Disparity in Quantitative Risk Assessment: A Review of Input Distributions

Monte Carlo simulations are commonplace in quantitative risk assessments (QRAs). Designed to propagate the variability and uncertainty associated with each individual exposure input parameter in a quantitative risk assessment, Monte Carlo methods statistically combine the individual parameter distributions to yield a single, overall distribution. Critical to such an assessment is the representativeness of each individual input distribution. The authors performed a literature review to collect and compare the distributions used in published QRAs for the parameters of body weight, food consumption, soil ingestion rates, breathing rates, and fluid intake. To provide a basis for comparison, all estimated exposure parameter distributions were evaluated with respect to four properties: consistency, accuracy, precision, and specificity. The results varied depending on the exposure parameter. Even where extensive, well-collected data exist, investigators used a variety of different distributional shapes to approximate these data. Where such data do not exist, investigators have collected their own data, often leading to substantial disparity in parameter estimates and subsequent choice of distribution. The present findings indicate that more attention must be paid to the data underlying these distributional choices. More emphasis should be placed on sensitivity analyses, quantifying the impact of assumptions, and on discussion of sources of variation as part of the presentation of any risk assessment results. If such practices and disclosures are followed, it is believed that Monte Carlo simulations can greatly enhance the accuracy and appropriateness of specific risk assessments. Without such disclosures, researchers will be increasing the size of the risk assessment "black box," a concern already raised by many critics of more traditional risk assessments.     

Hexavalent Chromium and Lung Cancer in the Chromate Industry: A Quantitative Risk Assessment

The purpose of this investigation was to estimate excess lifetime risk of lung cancer death resulting from occupational exposure to hexavalent-chromium-containing dusts and mists. The mortality experience in a previously studied cohort of 2,357 chromate chemical production workers with 122 lung cancer deaths was analyzed with Poisson regression methods. Extensive records of air samples evaluated for water-soluble total hexavalent chromium were available for the entire employment history of this cohort. Six different models of exposure-response for hexavalent chromium were evaluated by comparing deviances and inspection of cubic splines. Smoking (pack-years) imputed from cigarette use at hire was included in the model. Lifetime risks of lung cancer death from exposure to hexavalent chromium (assuming up to 45 years of exposure) were estimated using an actuarial calculation that accounts for competing causes of death. A linear relative rate model gave a good and readily interpretable fit to the data. The estimated rate ratio for 1 mg/m3-yr of cumulative exposure to hexavalent chromium (as CrO3), with a lag of five years, was RR=2.44 (95% CI=1.54-3.83). The excess lifetime risk of lung cancer death from exposure to hexavalent chromium at the current OSHA permissible exposure limit (PEL) (0.10 mg/m3) was estimated to be 255 per 1,000 (95% CI: 109-416). This estimate is comparable to previous estimates by U.S. EPA, California EPA, and OSHA using different occupational data. Our analysis predicts that current occupational standards for hexavalent chromium permit a lifetime excess risk of dying of lung cancer that exceeds 1 in 10, which is consistent with previous risk assessments.     

Compressed Natural Gas Bus Safety: A Quantitative Risk Assessment

This study assesses the fire safety risks associated with compressed natural gas (CNG) vehicle systems, comprising primarily a typical school bus and supporting fuel infrastructure. The study determines the sensitivity of the results to variations in component failure rates and consequences of fire events. The components and subsystems that contribute most to fire safety risk are determined. Finally, the results are compared to fire risks of the present generation of diesel-fueled school buses. Direct computation of the safety risks associated with diesel-powered vehicles is possible because these are mature technologies for which historical performance data are available. Because of limited experience, fatal accident data for CNG bus fleets are minimal. Therefore, this study uses the probabilistic risk assessment (PRA) approach to model and predict fire safety risk of CNG buses. Generic failure data, engineering judgments, and assumptions are used in this study. This study predicts the mean fire fatality risk for typical CNG buses as approximately 0.23 fatalities per 100-million miles for all people involved, including bus passengers. The study estimates mean values of 0.16 fatalities per 100-million miles for bus passengers only. Based on historical data, diesel school bus mean fire fatality risk is 0.091 and 0.0007 per 100-million miles for all people and bus passengers, respectively. One can therefore conclude that CNG buses are more prone to fire fatality risk by 2.5 times that of diesel buses, with the bus passengers being more at risk by over two orders of magnitude. The study estimates a mean fire risk frequency of 2.2 x 10(-5) fatalities/bus per year. The 5% and 95% uncertainty bounds are 9.1 x 10(-6) and 4.0 x 10(-5), respectively. The risk result was found to be affected most by failure rates of pressure relief valves, CNG cylinders, and fuel piping.     

