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.     

The Impact of Consumer Phase Models in Microbial Risk Analysis

In quantitative microbiological risk assessment (QMRA), the consumer phase model (CPM) describes the part of the food chain between purchase of the food product at retail and exposure. Construction of a CPM is complicated by the large variation in consumer food handling practices and a limited availability of data. Therefore, several subjective (simplifying) assumptions have to be made when a CPM is constructed, but with a single CPM their impact on the QMRA results is unclear. We therefore compared the performance of eight published CPMs for Campylobacter in broiler meat in an example of a QMRA, where all the CPMs were analyzed using one single input distribution of concentrations at retail, and the same dose‐response relationship. It was found that, between CPMs, there may be a considerable difference in the estimated probability of illness per serving. However, the estimated relative risk reductions are less different for scenarios modeling the implementation of control measures. For control measures affecting the Campylobacter prevalence, the relative risk is proportional irrespective of the CPM used. However, for control measures affecting the concentration the CPMs show some difference in the estimated relative risk. This difference is largest for scenarios where the aim is to remove the highly contaminated portion from human exposure. Given these results, we conclude that for many purposes it is not necessary to develop a new detailed CPM for each new QMRA. However, more observational data on consumer food handling practices and their impact on microbial transfer and survival are needed to generalize this conclusion.     

A Practical Framework for the Construction of a Biotracing Model: Application to Salmonella in the Pork Slaughter Chain

A novel purpose of the use of mathematical models in quantitative microbial risk assessment (QMRA) is to identify the sources of microbial contamination in a food chain (i.e., biotracing). In this article we propose a framework for the construction of a biotracing model, eventually to be used in industrial food production chains where discrete numbers of products are processed that may be contaminated by a multitude of sources. The framework consists of steps in which a Monte Carlo model, simulating sequential events in the chain following a modular process risk modeling (MPRM) approach, is converted to a Bayesian belief network (BBN). The resulting model provides a probabilistic quantification of concentrations of a pathogen throughout a production chain. A BBN allows for updating the parameters of the model based on observational data, and global parameter sensitivity analysis is readily performed in a BBN. Moreover, a BBN enables “backward reasoning” when downstream data are available and is therefore a natural framework for answering biotracing questions. The proposed framework is illustrated with a biotracing model of Salmonella in the pork slaughter chain, based on a recently published Monte Carlo simulation model. This model, implemented as a BBN, describes the dynamics of Salmonella in a Dutch slaughterhouse and enables finding the source of contamination of specific carcasses at the end of the chain.     

A Quantitative Microbial Risk Assessment Model for Legionnaires'' Disease: Animal Model Selection and Dose-Response Modeling

Legionnaires' disease (LD), first reported in 1976, is an atypical pneumonia caused by bacteria of the genus Legionella, and most frequently by L. pneumophila (Lp). Subsequent research on exposure to the organism employed various animal models, and with quantitative microbial risk assessment (QMRA) techniques, the animal model data may provide insights on human dose-response for LD. This article focuses on the rationale for selection of the guinea pig model, comparison of the dose-response model results, comparison of projected low-dose responses for guinea pigs, and risk estimates for humans. Based on both in vivo and in vitro comparisons, the guinea pig (Cavia porcellus) dose-response data were selected for modeling human risk. We completed dose-response modeling for the beta-Poisson (approximate and exact), exponential, probit, logistic, and Weibull models for Lp inhalation, mortality, and infection (end point elevated body temperature) in guinea pigs. For mechanistic reasons, including low-dose exposure probability, further work on human risk estimates for LD employed the exponential and beta-Poisson models. With an exposure of 10 colony-forming units (CFU) (retained dose), the QMRA model predicted a mild infection risk of 0.4 (as evaluated by seroprevalence) and a clinical severity LD case (e.g., hospitalization and supportive care) risk of 0.0009. The calculated rates based on estimated human exposures for outbreaks used for the QMRA model validation are within an order of magnitude of the reported LD rates. These validation results suggest the LD QMRA animal model selection, dose-response modeling, and extension to human risk projections were appropriate.     

