Modeling of Clostridium perfringens vegetative cell inactivation in beef-in-sauce products: a meta-analysis using mixed linear models

The importance of what we cannot observe: Experimental limitations as a source of bias for meta-regression models in predictive microbiology

Meta-regression models have gained in popularity during the last years as a way to create more generic models for Microbial Risk Assessments that also include variability. However, as with most meta-analyses and empirical models, systematic biases in the data can result in inaccurate models. In this article, we define experimental bias as a type of selection bias due to the practical limitations of microbial inactivation experiments. Conditions with extremely high D-values (i.e. slow inactivation) need very long experimental runs to cause significant reductions. On the other hand, when the D-value is extremely low, not enough data points can be gathered before the microbial population is below the detection limit. Consequently, experimental designs favour conditions within a practical experimental range, introducing a selection bias in the D-values. We demonstrate the impact of experimental bias in meta-regression models using numerical simulations. Models fitted to data with experimental bias overestimated the z-value and underestimated variability. We propose a rapid heuristic method to identify experimental bias in datasets, and we propose truncated regression to mitigate its impact in meta-regression models. Both methods were validated using simulated data. Thereafter the procedures were tested by building a meta-regression model for actual data for the inactivation of Bacillus cereus spores. We concluded that the dataset included experimental bias, and that it would cause an overestimation of the microbial resistance at high temperatures (>120 °C) for classical meta-regression models. This effect was mitigated when the model was built using truncated regression. In conclusion, we demonstrate that experimental bias could potentially result in inaccurate models for predictive microbiology. Therefore, checking for experimental bias should be a routine step in meta-regression modelling, and be included in guidelines on data analysis for meta-regression.

The Most Probable Curve method - A robust approach to estimate kinetic models from low plate count data resulting in reduced uncertainty

A novel method is proposed for fitting microbial inactivation models to data on liquid media: the Most Probable Curve (MPC) method. It is a multilevel model that makes a separation between the "true" microbial concentration according to the model, the "actual" concentration in the media considering chance, and the actual counts on the plate. It is based on the assumptions that stress resistance is homogeneous within a microbial population, and that there is no aggregation of microbial cells. Under these assumptions, the number of colonies in/on a plate follows a Poisson distribution with expected value depending on the proposed kinetic model, the number of dilutions and the plated volume. The novel method is compared against (non)linear regression based on a normal likelihood distribution (traditional method), Poisson regression and gamma-Poisson regression using data on the inactivation of Listeria monocytogenes. The conclusion is that the traditional method has limitations when the data includes plates with low (or zero) cell counts, which can be mitigated using more complex (discrete) likelihoods. However, Poisson regression uses an unrealistic likelihood function, making it unsuitable for survivor curves with several log-reductions. Gamma-Poisson regression uses a more realistic likelihood function, even though it is based mostly on empirical hypotheses. We conclude that the MPC method can be used reliably, especially when the data includes plates with low or zero counts. Furthermore, it generates a more realistic description of uncertainty, integrating the contribution of the plating error and reducing the uncertainty of the primary model parameters. Consequently, although it increases modelling complexity, the MPC method can be of great interest in predictive microbiology, especially in studies focused on variability analysis.

A Bayesian non-parametric mixed-effects model of microbial growth curves

Substantive changes in gene expression, metabolism, and the proteome are manifested in overall changes in microbial population growth. Quantifying how microbes grow is therefore fundamental to areas such as genetics, bioengineering, and food safety. Traditional parametric growth curve models capture the population growth behavior through a set of summarizing parameters. However, estimation of these parameters from data is confounded by random effects such as experimental variability, batch effects or differences in experimental material. A systematic statistical method to identify and correct for such confounding effects in population growth data is not currently available. Further, our previous work has demonstrated that parametric models are insufficient to explain and predict microbial response under non-standard growth conditions. Here we develop a hierarchical Bayesian non-parametric model of population growth that identifies the latent growth behavior and response to perturbation, while simultaneously correcting for random effects in the data. This model enables more accurate estimates of the biological effect of interest, while better accounting for the uncertainty due to technical variation. Additionally, modeling hierarchical variation provides estimates of the relative impact of various confounding effects on measured population growth.

