Source Attribution of Food-Borne Zoonoses in New Zealand: A Modified Hald Model

A Bayesian approach was developed by Hald et al .^{( 1 )} to estimate the contribution of different food sources to the burden of human salmonellosis in Denmark. This article describes the development of several modifications that can be used to adapt the model to different countries and pathogens. Our modified Hald model has several advantages over the original approach, which include the introduction of uncertainty in the estimates of source prevalence and an improved strategy for identifiability. We have applied our modified model to the two major food-borne zoonoses in New Zealand, namely, campylobacteriosis and salmonellosis. Major challenges were the data quality for salmonellosis and the inclusion of environmental sources of campylobacteriosis. We conclude that by modifying the Hald model we have improved its identifiability, made it more applicable to countries with less intensive surveillance, and feasible for other pathogens, in particular with respect to the inclusion of nonfood sources. The wider application and better understanding of this approach is of particular importance due to the value of the model for decision making and risk management.     

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.     

Risk Ranking for Foodborne Microbial Hazards in New Zealand: Burden of Disease Estimates

Priority setting for food safety management at a national level requires risks to be ranked according to defined criteria. In this study, two approaches (disability‐adjusted life years (DALYs) and cost of illness (COI)) were used to generate estimates of the burden of disease for certain potentially foodborne diseases (campylobacteriosis, salmonellosis, listeriosis (invasive, perinatal, and nonperinatal), infection with Shiga toxin‐producing Escherichia coli (STEC), yersiniosis, and norovirus infection) and their sequelae in New Zealand. A modified Delphi approach was used to estimate the food‐attributable proportion for these diseases. The two approaches gave a similar ranking for the selected diseases, with campylobacteriosis and its sequelae accounting for the greatest proportion of the overall burden of disease by far.     

Uncertainty of Population Risk Estimates for Pathogens Based on QMRA or Epidemiology: A Case Study of Campylobacter in the Netherlands

Epidemiology and quantitative microbiological risk assessment are disciplines in which the same public health measures are estimated, but results differ frequently. If large, these differences can confuse public health policymakers. This article aims to identify uncertainty sources that explain apparent differences in estimates for Campylobacter spp. incidence and attribution in the Netherlands, based on four previous studies (two for each discipline). An uncertainty typology was used to identify uncertainty sources and the NUSAP method was applied to characterize the uncertainty and its influence on estimates. Model outcomes were subsequently calculated for alternative scenarios that simulated very different but realistic alternatives in parameter estimates, modeling, data handling, or analysis to obtain impressions of the total uncertainty. For the epidemiological assessment, 32 uncertainty sources were identified and for QMRA 67. Definitions (e.g., of a case) and study boundaries (e.g., of the studied pathogen) were identified as important drivers for the differences between the estimates of the original studies. The range in alternatively calculated estimates usually overlapped between disciplines, showing that proper appreciation of uncertainty can explain apparent differences between the initial estimates from both disciplines. Uncertainty was not estimated in the original QMRA studies and underestimated in the epidemiological studies. We advise to give appropriate attention to uncertainty in QMRA and epidemiological studies, even if only qualitatively, so that scientists and policymakers can interpret reported outcomes more correctly. Ideally, both disciplines are joined by merging their strong respective properties, leading to unified public health measures.     

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.     

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.     

A Bayesian Analysis of Abundance,Trend, and Population Viability for Harbor Seals in Iliamna Lake,Alaska

Harbor seals in Iliamna Lake, Alaska, are a small, isolated population, and one of only two freshwater populations of harbor seals in the world, yet little is known about their abundance or risk for extinction. Bayesian hierarchical models were used to estimate abundance and trend of this population. Observational models were developed from aerial survey and harvest data, and they included effects for time of year and time of day on survey counts. Underlying models of abundance and trend were based on a Leslie matrix model that used prior information on vital rates from the literature. We developed three scenarios for variability in the priors and used them as part of a sensitivity analysis. The models were fitted using Markov chain Monte Carlo methods. The population production rate implied by the vital rate estimates was about 5% per year, very similar to the average annual harvest rate. After a period of growth in the 1980s, the population appears to be relatively stable at around 400 individuals. A population viability analysis assessing the risk of quasi‐extinction, defined as any reduction to 50 animals or below in the next 100 years, ranged from 1% to 3%, depending on the prior scenario. Although this is moderately low risk, it does not include genetic or catastrophic environmental events, which may have occurred to the population in the past, so our results should be applied cautiously.     

