessment of Vibrio parahaemolyticus associated with raw oysters produced and consumed in São Paulo State was developed. The model was built according to the United States Food and Drug Administration framework for risk assessment. The outcome of the exposure assessment estimated the prevalence and density of pathogenic V. parahaemolyticus in raw oysters from harvest to consumption. The result of the exposure step was combined with a Beta–Poisson dose–response model to estimate the probability of illness. The model predicted that the average risks per serving of raw oysters were 4.7×10−4, 6.0×10−4, 4.7×10−4 and 3.1×10−4 for spring, summer, fall and winter, respectively. Sensitivity analyses indicated that the most influential variables on the risk of illness were the total density of V. parahaemolyticus at harvest, transport temperature, relative prevalence of pathogenic strains and storage time at retail. Only storage time under refrigeration at retail showed negative correlation with the risk of illness.

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.

From the Editors

From the Editors

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.

Dose-response time modelling for highly pathogenic avian influenza A (H5N1) virus infection

Aims: To develop time‐dependent dose–response models for highly pathogenic avian influenza A (HPAI) of the H5N1 subtype virus. Methods and Results: A total of four candidate time‐dependent dose–response models were fitted to four survival data sets for animals (mice or ferrets) exposed to graded doses of HPAI H5N1 virus using the maximum‐likelihood estimation. A beta‐Poisson dose–response model with the N 50 parameter modified by an exponential‐inverse‐power time dependency or an exponential dose–response model with the k parameter modified by an exponential‐inverse time dependency provided a statistically adequate fit to the observed survival data. Conclusions: We have successfully developed the time‐dependent dose–response models to describe the mortality of animals exposed to an HPAI H5N1 virus. The developed model describes the mortality over time and represents observed experimental responses accurately. Significance and Impact of the Study: This is the first study describing time‐dependent dose–response models for HPAI H5N1 virus. The developed models will be a useful tool for estimating the mortality of HPAI H5N1 virus, which may depend on time postexposure, for the preparation of a future influenza pandemic caused by this lethal virus.

A Model for In-vivo Delivered Dose Estimation for Inhaled Bacillus anthracis Spores in Humans with Interspecies Extrapolation

The quantitative yardstick for quantitative microbial risk assessment (QMRA) is the dose response assessment phase. In this phase of the QMRA paradigm a mathematical model is used to describe the relationship between host response (infection, disease, etc.) and pathogen dose. There are, however, key uncertainties which if addressed can expand our understanding of the dose response relationship and improve its accuracy. The dose response models most frequently used in this phase of QMRA are based on the average exposed dose (i.e., inhaled, ingested, etc.). However once inhaled, spores are considered infectious after being transported to a specific region of the lungs (alveoli), therefore, average exposed dose does not account for this required spore transport through the respiratory system. It is the aim of this manuscript to develop a model for the in vivo delivered dose to the alveolated region of the lungs that accounts for losses of spores through the respiratory system. A stochastic system is used to account for the physics in the respiratory system that account for the various sinks during respiration. This stochastic system is then integrated into the exponential and beta Poisson dose response models. The stochastic model is also then expanded to the respiratory systems of guinea pigs and rhesus macaques as these are common animal models. This work develops a framework for a new class of dose response models accounting for host physiology, making progress to understanding dose response heterogeneity among hosts.

Consumption of raw vegetables and fruits: A risk factor for Campylobacter infections

The purpose of this study was to determine the prevalence of Campylobacter in fresh vegetables and fruits at retail level in the Netherlands, and to estimate its implications on the importance of vegetables and fruits as risk factor for campylobacteriosis.Thirteen of the 5640 vegetable and fruit samples were Campylobacter positive, resulting in a prevalence of 0.23% (95% confidence interval (Cl): 0.12–0.39%). The prevalence of packaged products (0.36%, 95% Cl: 0.17–0.66) was significantly higher than of unpackaged products (0.07; 95% Cl: 0.01–0.27). No statistical differences were found between seasons.Combining the mean prevalence found in this study with data on the consumption of vegetables and fruits, an exposure of 0.0048 campylobacters ingested per person per day in the Netherlands by transmission via vegetables and fruits, was calculated. This exposure, as input in a Beta-Poisson dose–response model, resulted in an estimated number of 5.3×105 cases of infection with Campylobacter per year for the whole Dutch population. This constitutes the consumption of raw vegetables and fruits, especially when packaged, to be a risk factor for Campylobacter infections.

