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.     

Microbiological and Modeling Approach to Derive Performance Objectives for Bacillus cereus Group in Ready‐to‐Eat Salads

In this article, the performance objectives (POs) for Bacillus cereus group (BC) in celery, cheese, and spelt added as ingredients in a ready‐to‐eat mixed spelt salad, packaged under modified atmosphere, were calculated using a Bayesian approach. In order to derive the POs, BC detection and enumeration were performed in nine lots of naturally contaminated ingredients and final product. Moreover, the impact of specific production steps on the BC contamination was quantified. Finally, a sampling plan to verify the ingredient lots' compliance with each PO value at a 95% confidence level (CL) was defined. To calculate the POs, detection results as well as results above the limit of detection but below the limit of quantification (i.e., censored data) were analyzed. The most probable distribution of the censored data was determined and two‐dimensional (2D) Monte Carlo simulations were performed. The PO values were calculated to meet a food safety objective of 4 log₁₀ cfu of BC for g of spelt salad at the time of consumption. When BC grows during storage between 0.90 and 1.90 log₁₀ cfu/g, the POs for BC in celery, cheese, and spelt ranged between 1.21 log₁₀ cfu/g for celery and 2.45 log₁₀ cfu/g for spelt. This article represents the first attempt to manage the concept of PO and 2D Monte Carlo simulation in the flow chart of a complex food matrix, including raw and cooked ingredients.     

Combining QMRA and Epidemiology to Estimate Campylobacteriosis Incidence

The disease burden of pathogens as estimated by QMRA (quantitative microbial risk assessment) and EA (epidemiological analysis) often differs considerably. This is an unsatisfactory situation for policymakers and scientists. We explored methods to obtain a unified estimate using campylobacteriosis in the Netherlands as an example, where previous work resulted in estimates of 4.9 million (QMRA) and 90,600 (EA) cases per year. Using the maximum likelihood approach and considering EA the gold standard, the QMRA model could produce the original EA estimate by adjusting mainly the dose‐infection relationship. Considering QMRA the gold standard, the EA model could produce the original QMRA estimate by adjusting mainly the probability that a gastroenteritis case is caused by Campylobacter. A joint analysis of QMRA and EA data and models assuming identical outcomes, using a frequentist or Bayesian approach (using vague priors), resulted in estimates of 102,000 or 123,000 campylobacteriosis cases per year, respectively. These were close to the original EA estimate, and this will be related to the dissimilarity in data availability. The Bayesian approach further showed that attenuating the condition of equal outcomes immediately resulted in very different estimates of the number of campylobacteriosis cases per year and that using more informative priors had little effect on the results. In conclusion, EA was dominant in estimating the burden of campylobacteriosis in the Netherlands. However, it must be noted that only statistical uncertainties were taken into account here. Taking all, usually difficult to quantify, uncertainties into account might lead to a different conclusion.     

Outbreak-Based Giardia Dose–Response Model Using Bayesian Hierarchical Markov Chain Monte Carlo Analysis

Giardia is a zoonotic gastrointestinal parasite responsible for a substantial global public health burden, and quantitative microbial risk assessment (QMRA) is often used to forecast and manage this burden. QMRA requires dose–response models to extrapolate available dose–response data, but the existing model for Giardia ignores valuable dose–response information, particularly data from several well-documented waterborne outbreaks of giardiasis. The current study updates Giardia dose–response modeling by synthesizing all available data from outbreaks and experimental studies using a Bayesian random effects dose–response model. For outbreaks, mean doses (D) and the degree of spatial and temporal aggregation among cysts were estimated using exposure assessment implemented via two-dimensional Monte Carlo simulation, while potential overreporting of outbreak cases was handled using published overreporting factors and censored binomial regression. Parameter estimation was by Markov chain Monte Carlo simulation and indicated that a typical exponential dose–response parameter for Giardia is r = 1.6 × 10⁻² [3.7 × 10⁻³, 6.2 × 10⁻²] (posterior median [95% credible interval]), while a typical morbidity ratio is m = 3.8 × 10⁻¹ [2.3 × 10⁻¹, 5.5 × 10⁻¹]. Corresponding (logistic-scale) variance components were σ_r = 5.2 × 10⁻¹ [1.1 × 10⁻¹, 9.6 × 10⁻¹] and σ_m = 9.3 × 10⁻¹ [7.0 × 10⁻², 2.8 × 10⁰], indicating substantial variation in the Giardia dose–response relationship. Compared to the existing Giardia dose–response model, the current study provides more representative estimation of uncertainty in r and novel quantification of its natural variability. Several options for incorporating variability in r (and m) into QMRA predictions are discussed, including incorporation via Monte Carlo simulation as well as evaluation of the current study's model using the approximate beta-Poisson.     