Multilevel modelling as a tool to include variability and uncertainty in quantitative microbiology and risk assessment. Thermal inactivation of Listeria monocytogenes as proof of concept

Variability is inherent in biology and also substantial for microbial populations. In the context of food safety risk assessment, it refers to differences in the response of different bacterial strains (between-strain variability) and different cells (within-strain variability) to the same condition (e.g. inactivation treatment). However, its quantification based on empirical observations and its incorporation in predictive models is a challenge for both experimental design and (statistical) analysis. In this article we propose the use of multilevel models to quantify (different levels of) variability and uncertainty and include them in the predictions. As proof of concept, we analyse the microbial inactivation of Listeria monocytogenes to thermal treatments including different levels of variability (between-strain and within-strain) and uncertainty. The relationship between the microbial count and time was expressed using a (non-linear) Weibullian model. Moreover, we defined stochastic hypotheses to describe the different types of variation at the level of the kinetic parameters, as well as in the observations (microbial counts). The model parameters (kinetic parameters and variances) are estimated using Bayesian statistics. The multilevel approach was compared against an analogous, single-level model. The multilevel methodology shrinks extreme parameter estimates towards the mean according to uncertainty, thus mitigating overfitting. In addition, this approach enables to easily incorporate different levels of variation (between-strain and/or within-strain variability and/or uncertainty) in the predictions. On the other hand, multilevel (Bayesian) models are more complex to define, implement, analyse and communicate than single-level models. Nevertheless, their ability to incorporate different sources of variability in predictions make them very suitable for Quantitative Microbial Risk Assessment.

A Systematic Review of Beef Meat Quantitative Microbial Risk Assessment Models

Each year in Europe, meat is associated with 2.3 million foodborne illnesses, with a high contribution from beef meat. Many of these illnesses are attributed to pathogenic bacterial contamination and inadequate operations leading to growth and/or insufficient inactivation occurring along the whole farm-to-fork chain. To ensure consumer health, decision-making processes in food safety rely on Quantitative Microbiological Risk Assessment (QMRA) with many applications in recent decades. The present study aims to conduct a critical analysis of beef QMRAs and to identify future challenges. A systematic approach, the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines, was used to collate beef QMRA models, identify steps of the farm-to-fork chain considered, and analyze inputs and outputs included as well as modelling methods. A total of 2343 articles were collected and 67 were selected. These studies focused mainly on western countries and considered Escherichia coli (EHEC) and Salmonella spp. pathogens. Future challenges were identified and included the need of whole-chain assessments, centralization of data collection processes, and improvement of model interoperability through harmonization. The present analysis can serve as a source of data and information to inform QMRA framework for beef meat and will help the scientific community and food safety authorities to identify specific monitoring and research needs.

Inactivation of Listeria monocytogenes, Staphylococcus aureus, and Salmonella enterica under High Hydrostatic Pressure: A Quantitative Analysis of Existing Literature Data

High hydrostatic pressure processing (HPP) is a mild preservation technique, and its use for processing foods has been widely documented in the literature. However, very few quantitative synthesis studies have been conducted to gather and analyze bacterial inactivation data to identify the mechanisms of HPP-induced bacterial inactivation. The purpose of this study was to conduct a quantitative analysis of three-decimal reduction times (t_3δ) from a large set of existing studies to determine the main influencing factors of HPP-induced inactivation of three foodborne pathogens (Listeria monocytogenes, Staphylococcus aureus, and Salmonella enterica) in various foods. Inactivation kinetics data sets from 1995 to 2017 were selected, and t_3δ values were first estimated by using the nonlinear Weibull model. Bayesian inference was then used within a metaregression analysis to build and test several models and submodels. The best model (lowest error and most parsimonious) was a hierarchical mixed-effects model including pressure intensity, temperature, study, pH, species, and strain as explicative variables and significant factors. Values for t_3δ and Z_P associated with inactivation under HPP were estimated for each bacterial pathogen, with their associated variability. Interstudy variability explained most of the variability in t_3δ values. Strain variability was also important and exceeded interstudy variability for S. aureus, which prevented the development of an overall model for this pathogen. Meta-analysis is not often used in food microbiology but was a valuable quantitative tool for modeling inactivation of L. monocytogenes and Salmonella in response to HPP treatment. Results of this study could be useful for refining quantitative assessment of the effects of HPP on vegetative foodborne pathogens or for more precisely designing costly and labor-intensive experiments with foodborne pathogens.

Modeling for Survival of Clostridium perfringens in Saeng-sik, a Powdered Ready-to-Eat Food with Low Water Activity

HIGHLIGHTS

We developed a mathematical model to predict the survival of C. perfringens in food. C. perfringens vegetative cells and spores were inoculated into dried powder food. The a_w of saeng-sik was below 0.1. Weibull and Davey models can successfully describe the survival of C. perfringens. The developed model can be applied to samples with different microbial communities.