Dose‐Response Model of Coxiella burnetii (Q Fever)

Q fever is a zoonotic disease caused by the intracellular gram-negative bacterium Coxiella burnetii (C. burnetii), which only multiplies within the phagolysosomal vacuoles. Q fever may manifest as acute or chronic disease. The acute form is generally not fatal and manifestes as self-controlled febrile illness. Chronic Q fever is usually characterized by endocarditis. Many animal models, including humans, have been studied for Q fever infection through various exposure routes. The studies considered different endpoints including death for animal models and clinical signs for human infection. In this article, animal experimental data available in the open literature were fit to suitable dose-response models using maximum likelihood estimation. Research results for tests of severe combined immunodeficient mice inoculated intraperitoneally (i.p.) with C. burnetii were best estimated with the Beta-Poisson dose-response model. Similar inoculation (i.p.) trial outcomes conducted on C57BL/6J mice were best fit by an exponential model, whereas those tests run on C57BL/10ScN mice were optimally represented by a Beta-Poisson dose-response model.

Quantitative Risk Assessment of Vibrio parahaemolyticus in Finfish: A Model of Raw Horse Mackerel Consumption in Japan

The aim of this study was to evaluate the effects of implemented control measures to reduce illness induced by Vibrio parahaemolyticus (V. parahaemolyticus) in horse mackerel (Trachurus japonicus), seafood that is commonly consumed raw in Japan. On the basis of currently available experimental and survey data, we constructed a quantitative risk model of V. parahaemolyticus in horse mackerel from harvest to consumption. In particular, the following factors were evaluated: bacterial growth at all stages, effects of washing the fish body and storage water, and bacterial transfer from the fish surface, gills, and intestine to fillets during preparation. New parameters of the beta-Poisson dose-response model were determined from all human feeding trials, some of which have been used for risk assessment by the U.S. Food and Drug Administration (USFDA). The probability of illness caused by V. parahaemolyticus was estimated using both the USFDA dose-response parameters and our parameters for each selected pathway of scenario alternatives: washing whole fish at landing, storage in contaminated water, high temperature during transportation, and washing fish during preparation. The last scenario (washing fish during preparation) was the most effective for reducing the risk of illness by about a factor of 10 compared to no washing at this stage. Risk of illness increased by 50% by exposure to increased temperature during transportation, according to our assumptions of duration and temperature. The other two scenarios did not significantly affect risk. The choice of dose-response parameters was not critical for evaluation of control measures.

Quantification of the Effects of Age on the Dose Response of Variola major in Suckling Mice

ABSTRACT Dose-response data for Variola major (V. major), the causative agent of smallpox, were obtained from the open literature, summarized, and fitted with three dose-response models. It is known from prior outbreak experience that there is generally a difference in infectivity of the agent and its subsequent mortality depending on the age of the patient. A source of animal dose-response data were found with age delineation for the exposure group (suckling mice, intraperitoneal exposure). This delineation was used to adapt current dose-response models to include an age dependency parameter. The degree of the models' fit to the data was ascertained using maximum likelihood estimation (MLE). The effect of host age could be described quantitatively using modifications to the beta Poisson and exponential dose-response models. The modifications improvement in the accuracy of risk prediction by 72% for the beta Poisson model and 7% for the exponential model, compared to the original (unmodified) models.

Time‐Dose‐Response Models for Microbial Risk Assessment

While microbial risk assessment (MRA) has been used for over 25 years, traditional dose-response analysis has only predicted the overall risk of adverse consequences from exposure to a given dose. An important issue for consequence assessment from bioterrorist and other microbiological exposure is the distribution of cases over time due to the initial exposure. In this study, the classical exponential and beta-Poisson dose-response models were modified to include exponential-power dependency of time post inoculation (TPI) or its simplified form, exponential-reciprocal dependency of TPI, to quantify the time of onset of an effect presumably associated with the kinetics of in vivo bacterial growth. Using the maximum likelihood estimation approach, the resulting time-dose-response models were found capable of providing statistically acceptable fits to all tested pooled animal survival dose-response data. These new models can consequently describe the development of animal infectious response over time and represent observed responses fairly accurately. This is the first study showing that a time-dose-response model can be developed for describing infections initiated by various pathogens. It provides an advanced approach for future MRA frameworks.