Quantitative Risk Assessment of Listeria monocytogenes in French Cold-Smoked Salmon: II. Risk Characterization

A model for the assessment of exposure to Listeria monocytogenes from cold-smoked salmon consumption in France was presented in the first of this pair of articles (Pouillot et al ., 2007, Risk Analysis, 27:683–700). In the present study, the exposure model output was combined with an internationally accepted hazard characterization model, adapted to the French situation, to assess the risk of invasive listeriosis from cold-smoked salmon consumption in France in a second-order Monte Carlo simulation framework. The annual number of cases of invasive listeriosis due to cold-smoked salmon consumption in France is estimated to be 307, with a very large credible interval ([10; 12,453]), reflecting data uncertainty. This uncertainty is mainly associated with the dose-response model. Despite the significant uncertainty associated with the predictions, this model provides a scientific base for risk managers and food business operators to manage the risk linked to cold-smoked salmon contaminated with L. monocytogenes. Under the modeling assumptions, risk would be efficiently reduced through a decrease in the prevalence of L. monocytogenes or better control of the last steps of the cold chain (shorter and/or colder storage during the consumer step), whereas reduction of the initial contamination levels of the contaminated products and improvement in the first steps of the cold chain do not seem to be promising strategies. An attempt to apply the recent risk-based concept of FSO (food safety objective) on this example underlines the ambiguity in practical implementation of the risk management metrics and the need for further elaboration on these concepts.     

Quantitative microbiological risk assessment of nontyphoidal Salmonella in ground pork in households in Chengdu,China

Foodborne disease caused by nontyphoidal Salmonella (NTS) is one of the most important food safety issues worldwide. The objectives of this study were to carry out microbial monitoring on the prevalence of NTS in commercial ground pork, investigate consumption patterns, and conduct a quantitative microbiological risk assessment (QMRA) that considers cross-contamination to determine the risk caused by consuming ground pork and ready-to-eat food contaminated during food handling in the kitchen in Chengdu, China. The food pathway of ground pork was simplified and assumed to be several units according to the actual situation and our survey data, which were collected from our research or references and substituted into the QMRA model for simulation. The results showed that the prevalence of NTS in ground pork purchased in Chengdu was 69.64% (95% confidence interval [CI], 60.2–78.0), with a mean contamination level of −0.164 log CFU/g. After general cooking, NTS in ground pork could be eliminated (contamination level of zero). The estimated probability of causing salmonellosis per day was 9.43E-06 (95% CI: 8.82E-06–1.00E-05), while the estimated salmonellosis cases per million people per year were 3442 (95% CI: 3218–3666). According to the sensitivity analysis, the occurrence of cross-contamination was the most important factor affecting the probability of salmonellosis. To reduce the risk of salmonellosis caused by NTS through ground pork consumption, reasonable hygiene prevention and control measures should be adopted during food preparation to reduce cross-contamination. This study provides valuable information for household cooking and food safety management in China.     

Classification of Listeria monocytogenes Persistence in Retail Delicatessen Environments Using Expert Elicitation and Machine Learning

Increasing evidence suggests that persistence of Listeria monocytogenes in food processing plants has been the underlying cause of a number of human listeriosis outbreaks. This study extracts criteria used by food safety experts in determining bacterial persistence in the environment, using retail delicatessen operations as a model. Using the Delphi method, we conducted an expert elicitation with 10 food safety experts from academia, industry, and government to classify L. monocytogenes persistence based on environmental sampling results collected over six months for 30 retail delicatessen stores. The results were modeled using variations of random forest, support vector machine, logistic regression, and linear regression; variable importance values of random forest and support vector machine models were consolidated to rank important variables in the experts’ classifications. The duration of subtype isolation ranked most important across all expert categories. Sampling site category also ranked high in importance and validation errors doubled when this covariate was removed. Support vector machine and random forest models successfully classified the data with average validation errors of 3.1% and 2.2% (n = 144), respectively. Our findings indicate that (i) the frequency of isolations over time and sampling site information are critical factors for experts determining subtype persistence, (ii) food safety experts from different sectors may not use the same criteria in determining persistence, and (iii) machine learning models have potential for future use in environmental surveillance and risk management programs. Future work is necessary to validate the accuracy of expert and machine classification against biological measurement of L. monocytogenes persistence.     

Development of a Quantitative Microbial Risk Assessment for Human Salmonellosis Through Household Consumption of Fresh Minced Pork Meat in Belgium

A quantitative microbial risk assessment (QMRA) according to the Codex Alimentarius Principles is conducted to evaluate the risk of human salmonellosis through household consumption of fresh minced pork meat in Belgium. The quantitative exposure assessment is carried out by building a modular risk model, called the METZOON-model, which covers the pork production from farm to fork. In the METZOON-model, the food production pathway is split up in six consecutive modules: (1) primary production, (2) transport and lairage, (3) slaughterhouse, (4) postprocessing, (5) distribution and storage, and (6) preparation and consumption. All the modules are developed to resemble as closely as possible the Belgian situation, making use of the available national data. Several statistical refinements and improved modeling techniques are proposed. The model produces highly realistic results. The baseline predicted number of annual salmonellosis cases is 20,513 ( SD 9061.45). The risk is estimated higher for the susceptible population (estimate  4.713 × 10⁻⁵; SD 1.466 × 10⁻⁵  ) compared to the normal population  (estimate 7.704 × 10⁻⁶; SD 5.414 × 10⁻⁶)  and is mainly due to undercooking and to a smaller extent to cross-contamination in the kitchen via cook's hands.     

