Sensitivity Analysis for Critical Control Points Determination and Uncertainty Analysis to Link FSO and Process Criteria: Application to Listeria monocytogenes in Soft Cheese Made from Pasteurized Milk

Microbiological food safety is an important economic and health issue in the context of globalization and presents food business operators with new challenges in providing safe foods. The hazard analysis and critical control point approach involve identifying the main steps in food processing and the physical and chemical parameters that have an impact on the safety of foods. In the risk‐based approach, as defined in the Codex Alimentarius, controlling these parameters in such a way that the final products meet a food safety objective (FSO), fixed by the competent authorities, is a big challenge and of great interest to the food business operators. Process risk models, issued from the quantitative microbiological risk assessment framework, provide useful tools in this respect. We propose a methodology, called multivariate factor mapping (MFM), for establishing a link between process parameters and compliance with a FSO. For a stochastic and dynamic process risk model of in soft cheese made from pasteurized milk with many uncertain inputs, multivariate sensitivity analysis and MFM are combined to (i) identify the critical control points (CCPs) for throughout the food chain and (ii) compute the critical limits of the most influential process parameters, located at the CCPs, with regard to the specific process implemented in the model. Due to certain forms of interaction among parameters, the results show some new possibilities for the management of microbiological hazards when a FSO is specified.     

Risk‐Based Approach for Microbiological Food Safety Management in the Dairy Industry: The Case of Listeria monocytogenes in Soft Cheese Made from Pasteurized Milk

According to Codex Alimentarius Commission recommendations, management options applied at the process production level should be based on good hygiene practices, HACCP system, and new risk management metrics such as the food safety objective. To follow this last recommendation, the use of quantitative microbiological risk assessment is an appealing approach to link new risk‐based metrics to management options that may be applied by food operators. Through a specific case study, Listeria monocytogenes in soft cheese made from pasteurized milk, the objective of the present article is to practically show how quantitative risk assessment could be used to direct potential intervention strategies at different food processing steps. Based on many assumptions, the model developed estimates the risk of listeriosis at the moment of consumption taking into account the entire manufacturing process and potential sources of contamination. From pasteurization to consumption, the amplification of a primo‐contamination event of the milk, the fresh cheese or the process environment is simulated, over time, space, and between products, accounting for the impact of management options, such as hygienic operations and sampling plans. A sensitivity analysis of the model will help orientating data to be collected prioritarily for the improvement and the validation of the model. What‐if scenarios were simulated and allowed for the identification of major parameters contributing to the risk of listeriosis and the optimization of preventive and corrective measures.     

Food Safety Objectives Should Integrate the Variability of the Concentration of Pathogen

The World Trade Organization introduced the concept of appropriate level of protection (ALOP) as a public health target. For this public health objective to be interpretable by the actors in the food chain, the concept of food safety objective (FSO) was proposed by the International Commission on Microbiological Specifications for Foods and adopted later by the Codex Alimentarius Food Hygiene Committee. The way to translate an ALOP into a FSO is still in debate. The purpose of this article is to develop a methodological tool to derive a FSO from an ALOP being expressed as a maximal annual marginal risk. We explore the different models relating the annual marginal risk to the parameters of the FSO depending on whether the variability in the survival probability and in the concentration of the pathogen are considered or not. If they are not, determination of the FSO is straightforward. If they are, we propose to use stochastic Monte Carlo simulation models and logistic discriminant analysis in order to determine which sets of parameters are compatible with the ALOP. The logistic discriminant function was chosen such that the kappa coefficient is maximized. We illustrate this method by the example of the risks of listeriosis and salmonellosis in one type of soft cheese. We conclude that the definition of the FSO should integrate three dimensions: the prevalence of contamination, the average concentration per contaminated typical serving, and the dispersion of the concentration among those servings.     

Bayesian Versus Frequentist Approach of the Frailty Cox Model,Application to Calf Gastroenteritis

In the frailty Cox model, frequentist approaches often present problems of numerical resolution, convergence, and variance calculation. The Bayesian approach offers an alternative. The goal of this study was to compare, using real (calf gastroenteritis) and simulated data, the results obtained with the MCMC method used in the Bayesian approach versus two frequentist approaches: the Newton–Raphson algorithm to solve a penalized likelihood and the EM algorithm. The results obtained showed that when the number of groups in the population decreases, the Bayesian approach gives a less biased estimation of the frailty variance and of the group fixed effect than the frequentist approaches.     

Risk Assessment of Listeriosis Linked to the Consumption of Two Soft Cheeses Made from Raw Milk: Camembert of Normandy and Brie of Meaux

This article reports a quantitative risk assessment of human listeriosis linked to the consumption of soft cheeses made from raw milk. Risk assessment was based on data purposefully acquired inclusively over the period 2000-2001 for two French cheeses, namely: Camembert of Normandy and Brie of Meaux. Estimated Listeria monocytogenes concentration in raw milk was on average 0.8 and 0.3 cells/L, respectively, in Normandy and Brie regions. A Monte Carlo simulation was used to account for the time-temperature history of the milk and cheeses from farm to table. It was assumed that cell progeny did not spread within the solid cheese matrix (as they would be free to do in liquid broth). Interaction between pH and temperature was accounted for in the growth model. The simulated proportion of servings with no L. monocytogenes cell was 88% for Brie and 82% for Camembert. The 99th percentile of L. monocytogenes cell numbers in servings of 27 g of cheese was 131 for Brie and 77 for Camembert at the time of consumption, corresponding respectively to three and five cells of L. monocytogenes per gram. The expected number of severe listeriosis cases would be < or =10(-3) and < or =2.5 x 10(-3) per year for 17 million servings of Brie of Meaux and 480 million servings of Camembert of Normandy, respectively.     