Designing optimal food safety monitoring schemes using Bayesian network and integer programming: The case of monitoring dioxins and DL-PCBs

Efficient food safety monitoring should achieve optimal resource allocation. In this article, a methodology is presented to optimize the use of resources for food safety monitoring aimed at identifying noncompliant samples and estimating background level of hazards in food products. A Bayesian network (BN) model and an optimization model were combined in a single framework. The framework was applied to monitoring dioxins and dioxin-like polychlorinated biphenyls (DL-PCBs) in primary animal-derived food products in the Netherlands. The BN model was built using a national dataset with monitoring results of dioxins and DL-PCBs in animal-derived food products over a 10-year period (2008–2017). These data were used to estimate the probability of detecting suspect samples with dioxins and DL-PCBs levels above preset thresholds, given certain sample conditions. The results of the BN model were then inserted into the optimization model to compute an optimal monitoring scheme. Model estimates showed that the probability of dioxins and DL-PCBs exceeding threshold limits was higher in laying hen eggs and sheep meat than in other animal-derived food (except deer meat). Compared with the monitoring scheme used in the Netherlands in 2018, the optimal monitoring scheme would save around 10,000 EUR per year. This could be obtained by reallocating monitoring resources from products with lower probability of dioxin and DL-PCBs exceeding threshold limits (e.g., pig meat) to products with higher probability (e.g., bovine animal meat), and by shifting sample collection from the last quarter of the year toward the first three quarters of the year.     

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.     

A Quantitative Microbiological Risk Assessment for Campylobacter in Petting Zoos

The significance of petting zoos for transmission of Campylobacter to humans and the effect of interventions were estimated. A stochastic QMRA model simulating a child or adult visiting a Dutch petting zoo was built. The model describes the transmission of Campylobacter in animal feces from the various animal species, fences, and the playground to ingestion by visitors through touching these so‐called carriers and subsequently touching their lips. Extensive field and laboratory research was done to fulfill data needs. Fecal contamination on all carriers was measured by swabbing in 10 petting zoos, using Escherichia coli as an indicator. Carrier‐hand and hand‐lip touching frequencies were estimated by, in total, 13 days of observations of visitors by two observers at two petting zoos. The transmission from carrier to hand and from hand to lip by touching was measured using preapplied cow feces to which E. coli WG5 was added as an indicator. Via a Beta‐Poisson dose‐response function, the number of Campylobacter cases for the whole of the Netherlands (16 million population) in a year was estimated at 187 and 52 for children and adults, respectively, so 239 in total. This is significantly lower than previous QMRA results on chicken fillet and drinking water consumption. Scenarios of 90% reduction of the contamination (meant to mimic cleaning) of all fences and just goat fences reduces the number of cases by 82% and 75%, respectively. The model can easily be adapted for other fecally transmitted pathogens.     

MULTIPERIOD SEARCH MODELS FOR AN UNKNOWN NUMBER OF VALUABLE OBJECTS

In this paper we examine multiperiod search models for cases in which the number of valuable objects is unknown. The objective is to maximize the expected total returns during the planning horizon, subject to an effort constraint. Using a Bayesian approach, we examine the model for three different priors for the number of valuable objects, and we show that the different priors (binomial, Poisson and negative binomial) lead to such conceptually different results as adaptive and nonadaptive optimal policies. The models can be applied to many areas including mineral explorations, marketing promotion activities and intelligence information.     