A Poultry-Processing Model for Quantitative Microbiological Risk Assessment

A poultry-processing model for a quantitative microbiological risk assessment (QMRA) of campylobacter is presented, which can also be applied to other QMRAs involving poultry processing. The same basic model is applied in each consecutive stage of industrial processing. It describes the effects of inactivation and removal of the bacteria, and the dynamics of cross-contamination in terms of the transfer of campylobacter from the intestines to the carcass surface and the environment, from the carcasses to the environment, and from the environment to the carcasses. From the model it can be derived that, in general, the effect of inactivation and removal is dominant for those carcasses with high initial bacterial loads, and cross-contamination is dominant for those with low initial levels. In other QMRA poultry-processing models, the input-output relationship between the numbers of bacteria on the carcasses is usually assumed to be linear on a logarithmic scale. By including some basic mechanistics, it is shown that this may not be realistic. As nonlinear behavior may affect the predicted effects of risk mitigations; this finding is relevant for risk management. Good knowledge of the variability of bacterial loads on poultry entering the process is important. The common practice in microbiology to only present geometric mean of bacterial counts is insufficient: arithmetic mean are more suitable, in particular, to describe the effect of cross-contamination. The effects of logistic slaughter (scheduled processing) as a risk mitigation strategy are predicted to be small. Some additional complications in applying microbiological data obtained in processing plants are discussed.     

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.     

A Quantitative Risk Assessment for Bovine Spongiform Encephalopathy in Japan

A predictive case‐cohort model was applied to Japanese data to analyze the interaction between challenge and stability factors for bovine spongiform encephalopathy (BSE) for the period 1985–2020. BSE risk in cattle was estimated as the expected number of detectable cases per year. The model was comprised of a stochastic spreadsheet calculation model with the following inputs: (1) the origin and quantity of live cattle and meat and bone meal imported into Japan, (2) the age distribution of native cattle, and (3) the estimated annual basic reproduction ratio (R₀) for BSE. The estimated probability of having zero detectable cases in Japan in 2015 was 0.90 (95% CI 0.83–0.95). The corresponding value for 2020 was 0.99 (95% CI 0.98–0.99). The model predicted that detectable cases may occur in Japan beyond 2015 because of the assumption that continued transmission was permitted to occur (albeit at a very low level) after the 2001 ban on the importation and domestic use of all processed animal proteins for the production of animal feed and for fertilizer. These results reinforce the need for animal health authorities to monitor the efficacy of control measures so that the future course of the BSE epidemic in Japan can be predicted with greater certainty.     

Quantitative Risk Assessment of Listeria monocytogenes in French Cold-Smoked Salmon: I. Quantitative Exposure Assessment

A quantitative assessment of the exposure to Listeria monocytogenes from cold-smoked salmon (CSS) consumption in France is developed. The general framework is a second-order (or two-dimensional) Monte Carlo simulation, which characterizes the uncertainty and variability of the exposure estimate. The model takes into account the competitive bacterial growth between L. monocytogenes and the background competitive flora from the end of the production line to the consumer phase. An original algorithm is proposed to integrate this growth in conditions of varying temperature. As part of a more general project led by the French Food Safety Agency (Afssa), specific data were acquired and modeled for this quantitative exposure assessment model, particularly time-temperature profiles, prevalence data, and contamination-level data. The sensitivity analysis points out the main influence of the mean temperature in household refrigerators and the prevalence of contaminated CSS on the exposure level. The outputs of this model can be used as inputs for further risk assessment.     

Modeling Logistic Performance in Quantitative Microbial Risk Assessment

In quantitative microbial risk assessment (QMRA), food safety in the food chain is modeled and simulated. In general, prevalences, concentrations, and numbers of microorganisms in media are investigated in the different steps from farm to fork. The underlying rates and conditions (such as storage times, temperatures, gas conditions, and their distributions) are determined. However, the logistic chain with its queues (storages, shelves) and mechanisms for ordering products is usually not taken into account. As a consequence, storage times—mutually dependent in successive steps in the chain—cannot be described adequately. This may have a great impact on the tails of risk distributions. Because food safety risks are generally very small, it is crucial to model the tails of (underlying) distributions as accurately as possible. Logistic performance can be modeled by describing the underlying planning and scheduling mechanisms in discrete-event modeling. This is common practice in operations research, specifically in supply chain management. In this article, we present the application of discrete-event modeling in the context of a QMRA for  Listeria monocytogenes  in fresh-cut iceberg lettuce. We show the potential value of discrete-event modeling in QMRA by calculating logistic interventions (modifications in the logistic chain) and determining their significance with respect to food safety.     

A Simulation Study of Quantitative Risk Assessment for Bivariate Continuous Outcomes

The neurotoxic effects of chemical agents are often investigated in controlled studies on rodents, with binary and continuous multiple endpoints routinely collected. One goal is to conduct quantitative risk assessment to determine safe dose levels. Yu and Catalano (2005) describe a method for quantitative risk assessment for bivariate continuous outcomes by extending a univariate method of percentile regression. The model is likelihood based and allows for separate dose‐response models for each outcome while accounting for the bivariate correlation. The approach to benchmark dose (BMD) estimation is analogous to that for quantal data without having to specify arbitrary cutoff values. In this article, we evaluate the behavior of the BMD relative to background rates, sample size, level of bivariate correlation, dose‐response trend, and distributional assumptions. Using simulations, we explore the effects of these factors on the resulting BMD and BMDL distributions. In addition, we illustrate our method with data from a neurotoxicity study of parathion exposure in rats.     