Demonstrating the Benefits of Predictive Bayesian Dose–Response Relationships Using Six Exposure Studies of Cryptosporidium parvum

A conventional dose–response function can be refitted as additional data become available. A predictive dose–response function in contrast does not require a curve-fitting step, only additional data and presents the unconditional probabilities of illness, reflecting the level of information it contains. In contrast, the predictive Bayesian dose–response function becomes progressively less conservative as more information is included. This investigation evaluated the potential for using predictive Bayesian methods to develop a dose–response for human infection that improves on existing models, to show how predictive Bayesian statistical methods can utilize additional data, and expand the Bayesian methods for a broad audience including those concerned about an oversimplification of dose–response curve use in quantitative microbial risk assessment (QMRA). This study used a dose–response relationship incorporating six separate data sets for Cryptosporidium parvum. A Pareto II distribution with known priors was applied to one of the six data sets to calibrate the model, while the others were used for subsequent updating. While epidemiological principles indicate that local variations, host susceptibility, and organism strain virulence may vary, the six data sets all appear to be well characterized using the Bayesian approach. The adaptable model was applied to an existing data set for Campylobacter jejuni for model validation purposes, which yielded results that demonstrate the ability to analyze a dose–response function with limited data using and update those relationships with new data. An analysis of the goodness of fit compared to the beta-Poisson methods also demonstrated correlation between the predictive Bayesian model and the data.     

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.     

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.     

Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure

This paper presents a new approach to estimation and inference in panel data models with a general multifactor error structure. The unobserved factors and the individual‐specific errors are allowed to follow arbitrary stationary processes, and the number of unobserved factors need not be estimated. The basic idea is to filter the individual‐specific regressors by means of cross‐section averages such that asymptotically as the cross‐section dimension (N) tends to infinity, the differential effects of unobserved common factors are eliminated. The estimation procedure has the advantage that it can be computed by least squares applied to auxiliary regressions where the observed regressors are augmented with cross‐sectional averages of the dependent variable and the individual‐specific regressors. A number of estimators (referred to as common correlated effects (CCE) estimators) are proposed and their asymptotic distributions are derived. The small sample properties of mean group and pooled CCE estimators are investigated by Monte Carlo experiments, showing that the CCE estimators have satisfactory small sample properties even under a substantial degree of heterogeneity and dynamics, and for relatively small values of N and T.     

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.     

Interventions Targeting Deep Tissue Lymph Nodes May Not Effectively Reduce the Risk of Salmonellosis from Ground Pork Consumption: A Quantitative Microbial Risk Assessment

The inclusion of deep tissue lymph nodes (DTLNs) or nonvisceral lymph nodes contaminated with Salmonella in wholesale fresh ground pork (WFGP) production may pose risks to public health. To assess the relative contribution of DTLNs to human salmonellosis occurrence associated with ground pork consumption and to investigate potential critical control points in the slaughter‐to‐table continuum for the control of human salmonellosis in the United States, a quantitative microbial risk assessment (QMRA) model was established. The model predicted an average of 45 cases of salmonellosis (95% CI = [19, 71]) per 100,000 Americans annually due to WFGP consumption. Sensitivity analysis of all stochastic input variables showed that cooking temperature was the most influential parameter for reducing salmonellosis cases associated with WFGP meals, followed by storage temperature and Salmonella concentration on contaminated carcass surface before fabrication. The input variables were grouped to represent three main factors along the slaughter‐to‐table chain influencing Salmonella doses ingested via WFGP meals: DTLN‐related factors, factors at processing other than DTLNs, and consumer‐related factors. The evaluation of the impact of each group of factors by second‐order Monte Carlo simulation showed that DTLN‐related factors had the lowest impact on the risk estimate among the three groups of factors. These findings indicate that interventions to reduce Salmonella contamination in DTLNs or to remove DTLNs from WFGP products may be less critical for reducing human infections attributable to ground pork than improving consumers’ cooking habits or interventions of carcass decontamination at processing.     