Framework for Evaluation of Physiologically-Based Pharmacokinetic Models for Use in Safety or Risk Assessment

Proposed applications of increasingly sophisticated biologically-based computational models, such as physiologically-based pharmacokinetic models, raise the issue of how to evaluate whether the models are adequate for proposed uses, including safety or risk assessment. A six-step process for model evaluation is described. It relies on multidisciplinary expertise to address the biological, toxicological, mathematical, statistical, and risk assessment aspects of the modeling and its application. The first step is to have a clear definition of the purpose(s) of the model in the particular assessment; this provides critical perspectives on all subsequent steps. The second step is to evaluate the biological characterization described by the model structure based on the intended uses of the model and available information on the compound being modeled or related compounds. The next two steps review the mathematical equations used to describe the biology and their implementation in an appropriate computer program. At this point, the values selected for the model parameters (i.e., model calibration) must be evaluated. Thus, the fifth step is a combination of evaluating the model parameterization and calibration against data and evaluating the uncertainty in the model outputs. The final step is to evaluate specialized analyses that were done using the model, such as modeling of population distributions of parameters leading to population estimates for model outcomes or inclusion of early pharmacodynamic events. The process also helps to define the kinds of documentation that would be needed for a model to facilitate its evaluation and implementation.     

厚尾分布情形下的信用资产组合风险度量

本文研究风险因子多元厚尾分布情形下的信用资产组合风险度量问题.用多元t-Copula分布来描述标的资产收益率分布的厚尾性,同时将三步重要抽样技术发展到基多元t-Copula分布的资产组合模型中,拓宽和丰富了信用资产组合风险度量模型.同时,并运用了非线性优化技术中的Levenberg-Marquardt算法来解决重要抽样技术中风险因子期望向量估计.模拟结果表明该算法比普通Monte Carlo模拟法的计算效率更有效,且能很大程度上减少所要估计的损失概率的方差,从而更精确地估计出信用投资组合损失分布的尾部概率或给定置信度下组合VaR值.     

Probabilistic Modeling of the Fate of Listeria Monocytogenes in Diced Bacon During the Manufacturing Process

To assess the impact of the manufacturing process on the fate of Listeria monocytogenes, we built a generic probabilistic model intended to simulate the successive steps in the process. Contamination evolution was modeled in the appropriate units (breasts, dice, and then packaging units through the successive steps in the process). To calibrate the model, parameter values were estimated from industrial data, from the literature, and based on expert opinion. By means of simulations, the model was explored using a baseline calibration and alternative scenarios, in order to assess the impact of changes in the process and of accidental events. The results are reported as contamination distributions and as the probability that the product will be acceptable with regards to the European regulatory safety criterion. Our results are consistent with data provided by industrial partners and highlight that tumbling is a key step for the distribution of the contamination at the end of the process. Process chain models could provide an important added value for risk assessment models that basically consider only the outputs of the process in their risk mitigation strategies. Moreover, a model calibrated to correspond to a specific plant could be used to optimize surveillance.     

Advice to Risk Assessors Modeling Viral Health Risk Associated with Household Graywater

Quantitative microbial risk assessment (QMRA) is a valuable tool that can be used to predict the risk associated with human exposure to specific microbial contaminants in water sources. The transparency inherent in the QMRA process benefits discussions between multidisciplinary teams because members of such teams have different expertise and their confidence in the risk assessment output will depend upon whether they regard the selected input data and assumptions as being suitable and/or plausible. Selection of input data requires knowledge of the availability of appropriate data sets, the limitations of using a particular data set, and the logic of using alternative approaches. In performing QMRA modeling and in the absence of directly relevant data, compromises must be made. One such compromise made is to use available Escherichia coli data and apply a ratio of enteric viruses to indicator E. coli in wastewater obtained from prior studies to estimate the concentration of enteric viruses in other wastewater types/sources. In this article, we have provided an argument for why we do not recommend the use of a pathogen to E. coli ratio to estimate virus concentrations in single household graywater and additionally suggested circumstances in which use of such a ratio may be justified.     