Dose‐Response Models for Inhalation of Bacillus anthracis Spores: Interspecies Comparisons

Because experiments with Bacillus anthracis are costly and dangerous, the scientific, public health, and engineering communities are served by thorough collation and analysis of experiments reported in the open literature. This study identifies available dose-response data from the open literature for inhalation exposure to B. anthracis and, via dose-response modeling, characterizes the response of nonhuman animal models to challenges. Two studies involving four data sets amenable to dose-response modeling were found in the literature: two data sets of response of guinea pigs to intranasal dosing with the Vollum and ATCC-6605 strains, one set of responses of rhesus monkeys to aerosol exposure to the Vollum strain, and one data set of guinea pig response to aerosol exposure to the Vollum strain. None of the data sets exhibited overdispersion and all but one were best fit by an exponential dose-response model. The beta-Poisson dose-response model provided the best fit to the remaining data set. As indicated in prior studies, the response to aerosol challenges is a strong function of aerosol diameter. For guinea pigs, the LD(50) increases with aerosol size for aerosols at and above 4.5 mum. For both rhesus monkeys and guinea pigs there is about a 15-fold increase in LD(50) when aerosol size is increased from 1 mum to 12 mum. Future experimental research and dose-response modeling should be performed to quantify differences in responses of subpopulations to B. anthracis and to generate data allowing development of interspecies correction factors.

Quantitative modeling for risk assessment of Vibrio parahaemolyticus in bloody clams in southern Thailand

A risk assessment of Vibrio parahaemolyticus in bloody clams ( Anadara granosa) consumed in southern Thailand was conducted. This study estimated the prevalence and concentration of pathogenic V. parahaemolyticus in bloody clams at harvest and retail stages; and during this process, methods to detect the total and pathogenic V. parahaemolyticus were investigated. Consumption of bloody clams and cooking efficiency were studied using interviews and onsite observation of consumers. A beta-Poisson dose–response model was used to estimate probability of illness applying estimation methods for the most likely parameter values presented by USFDA. Microbial and behavioral data were analyzed by developing a stochastic model and the simulation gave a mean number of times a person would get ill with V. parahaemolyticus by consuming bloody clams at 5.6 × 10 − 4 /person/year. Sensitivity analysis demonstrated the fraction of people who did not boil the clams properly was the primary factor in increasing risk. This study serves as an example of how a microbiological risk assessment with limited data collection and international cooperation leads to valuable local insight.

Hierarchical dose response of E. coli O157:H7 from human outbreaks incorporating heterogeneity in exposure

The infectivity of pathogenic microorganisms is a key factor in the transmission of an infectious disease in a susceptible population. Microbial infectivity is generally estimated from dose-response studies in human volunteers. This can only be done with mildly pathogenic organisms. Here a hierarchical Beta-Poisson dose-response model is developed utilizing data from human outbreaks. On the lowest level each outbreak is modelled separately and these are then combined at a second level to produce a group dose-response relation. The distribution of foodborne pathogens often shows strong heterogeneity and this is incorporated by introducing an additional parameter to the dose-response model, accounting for the degree of overdispersion relative to Poisson distribution. It was found that heterogeneity considerably influences the shape of the dose-response relationship and increases uncertainty in predicted risk. This uncertainty is greater than previously reported surrogate and outbreak models using a single level of analysis. Monte Carlo parameter samples (alpha, beta of the Beta-Poisson model) can be readily incorporated in risk assessment models built using tools such as S-plus and @ Risk.

Evaluation of a real-time Taqman® PCR method for assessment of pathogenic coliform contamination in sediment: A risk-based approach

Management of contaminated sediments has focused predominately on chemical agents, overshadowing risks posed by pathogenic microorganisms. Current accepted bacterial indicator methods do not provide defensible data with respect to the occurrence and types of pathogens in sediments. In an effort to adapt new defensible methods for assessing the risk posed by pathogens in sediments, we evaluated the sensitivity of a commercially available real-time polymerase chain reaction TaqMan® Escherichia coli 0157:H7detection kit. The lower limit of linear quantitation of this assay was experimentally determined in sediment and sediment extract samples spiked with known amounts of E. coli 0157:H7 DNA. Parallel control experiments were conducted in pure water samples spiked with known amounts of Escherichia coli 0157:H7 DNA. The lower limit of quantification of the TaqMan® assay was 1000 colony forming units when interrogating 100 mg sediment samples. In contrast, the assay was 20-fold more sensitive with a lower limit of quantification of 50 colony forming units in pure water and sediment extract samples. These results suggest that the sensitivity of the TaqMan® Escherichia coli 0157:H7detection kit is more dependent on recovery of the desired target from the sediment matrix than efficiency of polymerase chain reaction amplification. The potential human health risk associated with the lower limit of quantification of the TaqMan® assay in the spiked sediment samples was estimated using a Beta-Poisson dose-response model. Using this approach, lower limit values corresponded to exposure levels of Escherichia coli 0157:H7 that meet United States Environmental Protection Agency accepted illness rates for recreational swimming.