Recognizing Structural Nonidentifiability: When Experiments Do Not Provide Information About Important Parameters and Misleading Models Can Still Have Great Fit

In the quest to model various phenomena, the foundational importance of parameter identifiability to sound statistical modeling may be less well appreciated than goodness of fit. Identifiability concerns the quality of objective information in data to facilitate estimation of a parameter, while nonidentifiability means there are parameters in a model about which the data provide little or no information. In purely empirical models where parsimonious good fit is the chief concern, nonidentifiability (or parameter redundancy) implies overparameterization of the model. In contrast, nonidentifiability implies underinformativeness of available data in mechanistically derived models where parameters are interpreted as having strong practical meaning. This study explores illustrative examples of structural nonidentifiability and its implications using mechanistically derived models (for repeated presence/absence analyses and dose–response of Escherichia coli O157:H7 and norovirus) drawn from quantitative microbial risk assessment. Following algebraic proof of nonidentifiability in these examples, profile likelihood analysis and Bayesian Markov Chain Monte Carlo with uniform priors are illustrated as tools to help detect model parameters that are not strongly identifiable. It is shown that identifiability should be considered during experimental design and ethics approval to ensure generated data can yield strong objective information about all mechanistic parameters of interest. When Bayesian methods are applied to a nonidentifiable model, the subjective prior effectively fabricates information about any parameters about which the data carry no objective information. Finally, structural nonidentifiability can lead to spurious models that fit data well but can yield severely flawed inferences and predictions when they are interpreted or used inappropriately.     

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.     

Potential Uncertainty Reduction in Model‐Averaged Benchmark Dose Estimates Informed by an Additional Dose Study

A methodology is presented for assessing the information value of an additional dosage experiment in existing bioassay studies. The analysis demonstrates the potential reduction in the uncertainty of toxicity metrics derived from expanded studies, providing insights for future studies. Bayesian methods are used to fit alternative dose‐response models using Markov chain Monte Carlo (MCMC) simulation for parameter estimation and Bayesian model averaging (BMA) is used to compare and combine the alternative models. BMA predictions for benchmark dose (BMD) are developed, with uncertainty in these predictions used to derive the lower bound BMDL. The MCMC and BMA results provide a basis for a subsequent Monte Carlo analysis that backcasts the dosage where an additional test group would have been most beneficial in reducing the uncertainty in the BMD prediction, along with the magnitude of the expected uncertainty reduction. Uncertainty reductions are measured in terms of reduced interval widths of predicted BMD values and increases in BMDL values that occur as a result of this reduced uncertainty. The methodology is illustrated using two existing data sets for TCDD carcinogenicity, fitted with two alternative dose‐response models (logistic and quantal‐linear). The example shows that an additional dose at a relatively high value would have been most effective for reducing the uncertainty in BMA BMD estimates, with predicted reductions in the widths of uncertainty intervals of approximately 30%, and expected increases in BMDL values of 5–10%. The results demonstrate that dose selection for studies that subsequently inform dose‐response models can benefit from consideration of how these models will be fit, combined, and interpreted.     

Evaluating the Potential for a Helicobacter pylori Drinking Water Guideline

Helicobacter pylori is a microaerophilic, gram‐negative bacterium that is linked to adverse health effects including ulcers and gastrointestinal cancers. The goal of this analysis is to develop the necessary inputs for a quantitative microbial risk assessment (QMRA) needed to develop a potential guideline for drinking water at the point of ingestion (e.g., a maximum contaminant level, or MCL) that would be protective of human health to an acceptable level of risk while considering sources of uncertainty. Using infection and gastric cancer as two discrete endpoints, and calculating dose‐response relationships from experimental data on humans and monkeys, we perform both a forward and reverse risk assessment to determine the risk from current reported surface water concentrations of H. pylori and an acceptable concentration of H. pylori at the point of ingestion. This approach represents a synthesis of available information on human exposure to H. pylori via drinking water. A lifetime risk of cancer model suggests that a MCL be set at <1 organism/L given a 5‐log removal treatment because we cannot exclude the possibility that current levels of H. pylori in environmental source waters pose a potential public health risk. Research gaps include pathogen occurrence in source and finished water, treatment removal rates, and determination of H. pylori risks from other water sources such as groundwater and recreational water.     

Development of an Interspecies Nested Dose‐Response Model for Mycobacterium avium subspecies paratuberculosis

Mycobacterium avium subspecies paratuberculosis (MAP) causes chronic inflammation of the intestines in humans, ruminants, and other species. It is the causative agent of Johne's disease in cattle, and has been implicated as the causative agent of Crohn's disease in humans. To date, no quantitative microbial risk assessment (QMRA) for MAP utilizing a dose‐response function exists. The objective of this study is to develop a nested dose‐response model for infection from oral exposure to MAP utilizing data from the peer‐reviewed literature. Four studies amenable to dose‐response modeling were identified in the literature search and optimized to the one‐parameter exponential or two‐parameter beta‐Poisson dose‐response models. A nesting analysis was performed on all permutations of the candidate data sets to determine the acceptability of pooling data sets across host species. Three of four data sets exhibited goodness of fit to at least one model. All three data sets exhibited good fit to the beta‐Poisson model, and one data set exhibited goodness of fit, and best fit, to the exponential model. Two data sets were successfully nested using the beta‐Poisson model with parameters α = 0.0978 and N₅₀ = 2.70 × 10² CFU. These data sets were derived from sheep and red deer host species, indicating successful interspecies nesting, and demonstrate the highly infective nature of MAP. The nested dose‐response model described should be used for future QMRA research regarding oral exposure to MAP.     

