Jean-Baptiste Denis

Estimation of uncertainty and variability in bacterial growth using Bayesian inference. Application to Listeria monocytogenes.

The usefulness of risk assessment is limited by its ability or inability to model and evaluate risk uncertainty and variability separately. A key factor of variability and uncertainty in microbial risk assessment could be growth variability between strains and growth model parameter uncertainty. In this paper, we propose a Bayesian procedure for growth parameter estimation which makes it possible to separate these two components by means of hyperparameters. This model incorporates in a single step the logistic equation with delay as a primary growth model and the cardinal temperature equation as a secondary growth model. The estimation of Listeria monocytogenes growth parameters in milk using literature data is proposed as a detailed application. While this model should be applied on genuine data, it is highlighted that the proposed approach may be convenient for estimating the variability and uncertainty of growth parameters separately, using a complete predictive microbiology model.

Modelling expectation and variance for genotype by environment data

An integration of two types of models for the analysis of genotype by environment interaction is presented. On the one hand, the expectation of G × E interaction is frequently modelled by regression models; on the other hand, for deviations from these regressions, either separate stability parameters are defined or extra components of variance are introduced. A class of mixed models is described that contains facilities for modelling expectation by regression and, in addition, has extensive possibilities for dealing with heteroscedasticity. Practical aspects of the use of these mixed models are illustrated on a data set involving sugar yield in beet.

Infectivity of GI and GII noroviruses established from oyster related outbreaks

Noroviruses (NoVs) are the major cause of acute epidemic gastroenteritis in industrialized countries. Outbreak strains are predominantly genogroup II (GII) NoV, but genogroup I (GI) strains are regularly found in oyster related outbreaks. The prototype Norwalk virus (GI), has been shown to have high infectivity in a human challenge study. Whether other NoVs are equally infectious via natural exposure remains to be established. Human susceptibility to NoV is partly determined by the secretor status (Se+/-). Data from five published oyster related outbreaks were analyzed in a Bayesian framework. Infectivity estimates where high and consistent with NV(GI) infectivity, for both GII and GI strains. The median and CI95 probability of infection and illness, in Se+ subjects, associated with exposure to a mean of one single NoV genome copy were around 0.29[0.015-0.61] for GI and 0.4[0.04-0.61] for GII, and for illness 0.13[0.007-0.39] for GI and 0.18[0.017-0.42] for GII. Se- subjects were strongly protected against infection. The high infectivity estimates for Norwalk virus GI and GII, makes NoVs critical target for food safety regulations.

Asymptotic confidence regions for biadditive models : Interpreting genotype-environment interactions

An understanding of how genotypes of an agricultural crop interact with the environment in which they are grown is important for assessing plant production. A breeding trial for 21 genotypes of rye-grass grown at seven locations is used to illustrate the interpretation of genotype-environment interactions. Statisticians have proposed many ways of modelling these interactions, but a subclass of bilinear models, that we term biadditive, fits especially well. We emphasize assessing and interpreting the interaction parameters of biadditive models by constructing confidence regions in biplot representations. When a biadditive model is valid, this new development underpins better informed decisions on variety recom- mendation and genotype selection.

Analysing genotype by environment interaction in Dutch potato variety trials using factorial regression

SummaryGenotype by environment interaction was investigated for yield data from the official Dutch Variety List trials for potato. The data set included 64 genotypes by 26 environments, where environments consisted of year by soil type combinations. Factorial regression models incorporating genotypic and environmental covariates in the interaction were used to analyse the data. The merits of factorial regression models were compared with those of biadditive models. Factorial regression models and biadditive models described comparable amounts of interaction, but factorial regression models provided a better basis for biological interpreration of the interaction.

A meta-analysis accounting for sources of variability to estimate heat resistance reference parameters of bacteria using hierarchical Bayesian modeling: Estimation of D at 121.1 °C and pH 7, zT and zpH of Geobacillus stearothermophilus

Predicting microbial survival requires reference parameters for each micro-organism of concern. When data are abundant and publicly available, a meta-analysis is a useful approach for assessment of these parameters, which can be performed with hierarchical Bayesian modeling. Geobacillus stearothermophilus is a major agent of microbial spoilage of canned foods and is therefore a persistent problem in the food industry. The thermal inactivation parameters of G. stearothermophilus (D(ref), i.e.the decimal reduction time D at the reference temperature 121.1°C and pH 7.0, z(T) and z(pH)) were estimated from a large set of 430 D values mainly collected from scientific literature. Between-study variability hypotheses on the inactivation parameters D(ref), z(T) and z(pH) were explored, using three different hierarchical Bayesian models. Parameter estimations were made using Bayesian inference and the models were compared with a graphical and a Bayesian criterion. Results show the necessity to account for random effects associated with between-study variability. Assuming variability on D(ref), z(T) and z(pH), the resulting distributions for D(ref), z(T) and z(pH) led to a mean of 3.3 min for D(ref) (95% Credible Interval CI=[0.8; 9.6]), to a mean of 9.1°C for z(T) (CI=[5.4; 13.1]) and to a mean of 4.3 pH units for z(pH) (CI=[2.9; 6.3]), in the range pH 3 to pH 7.5. Results are also given separating variability and uncertainty in these distributions, as well as adjusted parametric distributions to facilitate further use of these results in aqueous canned foods such as canned vegetables.