Quantitative risk assessment of human campylobacteriosis associated with thermophilic Campylobacter species in chickens

A quantitative risk assessment comprising the elements hazard identification, hazard characterization, exposure assessment, and risk characterization has been prepared to assess the effect of different mitigation strategies on the number of human cases in Denmark associated with thermophilic Campylobacter spp. in chickens. To estimate the human exposure to Campylobacter from a chicken meal and the number of human cases associated with this exposure, a mathematical risk model was developed. The model details the spread and transfer of Campylobacter in chickens from slaughter to consumption and the relationship between ingested dose and the probability of developing campylobacteriosis. Human exposure was estimated in two successive mathematical modules. Module 1 addresses changes in prevalence and numbers of Campylobacter on chicken carcasses throughout the processing steps of a slaughterhouse. Module 2 covers the transfer of Campylobacter during food handling in private kitchens. The age and sex of consumers were included in this module to introduce variable hygiene levels during food preparation and variable sizes and compositions of meals. Finally, the outcome of the exposure assessment modules was integrated with a Beta–Poisson dose–response model to provide a risk estimate. Simulations designed to predict the effect of different mitigation strategies showed that the incidence of campylobacteriosis associated with consumption of chicken meals could be reduced 30 times by introducing a 2 log reduction of the number of Campylobacter on the chicken carcasses. To obtain a similar reduction of the incidence, the flock prevalence should be reduced approximately 30 times or the kitchen hygiene improved approximately 30 times. Cross-contamination from positive to negative flocks during slaughter had almost no effect on the human Campylobacter incidence, which indicates that implementation of logistic slaughter will only have a minor influence on the risk. Finally, the simulations showed that people in the age of 18–29 years had the highest risk of developing campylobacteriosis.

Quantitative risk assessment of human salmonellosis from the consumption of a turkey product in collective catering establishments

The quantitative risk assessment (QRA) approach recommended by the Codex Alimentarius Commission was used to assess the risk of human salmonellosis from the consumption of ‘cordon bleu’, a specific turkey product, in collective catering establishments (CCEs) of a French department. The complete process was modeled and simulated, from the initial storage in the CCE freezer to the consumption, using a Monte Carlo simulation software. Data concerning the prevalence of contaminated ‘cordon bleu’, the level of contamination of Salmonella, the cooking and storage process were collected from 21 CCEs and 8 retailers of ‘cordon bleu’ in the selected department. Thermal inactivation kinetics for Salmonella were established to estimate the effect of heat treatment on the concentration in the product and to calculate the dose that could be ingested by the consumer. The Beta-Poisson dose-response model of Rose and Gerba [Water Science and Technology 24 (1991) 29] with the specific parameters for Salmonella was used to estimate the probability of infection related to the ingestion of a particular dose and a factor was applied to estimate the probability of illness from ingestion. The individual risk of salmonellosis, the risk of outbreak and the number of cases were calculated using Monte Carlo simulation method. The risk of salmonellosis was close to zero when the ‘cordons bleus’ were cooked in the oven. Therefore, the risk was calculated for the fryer cooking since the insufficient cooking time observed was, sometimes, at the origin of low temperatures (37–89 °C). The influence of both the initial concentration of Salmonella in the product and the heat storage before consumption on the final risk was studied. For a high initial concentration of Salmonella in the product, when the ‘cordons bleus’ are fryer cooked, the average risk of salmonellosis was equal to 3.95×10 −3 without storage before consumption and 2.8×10 −4 if the product is consumed after storage. This paper presents the results of the QRA and discusses risk management options to minimize the risk of salmonellosis.

Dose-response envelope for Escherichia coli O157:H7.

Escherichia coli O157:H7 is an emerging food and waterborne pathogen in the U.S. and internationally. The objective of this work was to develop a dose-response model for illness by this organism that bounds the uncertainty in the dose-response relationship. No human clinical trial data are available for E. coli O157:H7, but such data are available for two surrogate pathogens: enteropathogenic E. coli (EPEC) and Shigella dysenteriae. E. coli O157:H7 outbreak data provide an initial estimate of the most likely value of the dose-response relationship within the bounds of an envelope defined by beta-Poisson dose-response models fit to the EPEC and S. dysenteriae data. The most likely value of the median effective dose for E. coli O157:H7 is estimated to be approximately 190[emsp4 ]000 colony forming units (cfu). At a dose level of 100[emsp4 ]cfu, the median response predicted by the model is six percent.

Development and Validation of Dose-Response Relationship for Listeria monocytogenes

Listeria monocytogenes is a foodborne pathogen internationally and in the U.S. The objective of this work was to develop and validate a dose-response model for infection by this organism. Only animal data was available in the literature. The beta-Poisson dose response model provided good fit to the data, and one of the two data sets was found to be concordant with attack rates noted in human outbreaks. There are differences, however, between the dose-response relationship and endemic illness rates computed from “market basket” surveys of the prevalence of L. monocytogenes. Further work to elucidate the bases for this difference is necessary.