A Stochastic Assessment of the Public Health Risks of the Use of Macrolide Antibiotics in Food Animals

Campylobacteriosis is an important food-borne illness with more than a million U.S. cases annually. Antibiotic treatment is usually not required. However, erythromycin, a macrolide antibiotic, is recommended for the treatment of severe cases. Therefore, it is considered a critically important antibiotic and given special attention as to the risk that food animal use will lead to resistant infections and compromised human treatment. To assess this risk, we used a retrospective approach; estimating the number of campylobacteriosis cases caused by specific meat consumption utilizing the preventable fraction. We then determined the number of cases with macrolide resistance Campylobacter spp. based on a linear model relating the resistance fraction to on-farm macrolide use. In this article, we considered the uncertainties in the parameter estimates, utilized a more elaborate model of resistance development and separated C. coli and C. jejuni . There are no published data for the probability of compromised treatment outcome due to macrolide resistance. Therefore, our estimates of compromised treatment outcome were based on data for fluoroquinolone-resistant infections. The conservative results show the human health risks are extremely low. For example, the predicted risk of suboptimal human treatment of infection with C. coli from swine is only 1 in 82 million; with a 95% chance it could be as high as 1 in 49 million. Risks from C. jejuni in poultry or beef are even less. Reduced antibiotic use can adversely impact animal health. These low human risks should be weighed against the alternative risks.     

Sign Restrictions,Structural Vector Autoregressions,and Useful Prior Information

This paper makes the following original contributions to the literature. (i) We develop a simpler analytical characterization and numerical algorithm for Bayesian inference in structural vector autoregressions (VARs) that can be used for models that are overidentified, just‐identified, or underidentified. (ii) We analyze the asymptotic properties of Bayesian inference and show that in the underidentified case, the asymptotic posterior distribution of contemporaneous coefficients in an n‐variable VAR is confined to the set of values that orthogonalize the population variance–covariance matrix of ordinary least squares residuals, with the height of the posterior proportional to the height of the prior at any point within that set. For example, in a bivariate VAR for supply and demand identified solely by sign restrictions, if the population correlation between the VAR residuals is positive, then even if one has available an infinite sample of data, any inference about the demand elasticity is coming exclusively from the prior distribution. (iii) We provide analytical characterizations of the informative prior distributions for impulse‐response functions that are implicit in the traditional sign‐restriction approach to VARs, and we note, as a special case of result (ii), that the influence of these priors does not vanish asymptotically. (iv) We illustrate how Bayesian inference with informative priors can be both a strict generalization and an unambiguous improvement over frequentist inference in just‐identified models. (v) We propose that researchers need to explicitly acknowledge and defend the role of prior beliefs in influencing structural conclusions and we illustrate how this could be done using a simple model of the U.S. labor market.     

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.     

Risk of Norovirus Gastroenteritis from Consumption of Vegetables Irrigated with Highly Treated Municipal Wastewater—Evaluation of Methods to Estimate Sewage Quality

Quantitative microbial risk assessment was used to assess the risk of norovirus gastroenteritis associated with consumption of raw vegetables irrigated with highly treated municipal wastewater, using Melbourne, Australia as an example. In the absence of local norovirus concentrations, three methods were developed: (1) published concentrations of norovirus in raw sewage, (2) an epidemiological method using Melbourne prevalence of norovirus, and (3) an adjustment of method 1 to account for prevalence of norovirus. The methods produced highly variable results with estimates of norovirus concentrations in raw sewage ranging from 10⁴ per milliliter to 10⁷ per milliliter and treated effluent from 1 × 10^?3 per milliliter to 3 per milliliter (95th percentiles). Annual disease burden was very low using method 1, from 4 to 5 log₁₀ disability adjusted life years (DALYs) below the 10^?6 threshold (0.005–0.1 illnesses per year). Results of method 2 were higher, with some scenarios exceeding the threshold by up to 2 log₁₀ DALYs (up to 95,000 illnesses per year). Method 3, thought to be most representative of Melbourne conditions, predicted annual disease burdens >2 log₁₀ DALYs lower than the threshold (～4 additional cases per year). Sensitivity analyses demonstrated that input parameters used to estimate norovirus concentration accounted for much of the model output variability. This model, while constrained by a lack of knowledge of sewage concentrations, used the best available information and sound logic. Results suggest that current wastewater reuse behaviors in Melbourne are unlikely to cause norovirus risks in excess of the annual DALY health target.     