NUSAP Method for Evaluating the Data Quality in a Quantitative Microbial Risk Assessment Model for Salmonella in the Pork Production Chain

The numeral unit spread assessment pedigree (NUSAP) system was implemented to evaluate the quality of input parameters in a quantitative microbial risk assessment (QMRA) model for Salmonella spp. in minced pork meat. The input parameters were grouped according to four successive exposure pathways: (1) primary production (2) transport, holding, and slaughterhouse, (3) postprocessing, distribution, and storage, and (4) preparation and consumption. An inventory of 101 potential input parameters was used for building the QMRA model. The characteristics of each parameter were defined using a standardized procedure to assess (1) the source of information, (2) the sampling methodology and sample size, and (3) the distributional properties of the estimate. Each parameter was scored by a panel of experts using a pedigree matrix containing four criteria (proxy, empirical basis, method, and validation) to assess the quality, and this was graphically represented by means of kite diagrams. The parameters obtained significantly lower scores for the validation criterion as compared with the other criteria. Overall strengths of parameters related to the primary production module were significantly stronger compared to the other modules (the transport, holding, and slaughterhouse module, the processing, distribution, and storage module, and the preparation and consumption module). The pedigree assessment contributed to select 20 parameters, which were subsequently introduced in the QMRA model. The NUSAP methodology and kite diagrams are objective tools to discuss and visualize the quality of the parameters in a structured way. These two tools can be used in the selection procedure of input parameters for a QMRA, and can lead to a more transparent quality assurance in the QMRA.     

Framework for Microbial Food‐Safety Risk Assessments Amenable to Bayesian Modeling

Regulatory agencies often perform microbial risk assessments to evaluate the change in the number of human illnesses as the result of a new policy that reduces the level of contamination in the food supply. These agencies generally have regulatory authority over the production and retail sectors of the farm‐to‐table continuum. Any predicted change in contamination that results from new policy that regulates production practices occurs many steps prior to consumption of the product. This study proposes a framework for conducting microbial food‐safety risk assessments; this framework can be used to quantitatively assess the annual effects of national regulatory policies. Advantages of the framework are that estimates of human illnesses are consistent with national disease surveillance data (which are usually summarized on an annual basis) and some of the modeling steps that occur between production and consumption can be collapsed or eliminated. The framework leads to probabilistic models that include uncertainty and variability in critical input parameters; these models can be solved using a number of different Bayesian methods. The Bayesian synthesis method performs well for this application and generates posterior distributions of parameters that are relevant to assessing the effect of implementing a new policy. An example, based on Campylobacter and chicken, estimates the annual number of illnesses avoided by a hypothetical policy; this output could be used to assess the economic benefits of a new policy. Empirical validation of the policy effect is also examined by estimating the annual change in the numbers of illnesses observed via disease surveillance systems.     

Validation of Quantitative Microbial Risk Assessment Using Epidemiological Data from Outbreaks of Waterborne Gastrointestinal Disease

The assumptions underlying quantitative microbial risk assessment (QMRA) are simple and biologically plausible, but QMRA predictions have never been validated for many pathogens. The objective of this study was to validate QMRA predictions against epidemiological measurements from outbreaks of waterborne gastrointestinal disease. I screened 2,000 papers and identified 12 outbreaks with the necessary data: disease rates measured using epidemiological methods and pathogen concentrations measured in the source water. Eight of the 12 outbreaks were caused by Cryptosporidium, three by Giardia, and one by norovirus. Disease rates varied from 5.5 × 10^?6 to 1.1 × 10^?2 cases/person‐day, and reported pathogen concentrations varied from 1.2 × 10^?4 to 8.6 × 10² per liter. I used these concentrations with single‐hit dose–response models for all three pathogens to conduct QMRA, producing both point and interval predictions of disease rates for each outbreak. Comparison of QMRA predictions to epidemiological measurements showed good agreement; interval predictions contained measured disease rates for 9 of 12 outbreaks, with point predictions off by factors of 1.0–120 (median = 4.8). Furthermore, 11 outbreaks occurred at mean doses of less than 1 pathogen per exposure. Measured disease rates for these outbreaks were clearly consistent with a single‐hit model, and not with a “two‐hit” threshold model. These results demonstrate the validity of QMRA for predicting disease rates due to Cryptosporidium and Giardia.     

