Estimation of True Salmonella Prevalence Jointly in Cattle Herd and Animal Populations Using Bayesian Hierarchical Modeling

The Finnish salmonella control program (FSCP) for beef production is based on both randomized and selective testing of herds and animals. Sampling of individual animals in abattoirs is randomized. Herds are selectively tested for salmonella on the basis of clinical symptoms and/or other factors. Risk assessment of FSCP is inherently difficult due to the complexity of the complete data set, especially if the detailed labeling of the testing types is lost. However, for a risk assessment of the whole production chain, methods for exploiting all available data should be considered. For this purpose, a hierarchical Bayesian model of true salmonella prevalence was constructed to combine information at different levels of aggregation: herds in geographical regions and individual animals arriving for slaughter. The conditional (municipality specific) probability of selection of a herd for testing was modeled given the underlying true infection status of the herd and information about the general sampling activity in the specific region. The model also accounted for the overall sensitivity of the sampling methods, both at the herd and at the animal level. In 1999, the 95% posterior probability intervals of true salmonella prevalence in the herd population, in individual cattle, and in slaughter animal populations were [0.54%, 1.4%] (mode 0.8%), [0.15%, 0.39%] (mode 0.2%), and [0.12%, 0.36%] (mode 0.2%), respectively. The results will be further exploited in other risk assessments focusing on the subsequent parts of the beef production chain, and in evaluation of the FSCP.     

Assessing Interventions to Reduce the Risk of Campylobacter Prevalence in Broilers

As part of a comprehensive risk assessment on the Campylobacter prevalence in the chicken production chain (from young born chicken till chicken fillet) in the Netherlands, we formulated a quantitative model on the transmission dynamics of Campylobacter at Dutch broiler farms. This model is used to quantify the risk of Campylobacter prevalence in broilers at the time that flocks leave the farm for processing. To this end, we assumed that the Campylobacter prevalence is primarily determined by two parameters, that is, the within- and between-flock transmission. The within-flock transmission was assessed fitting experimental data to a logistic growth model and the between-flock transmission was assessed fitting field data to a generalized linear model (GLM), which included three possible infection routes: (1) via an infected flock in the previous cycle, (2) via other infected flocks present on the farm, and (3) from other sources. This model was applied to assess the efficacy of three control scenarios; (1) a ban on other livestock on broiler farms, (2) a ban on thinning, and (3) a reduction of the between-flock transmission. In contrast to the other scenarios, the third one was shown to be most effective. Theoretically, this is accomplished by improved biosecurity. However, the impact of improved biosecurity cannot be specified into specific control measures, and therefore it is not clear what investments are needed. Finally, we also assessed the efficacy of scheduled treatment, that is, fresh meat production solely from test-negative flocks. We found that the reliability of negative test results, which is crucial, strongly depends on the length of time between testing and slaughter. The sensitivity and specificity of the test appeared to be of minor importance.     

Effectiveness and Efficiency of Controlling Campylobacter on Broiler Chicken Meat

Campylobacter bacteria are an important cause of foodborne infections. We estimated the potential costs and benefits of a large number of possible interventions to decrease human exposure to Campylobacter by consumption of chicken meat, which accounts for 20-40% of all cases of human campylobacteriosis in the Netherlands. For this purpose, a farm-to-fork risk assessment model was combined with economic analysis and epidemiological data. Reduction of contamination at broiler farms could be efficient in theory. However, it is unclear which hygienic measures need to be taken and the costs can be very high. The experimental treatment of colonized broiler flocks with bacteriophages has proven to be effective and could also be cost efficient, if confirmed in practice. Since a major decrease of infections at the broiler farm is not expected in the short term, additional measures in the processing plant were also considered. At this moment, guaranteed Campylobacter-free chicken meat at the retail level is not realistic. The most promising interventions in the processing plant are limiting fecal leakage during processing and separation of contaminated and noncontaminated flocks (scheduling), followed by decontamination of the contaminated flock. New (faster and more sensitive) test methods to detect Campylobacter colonization in broilers flocks are a prerequisite for successful scheduling scenarios. Other methods to decrease the contamination of meat of colonized flocks such as freezing and heat treatment are more expensive and/or less effective than chemical decontamination.     