A Linear Model for Managing the Risk of Antimicrobial Resistance Originating in Food Animals

A linear population risk model used by the U.S. Food and Drug Administration (FDA) Center for Veterinary Medicine (CVM) estimates the risk of human cases of campylobacteriosis caused by fluoroquinolone-resistant Campylobacter. Among the cases of campylobacteriosis attributed to domestically produced chicken, the fluoroquinolone resistance is assumed to result from the use of fluoroquinolones in poultry in the United States. Properties of the linear population risk model are contrasted with those of a farm-to-fork model commonly used for microbial risk assessments. The utility of the linear population model for the purpose for which it was used by CVM is discussed.     

Quantifying Cancer Risk from Radiation

Complex statistical models fitted to data from studies of atomic bomb survivors are used to estimate the human health effects of ionizing radiation exposures. We describe and illustrate an approach to estimate population risks from ionizing radiation exposure that relaxes many assumptions about radiation‐related mortality. The approach draws on developments in methods for causal inference. The results offer a different way to quantify radiation's effects and show that conventional estimates of the population burden of excess cancer at high radiation doses are driven strongly by projecting outside the range of current data. Summary results obtained using the proposed approach are similar in magnitude to those obtained using conventional methods, although estimates of radiation‐related excess cancers differ for many age, sex, and dose groups. At low doses relevant to typical exposures, the strength of evidence in data is surprisingly weak. Statements regarding human health effects at low doses rely strongly on the use of modeling assumptions.     

Assessing the effect on the public health risk of current and alternative border control of Salmonella Typhimurium and Enteritidis in imported frozen poultry meat in Jordan

The JFDA applies border control for Salmonella Typhimurium and Salmonella Enteritidis in frozen poultry products. A QMRA model was developed to evaluate the effectiveness of this system in controlling the risk for consumers. The model consists of three modules; consumer phase, risk estimation, and risk reduction. The model inputs were the occurrence of Salmonella in different types of imported poultry products, the LOD of the Rapid’Salmonella, the number of tested samples of each batch, and the criteria for rejection. The model outputs were public health impact as the Minimum Relative Residual Risk (MRRR) given the batches’ refusal and the percentage of Batches that are Not-compliant with the Microbiological Criteria (BNMC) of rejection. To estimate the overall MRRR of the border control, the estimated country and product-specific MRRR were summarized and weighted by the total imports of each product from each country. The current border control based on one sample per batch gives an overall MRRR value of 27%. The alternative scenarios based on three and five samples per batch are 12% and 8%, respectively. Overall, the higher the prevalence and/or concentration of Salmonella in imported products, the more the likelihood that batches will be rejected. For products with up-to-date data of occurrence, the estimated BNMC was similar to the observed proportion of rejected batches. The lack of data on the Salmonella concentrations in poultry products from different countries is the major source of the uncertainties in the model. It reduces our opportunities to obtain valid estimates of the absolute risk.     

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.     

Bayesian Estimation of Dynamic Discrete Choice Models

We propose a new methodology for structural estimation of infinite horizon dynamic discrete choice models. We combine the dynamic programming (DP) solution algorithm with the Bayesian Markov chain Monte Carlo algorithm into a single algorithm that solves the DP problem and estimates the parameters simultaneously. As a result, the computational burden of estimating a dynamic model becomes comparable to that of a static model. Another feature of our algorithm is that even though the number of grid points on the state variable is small per solution‐estimation iteration, the number of effective grid points increases with the number of estimation iterations. This is how we help ease the “curse of dimensionality.” We simulate and estimate several versions of a simple model of entry and exit to illustrate our methodology. We also prove that under standard conditions, the parameters converge in probability to the true posterior distribution, regardless of the starting values.