Consumer Trust in Food Safety—A Multidisciplinary Approach and Empirical Evidence from Taiwan

Food scandals that happened in recent years have increased consumers' risk perceptions of foods and decreased their trust in food safety. A better understanding of the consumer trust in food safety can improve the effectiveness of public policy and allow the development of the best practice in risk communication. This study proposes a research framework from a psychometric approach to investigate the relationships between the consumer's trust in food safety and the antecedents of risk perceptions of foods based on a reflexive modernization perspective and a cultural theory perspective in the hope of benefiting the future empirical study. The empirical results from a structural equation modeling analysis of Taiwan as a case in point reveal that this research framework based on a multidisciplinary perspective can be a valuable tool for a growing understanding of consumer trust in food safety. The antecedents in the psychometric research framework comprised reflexive modernization factors and cultural theory factors have all been supported in this study except the consumer's perception of pessimism toward food. Moreover, the empirical results of repeated measures analysis of variance give more detailed information to grasp empirical implications and to provide some suggestions to the actors and institutions involved in the food supply chain in Taiwan.     

Modeling Individual Cell Lag Time Distributions for Listeria monocytogenes

The food industry faces two paradoxical demands: on the one hand, foods need to be microbiologically safe for consumption and on the other hand, consumers want fresh, minimally processed foods. To meet these demands, more insight into the mechanisms of microbial growth is needed, which includes, among others, the microbial lag phase. This is the time needed by bacterial cells to adapt to a new environment (for example, after food product contamination) before starting an exponential growth regime. Since food products are often contaminated with low amounts of pathogenic microorganisms, it is important to know the distribution of these individual cell lag times to make accurate predictions concerning food safety. More precisely, cells with the shortest lag times (i.e., appearing in the left tail of the distribution) are largely decisive for the outgrowth of the population. In this study, an integrated modeling approach is proposed and applied to an existing data set of individual cell lag time measurements of Listeria monocytogenes. In a first step, a logistic modeling approach is applied to predict the fraction of zero-lag cells (which start growing immediately) as a function of temperature, pH, and water activity. For the nonzero-lag cells, the mean and variance of the lag time distribution are modeled with a hyperbolic-type model structure. This mean and variance allow identification of the parameters of a two-parameter Weibull distribution, representing the nonzero-lag cell lag time distribution. The integration of the developed models allows prediction of a global distribution of individual cell lag times for any combination of environmental conditions in the interpolation domain of the original temperature, pH, and water activity settings. The global fitting quality of the model is quantified using several measures indicating that the model gives accurate predictions, erring slightly on the fail-safe side when predicting the shortest lag times.     

Cross-Contamination During Food Preparation: A Mechanistic Model Applied to Chicken-Borne Campylobacter

We develop a model for bacterial cross-contamination during food preparation in the domestic kitchen and apply this to the case of Campylobacter-contaminated chicken breast. Building blocks of the model are the routines performed during food preparation, with their associated probabilities of bacterial transfer between food items and kitchen utensils. The model is used in a quantitative microbiological risk assessment (QMRA) of Campylobacter in the Netherlands. Using parameter values from the literature and performing elementary sensitivity analyses, we show that cross-contamination can contribute significantly to the risk of Campylobacter infection and find that cleaning frequency of kitchen utensils and thoroughness of rinsing of raw food items after preparation has more impact on cross-contamination than previously emphasized. Furthermore, we argue that especially more behavioral data on hygiene during food preparation is needed for a comprehensive Campylobacter risk assessment.     

Understanding Consumer Confidence in the Safety of Food: Its Two-Dimensional Structure and Determinants

Understanding of the determinants of consumer confidence in the safety of food is important if effective risk management and communication are to be developed. In the research reported here, we attempt to understand the roles of consumer trust in actors in the food chain and regulators, consumer recall of food safety incidents, consumer perceptions regarding the safety of particular product groups, personality characteristics, and sociodemographics, as potential determinants of consumer confidence in the safety of food. Consumer confidence in the safety of food was conceptualized as consisting of two distinct dimensions, namely, "optimism" and "pessimism." On the basis of a representative sample of 657 Dutch consumers, structural equation modeling was applied to simultaneously estimate the effect of the determinants on both "optimism" and "pessimism." The results indicated that, to a considerable extent, both optimism and pessimism about the safety of food arise from consumer trust in regulators and actors in the food chain and the perceived safety of meat and fish rather than other product categories. In addition, support was found for the notion that optimism and pessimism are conceptually distinct, as these dimensions of confidence were partly influenced by different determinants. The results of this study imply that consumer confidence in the safety of food could be enhanced by improving both consumer trust in societal actors, and consumer safety perceptions of particular product groups.