A Modular Bayesian Salmonella Source Attribution Model for Sparse Data

Several statistical models for salmonella source attribution have been presented in the literature. However, these models have often been found to be sensitive to the model parameterization, as well as the specifics of the data set used. The Bayesian salmonella source attribution model presented here was developed to be generally applicable with small and sparse annual data sets obtained over several years. The full Bayesian model was modularized into three parts (an exposure model, a subtype distribution model, and an epidemiological model) in order to separately estimate unknown parameters in each module. The proposed model takes advantage of the consumption and overall salmonella prevalence of the studied sources, as well as bacteria typing results from adjacent years. The latter were used for a smoothed estimation of the annual relative proportions of different salmonella subtypes in each of the sources. The source‐specific effects and the salmonella subtype‐specific effects were included in the epidemiological model to describe the differences between sources and between subtypes in their ability to infect humans. The estimation of these parameters was based on data from multiple years. Finally, the model combines the total evidence from different modules to proportion human salmonellosis cases according to their sources. The model was applied to allocate reported human salmonellosis cases from the years 2008 to 2015 to eight food sources.     

Salmonella Enteritidis Surveillance by Egg Immunology: Impact of the Sampling Scheme on the Release of Contaminated Table Eggs

Design of surveillance programs to detect infections could benefit from more insight into sampling schemes. We address the effect of sampling schemes for Salmonella Enteritidis surveillance in laying hens. Based on experimental estimates for the transmission rate in flocks, and the characteristics of an egg immunological test, we have simulated outbreaks with various sampling schemes, and with the current boot swab program with a 15‐week sampling interval. Declaring a flock infected based on a single positive egg was not possible because test specificity was too low. Thus, a threshold number of positive eggs was defined to declare a flock infected, and, for small sample sizes, eggs from previous samplings had to be included in a cumulative sample to guarantee a minimum flock level specificity. Effectiveness of surveillance was measured by the proportion of outbreaks detected, and by the number of contaminated table eggs brought on the market. The boot swab program detected 90% of the outbreaks, with 75% fewer contaminated eggs compared to no surveillance, whereas the baseline egg program (30 eggs each 15 weeks) detected 86%, with 73% fewer contaminated eggs. We conclude that a larger sample size results in more detected outbreaks, whereas a smaller sampling interval decreases the number of contaminated eggs. Decreasing sample size and interval simultaneously reduces the number of contaminated eggs, but not indefinitely: the advantage of more frequent sampling is counterbalanced by the cumulative sample including less recently laid eggs. Apparently, optimizing surveillance has its limits when test specificity is taken into account.     

A Model for Setting Performance Objectives for Salmonella in the Broiler Supply Chain

A stochastic model for setting performance objectives for Salmonella in the broiler supply chain was developed. The goal of this study was to develop a model by which performance objectives for Salmonella prevalence at various points in the production chain can be determined, based on a preset final performance objective at the end of the processing line. The transmission of Salmonella through the broiler production chain was modeled. The prevalence at flock level was calculated from the measured prevalence at sample level. The transmission model is based on data on the occurrence of Salmonella collected in the Dutch broiler production chain during several years. The developed model can be used by policymakers and industry to determine economically and politically acceptable performance objectives for various points of the production chain and to draw conclusions about which interventions are most appropriate.     

A probabilistic epidemiological model for infectious diseases: The case of COVID-19 at global-level

This study has developed a probabilistic epidemiological model a few weeks after the World Health Organization declared COVID-19 a pandemic (based on the little data available at that time). The aim was to assess relative risks for future scenarios and evaluate the effectiveness of different management actions for 1 year ahead. We quantified, categorized, and ranked the risks for scenarios such as business as usual, and moderate and strong mitigation. We estimated that, in the absence of interventions, COVID-19 would have a 100% risk of explosion (i.e., more than 25% infections in the world population) and 34% (2.6 billion) of the world population would have been infected until the end of simulation. We analyzed the suitability of model scenarios by comparing actual values against estimated values for the first 6 weeks of the simulation period. The results proved to be more suitable with a business-as-usual scenario in Asia and moderate mitigation in the other continents. If everything went on like this, we would have 55% risk of explosion and 22% (1.7 billion) of the world population would have been infected. Strong mitigation actions in all continents could reduce these numbers to, 7% and 3% (223 million), respectively. Although the results were based on the data available in March 2020, both the model and probabilistic approach proved to be practicable and could be a basis for risk assessment in future pandemic episodes with unknown virus, especially in the early stages, when data and literature are scarce.     