Uncertainty Distribution Associated with Estimating a Proportion in Microbial Risk Assessment

The uncertainty associated with estimates should be taken into account in quantitative risk assessment. Each inputs uncertainty can be characterized through a probabilistic distribution for use under Monte Carlo simulations. In this study, the sampling uncertainty associated with estimating a low proportion on the basis of a small sample size was considered. A common application in microbial risk assessment is the estimation of a prevalence, proportion of contaminated food products, on the basis of few tested units. Three Bayesian approaches (based on beta(0, 0), beta(1/2, 1/2), and beta(l, 1)) and one frequentist approach (based on the frequentist confidence distribution) were compared and evaluated on the basis of simulations. For small samples, we demonstrated some differences between the four tested methods. We concluded that the better method depends on the true proportion of contaminated products, which is by definition unknown in common practice. When no prior information is available, we recommend the beta (1/2, 1/2) prior or the confidence distribution. To illustrate the importance of these differences, the four methods were used in an applied example. We performed two-dimensional Monte Carlo simulations to estimate the proportion of cold smoked salmon packs contaminated by Listeria monocytogenes, one dimension representing within-factory uncertainty, modeled by each of the four studied methods, and the other dimension representing variability between companies.

Predicting cultivar differences using covariates.

In plant breeding, multilocation trials form the major means for the comparative evaluation of cultivars. Based on such trials, recommendations may be given to farmers. Commonly, cultivars that did best on average are recommended for all locations. However, the intended growing region can be ecologically heterogeneous and cultivarlocation interactions can be substantial. As a result, the cultivar with the largest mean is not generally the best in all locations of the region. When information is available on the response of a cultivar to varying environmental conditions, cultivar-location interactions can be (partly) predicted, thus allowing for more specific recommendations. This article discusses a regression-based approach for predicting cultivar performances using covariate information on locations such as average rainfall and soil type. Special emphasis is given to the selection of covariates useful for prediction. The mean squared error of prediction is used as a selection criterion.

Stochastically Modeling Listeria Monocytogenes Growth in Farm Tank Milk

This article presents a Listeria monocytogenes growth model in milk at the farm bulk tank stage. The main objective was to judge the feasibility and value to risk assessors of introducing a complex model, including a complete thermal model, within a microbial quantitative risk assessment scheme. Predictive microbiology models are used under varying temperature conditions to predict bacterial growth. Input distributions are estimated based on data in the literature, when it is available. If not, reasonable assumptions are made for the considered context. Previously published results based on a Bayesian analysis of growth parameters are used. A Monte Carlo simulation that forecasts bacterial growth is the focus of this study. Three scenarios that take account of the variability and uncertainty of growth parameters are compared. The effect of a sophisticated thermal model taking account of continuous variations in milk temperature was tested by comparison with a simplified model where milk temperature was considered as constant. Limited multiplication of bacteria within the farm bulk tank was modeled. The two principal factors influencing bacterial growth were found to be tank thermostat regulation and bacterial population growth parameters. The dilution phenomenon due to the introduction of new milk was the main factor affecting the final bacterial concentration. The results show that a model that assumes constant environmental conditions at an average temperature should be acceptable for this process. This work may constitute a first step toward exposure assessment for L. monocytogenes in milk. In addition, this partly conceptual work provides guidelines for other risk assessments where continuous variation of a parameter needs to be taken into account.

A Bayesian Evidence Synthesis for Estimating Campylobacteriosis Prevalence

Stakeholders making decisions in public health and world trade need improved estimations of the burden-of-illness of foodborne infectious diseases. In this article, we propose a Bayesian meta-analysis or more precisely a Bayesian evidence synthesis to assess the burden-of-illness of campylobacteriosis in France. Using this case study, we investigate campylobacteriosis prevalence, as well as the probabilities of different events that guide the disease pathway, by (i) employing a Bayesian approach on French and foreign human studies (from active surveillance systems, laboratory surveys, physician surveys, epidemiological surveys, and so on) through the chain of events that occur during an episode of illness and (ii) including expert knowledge about this chain of events. We split the target population using an exhaustive and exclusive partition based on health status and the level of disease investigation. We assume an approximate multinomial model over this population partition. Thereby, each observed data set related to the partition brings information on the parameters of the multinomial model, improving burden-of-illness parameter estimates that can be deduced from the parameters of the basic multinomial model. This multinomial model serves as a core model to perform a Bayesian evidence synthesis. Expert knowledge is introduced by way of pseudo-data. The result is a global estimation of the burden-of-illness parameters with their accompanying uncertainty.