Quantitative Risk Assessment of Haemolytic and Uremic Syndrome Linked to O157:H7 and Non‐O157:H7 Shiga‐Toxin Producing Escherichia coli Strains in Raw Milk Soft Cheeses

Shiga‐toxin producing Escherichia coli (STEC) strains may cause human infections ranging from simple diarrhea to Haemolytic Uremic Syndrome (HUS). The five main pathogenic serotypes of STEC (MPS‐STEC) identified thus far in Europe are O157:H7, O26:H11, O103:H2, O111:H8, and O145:H28. Because STEC strains can survive or grow during cheese making, particularly in soft cheeses, a stochastic quantitative microbial risk assessment model was developed to assess the risk of HUS associated with the five MPS‐STEC in raw milk soft cheeses. A baseline scenario represents a theoretical worst‐case scenario where no intervention was considered throughout the farm‐to‐fork continuum. The risk level assessed with this baseline scenario is the risk‐based level. The impact of seven preharvest scenarios (vaccines, probiotic, milk farm sorting) on the risk‐based level was expressed in terms of risk reduction. Impact of the preharvest intervention ranges from 76% to 98% of risk reduction with highest values predicted with scenarios combining a decrease of the number of cow shedding STEC and of the STEC concentration in feces. The impact of postharvest interventions on the risk‐based level was also tested by applying five microbiological criteria (MC) at the end of ripening. The five MCs differ in terms of sample size, the number of samples that may yield a value larger than the microbiological limit, and the analysis methods. The risk reduction predicted varies from 25% to 96% by applying MCs without preharvest interventions and from 1% to 96% with combination of pre‐ and postharvest interventions.     

Stochastic, Compartmental, and Dynamic Modeling of Cross-Contamination During Mechanical Smearing of Cheeses

Cheese smearing is a complex process and the potential for cross-contamination with pathogenic or undesirable microorganisms is critical. During ripening, cheeses are salted and washed with brine to develop flavor and remove molds that could develop on the surfaces. Considering the potential for cross-contamination of this process in quantitative risk assessments could contribute to a better understanding of this phenomenon and, eventually, improve its control. The purpose of this article is to model the cross-contamination of smear-ripened cheeses due to the smearing operation under industrial conditions. A compartmental, dynamic, and stochastic model is proposed for mechanical brush smearing. This model has been developed to describe the exchange of microorganisms between compartments. Based on the analytical solution of the model equations and on experimental data collected with an industrial smearing machine, we assessed the values of the transfer parameters of the model. Monte Carlo simulations, using the distributions of transfer parameters, provide the final number of contaminated products in a batch and their final level of contamination for a given scenario taking into account the initial number of contaminated cheeses of the batch and their contaminant load. Based on analytical results, the model provides indicators for smearing efficiency and propensity of the process for cross-contamination. Unlike traditional approaches in mechanistic models, our approach captures the variability and uncertainty inherent in the process and the experimental data. More generally, this model could represent a generic base to use in modeling similar processes prone to cross-contamination.     

Positivity of bid-ask spreads and symmetrical monotone risk aversion*

A usual argument in finance refers to no arbitrage opportunities for the positivity of the bid-ask spread. Here we follow the decision theory approach and show that if positivity of the bid-ask spread is identified with strong risk aversion for an expected utility market-maker, this is no longer true for a rank-dependent expected utility one. For such a decision-maker only a very weak form of risk aversion is required, a result which seems more in accordance with his actual behavior. We conclude by showing that the no-trade interval result of Dow and Werlang (1992a) remains valid for a rank-dependent expected utility market-maker merely exhibiting this weak form of risk aversion.     

Bayesian and fiducial inference for the inverse gaussian distribution via Gibbs sampler

This paper presents a kernel estimation of the distribution of the scale parameter of the inverse Gaussian distribution under type II censoring together with the distribution of the remaining time. Estimation is carried out via the Gibbs sampling algorithm combined with a missing data approach. Estimates and confidence intervals for the parameters of interest are also presented.     

Two-Term Edgeworth Expansions for the Classes of U- and V-statistics

Much effort has been devoted to deriving Edgeworth expansions for various classes of statistics that are asymptotically normally distributed, with derivations tailored to the individual structure of each class. Expansions with smaller error rates are needed for more accurate statistical inference. Two such Edgeworth expansions are derived analytically in this paper. One is a two-term expansion for the standardized U-statistic of order m, m ? 3, with an error rate o(n^{? 1}). The other is an expansion with the same error rate for the distribution of the standardized V-statistic of the same order. In deriving the Edgeworth expansion, we made use of the close connection between the V- and U-statistics, which permits to first derive the needed expansion for the related U-statistic, then extend it to the V-statistic, taking into consideration the estimation of all difference terms between the two statistics.