What Number is “Fifty‐Fifty”?: Redistributing Excessive 50% Responses in Elicited Probabilities

Studies using open-ended response modes to elicit probabilistic beliefs have sometimes found an elevated frequency (or blip) at 50 in their response distributions. Our previous research suggests that this is caused by intrusion of the phrase "fifty-fifty," which represents epistemic uncertainty, rather than a true numeric probability of 50%. Such inappropriate responses pose a problem for decision analysts and others relying on probabilistic judgments. Using an explicit numeric probability scale (ranging from 0-100%) reduces thinking about uncertain events in verbal terms like "fifty-fifty," and, with it, exaggerated use of the 50 response. Here, we present two procedures for adjusting response distributions for data already collected with open-ended response modes and hence vulnerable to an exaggerated presence of 50%. Each procedure infers the prevalence of 50s had a numeric probability scale been used, then redistributes the excess. The two procedures are validated on some of our own existing data and then applied to judgments elicited from experts in groundwater pollution and bioremediation.     

Effects of Uncertainties on Exposure Estimates to Methylmercury: A Monte Carlo Analysis of Exposure Biomarkers versus Dietary Recall Estimation

This article presents a general model for estimating population heterogeneity and "lack of knowledge" uncertainty in methylmercury (MeHg) exposure assessments using two-dimensional Monte Carlo analysis. Using data from fish-consuming populations in Bangladesh, Brazil, Sweden, and the United Kingdom, predictive model estimates of dietary MeHg exposures were compared against those derived from biomarkers (i.e., [Hg]hair and [Hg]blood). By disaggregating parameter uncertainty into components (i.e., population heterogeneity, measurement error, recall error, and sampling error) estimates were obtained of the contribution of each component to the overall uncertainty. Steady-state diet:hair and diet:blood MeHg exposure ratios were estimated for each population and were used to develop distributions useful for conducting biomarker-based probabilistic assessments of MeHg exposure. The 5th and 95th percentile modeled MeHg exposure estimates around mean population exposure from each of the four study populations are presented to demonstrate lack of knowledge uncertainty about a best estimate for a true mean. Results from a U.K. study population showed that a predictive dietary model resulted in a 74% lower lack of knowledge uncertainty around a central mean estimate relative to a hair biomarker model, and also in a 31% lower lack of knowledge uncertainty around central mean estimate relative to a blood biomarker model. Similar results were obtained for the Brazil and Bangladesh populations. Such analyses, used here to evaluate alternative models of dietary MeHg exposure, can be used to refine exposure instruments, improve information used in site management and remediation decision making, and identify sources of uncertainty in risk estimates.     

Bayesian Temporal Source Attribution of Foodborne Zoonoses: Campylobacter in Finland and Norway

Statistical source attribution approaches of food‐related zoonoses can generally be based on reported diagnosed human cases and surveillance results from different food sources or reservoirs of bacteria. The attribution model, or probabilistic classifier, can thus be based on the (sub)typing information enabling comparison between human infections and samples derived from source surveillance. Having time series of both data allows analyzing temporal patterns over time providing a repeated natural experiment. A Bayesian approach combining both sources of information over a long time series is presented in the case of Campylobacter in Finland and Norway. The full model is transparently presented and derived from the Bayes theorem. Previous statistical source attribution approaches are here advanced (1) by explicit modeling of the cases not associated with any of the sources under surveillance over time, (2) by modeling uncertain prevalence in a food source by bacteria type over time, and (3) by implementing formal model fit assessment using posterior predictive discrepancy functions. Large proportion of all campylobacteriosis can be attributed to broiler, but considerable uncertainty remains over time. The source attribution is inherently incomplete if only the sources under surveillance are included in the model. All statistical source attribution approaches should include a model fit assessment for judgment of model performance with respect to relevant quantities of interest. It is especially relevant when the model aims at a synthesis of several incomplete information sources under significant uncertainty of explanatory variables.     