Quantitative Risk Assessment of Norovirus Transmission in Food Establishments: Evaluating the Impact of Intervention Strategies and Food Employee Behavior on the Risk Associated with Norovirus in Foods

We developed a quantitative risk assessment model using a discrete event framework to quantify and study the risk associated with norovirus transmission to consumers through food contaminated by infected food employees in a retail food setting. This study focused on the impact of ill food workers experiencing symptoms of diarrhea and vomiting and potential control measures for the transmission of norovirus to foods. The model examined the behavior of food employees regarding exclusion from work while ill and after symptom resolution and preventive measures limiting food contamination during preparation. The mean numbers of infected customers estimated for 21 scenarios were compared to the estimate for a baseline scenario representing current practices. Results show that prevention strategies examined could not prevent norovirus transmission to food when a symptomatic employee was present in the food establishment. Compliance with exclusion from work of symptomatic food employees is thus critical, with an estimated range of 75-226% of the baseline mean for full to no compliance, respectively. Results also suggest that efficient handwashing, handwashing frequency associated with gloving compliance, and elimination of contact between hands, faucets, and door handles in restrooms reduced the mean number of infected customers to 58%, 62%, and 75% of the baseline, respectively. This study provides quantitative data to evaluate the relative efficacy of policy and practices at retail to reduce norovirus illnesses and provides new insights into the interactions and interplay of prevention strategies and compliance in reducing transmission of foodborne norovirus.

Meta-analysis of D-values of proteolytic Clostridium botulinum and its surrogate strain Clostridium sporogenes PA 3679

Foodborne botulism is a serious disease resulting from ingestion of preformed Clostridium botulinum neurotoxin in foodstuff. Since the 19th century, the heat resistance of this spore forming bacteria has been extensively studied in order to guarantee the public health associated with low acidic, ambient stable products. The most largely used heat resistance parameters in thermal settings of such products are the D121.1°C values (time required to have a 10-fold decrease of the spore count, at 121.1°C) and the z-values (temperature increase to have a 10-fold decrease of D-values). To determine D121.1°C and z-values of proteolytic C. botulinum and its nontoxigenic surrogate strain C. sporogenes PA3679, a dataset of 911 D-values was collected from 38 scientific studies. Within a meta-analysis framework, a mixed-effect linear model was developed with the log D-value (min) as response and the heat treatment temperature as explicative variable. The studies (38), the C. botulinum strains (11), and the heat treatment media (liquid media and various food matrices, split into nine categories in total) were considered as co-variables having a random effect. The species (C. botulinum and C. sporogenes) and the pH (five categories) were considered as co-variables having a fixed effect. Overall, the model gave satisfactory results with a residual standard deviation of 0.22. The heat resistance of proteolytic C. botulinum was found significantly lower than the C. sporogenes PA 3679 one: the mean D-values at the reference temperature of 121.1°C, in liquid media and pH neutral, were estimated to 0.19 and 1.28min for C. botulinum and C. sporogenes, respectively. On the other hand, the mean z-values of the two species were similar: 11.3 and 11.1°C for C. botulinum and C. sporogenes, respectively. These results will be applied to thermal settings of low-acid ambient stable products.

Meta-analysis of Campylobacter spp. survival data within a temperature range of 0 to 42°C

In Europe, Campylobacter is the leading reported cause of bacterial foodborne infectious disease. Quantifying its ability to survive at chilled and ambient temperatures and identifying the factors involved in variation in its survival may contribute to the development of efficient risk management strategies. A data set of 307 inactivation curves collected from the literature and the ComBase database, combined with 388 experimental curves, was analyzed with a log-linear model to obtain 695 D-values (time for 1 log inactivation). An additional 146 D-values collected from the literature or ComBase were added to the data set, for a total of 841 D-values. Because data were collected from different studies, the experimental conditions were somewhat heterogeneous (e.g., type of media or strain used). The full data set was then split into 19 different study types on which a meta-analysis was performed to determine the effect of temperature (range 0 to 42°C), Campylobacter species (C. coli and C. jejuni), and media (liquid media or meat matrix) on the survival ability of Campylobacter. A mixed-effects model, in which the study type and bacterial species were considered as random effects and the media and temperature as fixed effects, was run using a Bayesian approach. Overall, the model gave satisfactory results, with a residual standard deviation of 0.345 (the model response was the log D-value, expressed in days). In addition, the survival of Campylobacter was greater at 0 than at 42°C, with a log-linear pattern; the z-value (temperature to have a 10-fold decrease of D-value) was estimated to be 26.4°C (95 % interval: 23.9 to 29.4°C). Despite a significant media-species interaction term, it was established that both species were more resistant on the meat matrix than in liquid media. These results may be used to understand how Campylobacter can survive along the food chain, particularly in chilled environments, and consequently be transferred to other foodstuffs.

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.