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.     

Exposure Assessment for Pesticide Intake from Multiple Food Products: A Bayesian Latent‐Variable Approach

Pesticide risk assessment for food products involves combining information from consumption and concentration data sets to estimate a distribution for the pesticide intake in a human population. Using this distribution one can obtain probabilities of individuals exceeding specified levels of pesticide intake. In this article, we present a probabilistic, Bayesian approach to modeling the daily consumptions of the pesticide Iprodione though multiple food products. Modeling data on food consumption and pesticide concentration poses a variety of problems, such as the large proportions of consumptions and concentrations that are recorded as zero, and correlation between the consumptions of different foods. We consider daily food consumption data from the Netherlands National Food Consumption Survey and concentration data collected by the Netherlands Ministry of Agriculture. We develop a multivariate latent‐Gaussian model for the consumption data that allows for correlated intakes between products. For the concentration data, we propose a univariate latent‐t model. We then combine predicted consumptions and concentrations from these models to obtain a distribution for individual daily Iprodione exposure. The latent‐variable models allow for both skewness and large numbers of zeros in the consumption and concentration data. The use of a probabilistic approach is intended to yield more robust estimates of high percentiles of the exposure distribution than an empirical approach. Bayesian inference is used to facilitate the treatment of data with a complex structure.     

Bayesian Network Model with Application to Smart Power Semiconductor Lifetime Data

In this article, Bayesian networks are used to model semiconductor lifetime data obtained from a cyclic stress test system. The data of interest are a mixture of log‐normal distributions, representing two dominant physical failure mechanisms. Moreover, the data can be censored due to limited test resources. For a better understanding of the complex lifetime behavior, interactions between test settings, geometric designs, material properties, and physical parameters of the semiconductor device are modeled by a Bayesian network. Statistical toolboxes in MATLAB® have been extended and applied to find the best structure of the Bayesian network and to perform parameter learning. Due to censored observations Markov chain Monte Carlo (MCMC) simulations are employed to determine the posterior distributions. For model selection the automatic relevance determination (ARD) algorithm and goodness‐of‐fit criteria such as marginal likelihoods, Bayes factors, posterior predictive density distributions, and sum of squared errors of prediction (SSEP) are applied and evaluated. The results indicate that the application of Bayesian networks to semiconductor reliability provides useful information about the interactions between the significant covariates and serves as a reliable alternative to currently applied methods.     

Testing a Parametric Model Against a Nonparametric Alternative with Identification Through Instrumental Variables

This paper is concerned with inference about a function g that is identified by a conditional moment restriction involving instrumental variables. The paper presents a test of the hypothesis that g belongs to a finite‐dimensional parametric family against a nonparametric alternative. The test does not require nonparametric estimation of g and is not subject to the ill‐posed inverse problem of nonparametric instrumental variables estimation. Under mild conditions, the test is consistent against any alternative model. In large samples, its power is arbitrarily close to 1 uniformly over a class of alternatives whose distance from the null hypothesis is O(n^−1/2), where n is the sample size. In Monte Carlo simulations, the finite‐sample power of the new test exceeds that of existing tests.     

The Bayesian Microbial Subtyping Attribution Model: Robustness to Prior Information and a Proposition

Attributing foodborne illnesses to food sources is essential to conceive, prioritize, and assess the impact of public health policy measures. The Bayesian microbial subtyping attribution model by Hald et al. is one of the most advanced approaches to attribute sporadic cases; it namely allows taking into account the level of exposure to the sources and the differences between bacterial types and between sources. This step forward requires introducing type and source‐dependent parameters, and generates overparameterization, which was addressed in Hald's paper by setting some parameters to constant values. We question the impact of the choices made for the parameterization (parameters set and values used) on model robustness and propose an alternative parameterization for the Hald model. We illustrate this analysis with the 2005 French data set of non‐typhi Salmonella. Mullner's modified Hald model and a simple deterministic model were used to compare the results and assess the accuracy of the estimates. Setting the parameters for bacterial types specific to a unique source instead of the most frequent one and using data‐based values instead of arbitrary values enhanced the convergence and adequacy of the estimates and led to attribution estimates consistent with the other models’ results. The type and source parameters estimates were also coherent with Mullner's model estimates. The model appeared to be highly sensitive to parameterization. The proposed solution based on specific types and data‐based values improved the robustness of estimates and enabled the use of this highly valuable tool successfully with the French data set.