A Probabilistic Feasibility and Value Analysis of the Generalized Assignment Problem

We study the generalized assignment problem, under a probabilistic model for its cost and requirement parameters. First we address the issue of feasibility by deriving a tight condition on the probabilistic model that ensures that the corresponding problem instances are feasible with probability one as the number of jobs goes to infinity. Then, under an additional condition on the parameters, we show that the optimal solution value, normalized by dividing by the number of jobs, converges with probability one to a constant, again as the number of jobs goes to infinity. Finally, we discuss various examples.     

Estimation from Zero-Failure Data

When performing quantitative (or probabilistic) risk assessments, it is often the case that data for many of the potential events in question are sparse or nonexistent. Some of these events may be well-represented by the binomial probability distribution. In this paper, a model for predicting the binomial failure probability, P , from data that include no failures is examined. A review of the literature indicates that the use of this model is currently limited to risk analysis of energetic initiation in the explosives testing field. The basis for the model is discussed, and the behavior of the model relative to other models developed for the same purpose is investigated. It is found that the qualitative behavior of the model is very similar to that of the other models, and for larger values of n (the number of trials), the predicted P values varied by a factor of about eight among the five models examined. Analysis revealed that the estimator is nearly identical to the median of a Bayesian posterior distribution, derived using a uniform prior. An explanation of the application of the estimator in explosives testing is provided, and comments are offered regarding the use of the estimator versus other possible techniques.     

Comparative assessment of analytical approaches to quantify the risk for introduction of rare animal diseases: the example of avian influenza in Spain

Trade of animals and animal products imposes an uncertain and variable risk for exotic animal diseases introduction into importing countries. Risk analysis provides importing countries with an objective, transparent, and internationally accepted method for assessing that risk. Over the last decades, European Union countries have conducted probabilistic risk assessments quite frequently to quantify the risk for rare animal diseases introduction into their territories. Most probabilistic animal health risk assessments have been typically classified into one-level and multilevel binomial models. One-level models are more simple than multilevel models because they assume that animals or products originate from one single population. However, it is unknown whether such simplification may result in substantially different results compared to those obtained through the use of multilevel models. Here, data used on a probabilistic multilevel binomial model formulated to assess the risk for highly pathogenic avian influenza introduction into Spain were reanalyzed using a one-level binomial model and their outcomes were compared. An alternative ordinal model is also proposed here, which makes use of simpler assumptions and less information compared to those required by traditional one-level and multilevel approaches. Results suggest that, at least under certain circumstances, results of the one-level and ordinal approaches are similar to those obtained using multilevel models. Consequently, we argue that, when data are insufficient to run traditional probabilistic models, the ordinal approach presented here may be a suitable alternative to rank exporting countries in terms of the risk that they impose for the spread of rare animal diseases into disease-free countries.     

An exact algorithm for the maximum probabilistic clique problem

The maximum clique problem is a classical problem in combinatorial optimization that has a broad range of applications in graph-based data mining, social and biological network analysis and a variety of other fields. This article investigates the problem when the edges fail independently with known probabilities. This leads to the maximum probabilistic clique problem, which is to find a subset of vertices of maximum cardinality that forms a clique with probability at least \(\theta \in [0,1]\) , which is a user-specified probability threshold. We show that the probabilistic clique property is hereditary and extend a well-known exact combinatorial algorithm for the maximum clique problem to a sampling-free exact algorithm for the maximum probabilistic clique problem. The performance of the algorithm is benchmarked on a test-bed of DIMACS clique instances and on a randomly generated test-bed.     

A probabilistic transmission and population dynamic model to assess tuberculosis infection risk

