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.     

Risk of Illness with Salmonella due to Consumption of Raw Unwashed Vegetables Irrigated with Water from the Bogotá River

The Bogotá River receives untreated wastewater from the city of Bogotá and many other towns. Downstream from Bogotá, water from the river is used for irrigation of crops. Concentrations of indicator organisms in the river are high, which is consistent with fecal contamination. To investigate the probability of illness due to exposure to enteric pathogens from the river, specifically Salmonella, we took water samples from the Bogotá River at six sampling locations in an area where untreated water from the river is used for irrigation of lettuce, broccoli, and cabbage. Salmonella concentrations were quantified by direct isolation and qPCR. Concentrations differed, depending on the quantification technique used, ranging between 10^7.7 and 10^9.9 number of copies of gene invA per L and 10^5.3 and 10^8.4 CFU/L, for qPCR and direct isolation, respectively. A quantitative microbial risk assessment model that estimates the daily risk of illness with Salmonella resulting from consuming raw unwashed vegetables irrigated with water from the Bogotá River was constructed using the Salmonella concentration data. The daily probability of illness from eating raw unwashed vegetables ranged between 0.62 and 0.85, 0.64 and 0.86, and 0.64 and 0.85 based on concentrations estimated by qPCR (0.47–0.85, 0.47–0.86, and 0.41–0.85 based on concentrations estimated by direct isolation) for lettuce, cabbage, and broccoli, respectively, which are all above the commonly propounded benchmark of 10^?4 per year. Results obtained in this study highlight the necessity for appropriate wastewater treatment in the region, and emphasize the importance of postharvest practices, such as washing, disinfecting, and cooking.     

Application of a QMRA Framework to Inform Selection of Drinking Water Interventions in the Developing Context

The aim of this study was to develop a modified quantitative microbial risk assessment (QMRA) framework that could be applied as a decision support tool to choose between alternative drinking water interventions in the developing context. The impact of different household water treatment (HWT) interventions on the overall incidence of diarrheal disease and disability adjusted life years (DALYs) was estimated, without relying on source water pathogen concentration as the starting point for the analysis. A framework was developed and a software tool constructed and then implemented for an illustrative case study for Nepal based on published scientific data. Coagulation combined with free chlorine disinfection provided the greatest estimated health gains in the short term; however, when long‐term compliance was incorporated into the calculations, the preferred intervention was porous ceramic filtration. The model demonstrates how the QMRA framework can be used to integrate evidence from different studies to inform management decisions, and in particular to prioritize the next best intervention with respect to estimated reduction in diarrheal incidence. This study only considered HWT interventions; it is recognized that a systematic consideration of sanitation, recreation, and drinking water pathways is important for effective management of waterborne transmission of pathogens, and the approach could be expanded to consider the broader water‐related context.     

Inferring an Augmented Bayesian Network to Confront a Complex Quantitative Microbial Risk Assessment Model with Durability Studies: Application to Bacillus Cereus on a Courgette Purée Production Chain

The Monte Carlo (MC) simulation approach is traditionally used in food safety risk assessment to study quantitative microbial risk assessment (QMRA) models. When experimental data are available, performing Bayesian inference is a good alternative approach that allows backward calculation in a stochastic QMRA model to update the experts’ knowledge about the microbial dynamics of a given food‐borne pathogen. In this article, we propose a complex example where Bayesian inference is applied to a high‐dimensional second‐order QMRA model. The case study is a farm‐to‐fork QMRA model considering genetic diversity of Bacillus cereus in a cooked, pasteurized, and chilled courgette purée. Experimental data are Bacillus cereus concentrations measured in packages of courgette purées stored at different time‐temperature profiles after pasteurization. To perform a Bayesian inference, we first built an augmented Bayesian network by linking a second‐order QMRA model to the available contamination data. We then ran a Markov chain Monte Carlo (MCMC) algorithm to update all the unknown concentrations and unknown quantities of the augmented model. About 25% of the prior beliefs are strongly updated, leading to a reduction in uncertainty. Some updates interestingly question the QMRA model.     

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.