The purpose of this study was to examine tuberculosis (TB) population dynamics and to assess potential infection risk in Taiwan. A well‐established mathematical model of TB transmission built on previous models was adopted to study the potential impact of TB transmission. A probabilistic risk model was also developed to estimate site‐specific risks of developing disease soon after recent primary infection, exogenous reinfection, or through endogenous reactivation (latently infected TB) among Taiwan regions. Here, we showed that the proportion of endogenous reactivation (53–67%) was larger than that of exogenous reinfection (32–47%). Our simulations showed that as epidemic reaches a steady state, age distribution of cases would finally shift toward older age groups dominated by latently infected TB cases as a result of endogenous reactivation. A comparison of age‐weighted TB incidence data with our model simulation output with 95% credible intervals revealed that the predictions were in an apparent agreement with observed data. The median value of overall basic reproduction number (R₀) in eastern Taiwan ranged from 1.65 to 1.72, whereas northern Taiwan had the lowest R₀ estimate of 1.50. We found that total TB incidences in eastern Taiwan had 25–27% probabilities of total proportion of infected population exceeding 90%, whereas there were 36–66% probabilities having exceeded 20% of total proportion of infected population attributed to latently infected TB. We suggested that our Taiwan‐based analysis can be extended to the context of developing countries, where TB remains a substantial cause of elderly morbidity and mortality.     

Bayesian Development of a Dose‐Response Model for Aspergillus fumigatus and Invasive Aspergillosis

Invasive aspergillosis (IA) is a major cause of mortality in immunocompromized hosts, most often consecutive to the inhalation of spores of Aspergillus. However, the relationship between Aspergillus concentration in the air and probability of IA is not quantitatively known. In this study, this relationship was examined in a murine model of IA. Immunosuppressed Balb/c mice were exposed for 60 minutes at day 0 to an aerosol of A. fumigatus spores (Af293 strain). At day 10, IA was assessed in mice by quantitative culture of the lungs and galactomannan dosage. Fifteen separate nebulizations with varying spore concentrations were performed. Rates of IA ranged from 0% to 100% according to spore concentrations. The dose‐response relationship between probability of infection and spore exposure was approximated using the exponential model and the more flexible beta‐Poisson model. Prior distributions of the parameters of the models were proposed then updated with data in a Bayesian framework. Both models yielded close median dose‐responses of the posterior distributions for the main parameter of the model, but with different dispersions, either when the exposure dose was the concentration in the nebulized suspension or was the estimated quantity of spores inhaled by a mouse during the experiment. The median quantity of inhaled spores that infected 50% of mice was estimated at 1.8 × 10⁴ and 3.2 × 10⁴ viable spores in the exponential and beta‐Poisson models, respectively. This study provides dose‐response parameters for quantitative assessment of the relationship between airborne exposure to the reference A. fumigatus strain and probability of IA in immunocompromized hosts.     

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.     

Risk Assessment of Human Listeriosis from Semisoft Cheeses Made from Raw Sheep's Milk in Lazio and Tuscany (Italy)

Semisoft cheese made from raw sheep's milk is traditionally and economically important in southern Europe. However, raw milk cheese is also a known vehicle of human listeriosis and contamination of sheep cheese with Listeria monocytogenes has been reported. In the present study, we have developed and applied a quantitative risk assessment model, based on available evidence and challenge testing, to estimate risk of invasive listeriosis due to consumption of an artisanal sheep cheese made with raw milk collected from a single flock in central Italy. In the model, contamination of milk may originate from the farm environment or from mastitic animals, with potential growth of the pathogen in bulk milk and during cheese ripening. Based on the 48‐day challenge test of a local semisoft raw sheep's milk cheese we found limited growth only during the initial phase of ripening (24 hours) and no growth or limited decline during the following ripening period. In our simulation, in the baseline scenario, 2.2% of cheese servings are estimated to have at least 1 colony forming unit (CFU) per gram. Of these, 15.1% would be above the current E.U. limit of 100 CFU/g (5.2% would exceed 1,000 CFU/g). Risk of invasive listeriosis per random serving is estimated in the 10^?12 range (mean) for healthy adults, and in the 10^?10 range (mean) for vulnerable populations. When small flocks (10–36 animals) are combined with the presence of a sheep with undetected subclinical mastitis, risk of listeriosis increases and such flocks may represent a public health risk.     

概率预期下在线报童问题的最小风险策略

报童问题是库存管理中一个基本模型。已有的报童模型主要利用均值-方差方法和期望效用目标方法进行风险的描述和度量。这些方法假设需求分布信息已知,而实际中需求分布信息往往难以完全刻画。本文使用概率预期作为刻画不完全需求分布信息的格式,基于在线风险补偿的思想,为需求分布信息不完全的报童问题建立了最小风险模型。使用该模型设计了最小风险策略,使报童可以根据自己设定的不同收益和未来概率预期选择最优订购量。