Quantitative Risk Assessment of Listeria monocytogenes in French Cold-Smoked Salmon: II. Risk Characterization

A model for the assessment of exposure to Listeria monocytogenes from cold-smoked salmon consumption in France was presented in the first of this pair of articles (Pouillot et al ., 2007, Risk Analysis, 27:683–700). In the present study, the exposure model output was combined with an internationally accepted hazard characterization model, adapted to the French situation, to assess the risk of invasive listeriosis from cold-smoked salmon consumption in France in a second-order Monte Carlo simulation framework. The annual number of cases of invasive listeriosis due to cold-smoked salmon consumption in France is estimated to be 307, with a very large credible interval ([10; 12,453]), reflecting data uncertainty. This uncertainty is mainly associated with the dose-response model. Despite the significant uncertainty associated with the predictions, this model provides a scientific base for risk managers and food business operators to manage the risk linked to cold-smoked salmon contaminated with L. monocytogenes. Under the modeling assumptions, risk would be efficiently reduced through a decrease in the prevalence of L. monocytogenes or better control of the last steps of the cold chain (shorter and/or colder storage during the consumer step), whereas reduction of the initial contamination levels of the contaminated products and improvement in the first steps of the cold chain do not seem to be promising strategies. An attempt to apply the recent risk-based concept of FSO (food safety objective) on this example underlines the ambiguity in practical implementation of the risk management metrics and the need for further elaboration on these concepts.     

The BSE Risk of Processing Meat and Bone Meal in Nonruminant Feed: A Quantitative Assessment for the Netherlands

The total ban on use of meat and bone meal (MBM) in livestock feed has been very successful in reducing bovine spongiform encephalopathy (BSE) spread, but also implies a waste of high-quality proteins resulting in economic and ecological loss. Now that the BSE epidemic is fading out, a partial lifting of the MBM ban might be considered. The objective of this study was to assess the BSE risk for the Netherlands if MBM derived from animals fit for human consumption, i.e., category 3 MBM, would be used in nonruminant feed. A stochastic simulation model was constructed that calculates (1) the probability that infectivity of undetected BSE-infected cows ends up with calves and (2) the quantity of infectivity ( Q_inf ) consumed by calves in case of such an incident. Three pathways were considered via which infectivity can reach cattle: (1) cross-contamination in the feed mill, (2) cross-contamination on the primary farm, and (3) pasture contamination. Model calculations indicate that the overall probability that infectivity ends up with calves is 3.2%. In most such incidents the Q_inf is extremely small (median = 6.5 × 10⁻¹² ID₅₀; mean = 1.8 × 10⁻⁴ ID₅₀), corresponding to an average probability of 1.3 × 10⁻⁴ that an incident results in ≥1 new BSE infections. Cross-contamination in the feed mill is the most risky pathway. Combining model results with Dutch BSE prevalence estimates for the coming years, it can be concluded that the BSE risk of using category 3 MBM derived from Dutch cattle in nonruminant feed is very low.     

Correlated Inputs in Quantitative Risk Assessment: The Effects of Distributional Shape

Application of Monte Carlo simulation methods to quantitative risk assessment are becoming increasingly popular. With this methodology, investigators have become concerned about correlations among input variables which might affect the resulting distribution of risk. We show that the choice of input distributions in these simulations likely has a larger effect on the resultant risk distribution than does the inclusion or exclusion of correlations. Previous investigators have studied the effect of correlated input variables for the addition of variables with any underlying distribution and for the product of lognormally distributed variables. The effects in the main part of the distribution are small unless the correlation and variances are large. We extend this work by considering addition, multiplication and division of two variables with assumed normal, lognormal, uniform and triangular distributions. For all possible pairwise combinations, we find that the effects of correlated input variables are similar to those observed for lognormal distributions, and thus relatively small overall. The effect of using different distributions, however, can be large.     

Biological Models of Carcinogenesis and Quantitative Cancer Risk Assessment

Biologically-based models of carcinogenesis were originally developed to explain certain quanti-tative phenomena associated with carcinogenesis, and to provide a framework within which questions regarding the process could be addressed. Some limitations in the use of these models for quantitative cancer risk assessment are discussed.     

A Quantitative Microbial Risk Assessment Model for Legionnaires'' Disease: Animal Model Selection and Dose-Response Modeling

Legionnaires' disease (LD), first reported in 1976, is an atypical pneumonia caused by bacteria of the genus Legionella, and most frequently by L. pneumophila (Lp). Subsequent research on exposure to the organism employed various animal models, and with quantitative microbial risk assessment (QMRA) techniques, the animal model data may provide insights on human dose-response for LD. This article focuses on the rationale for selection of the guinea pig model, comparison of the dose-response model results, comparison of projected low-dose responses for guinea pigs, and risk estimates for humans. Based on both in vivo and in vitro comparisons, the guinea pig (Cavia porcellus) dose-response data were selected for modeling human risk. We completed dose-response modeling for the beta-Poisson (approximate and exact), exponential, probit, logistic, and Weibull models for Lp inhalation, mortality, and infection (end point elevated body temperature) in guinea pigs. For mechanistic reasons, including low-dose exposure probability, further work on human risk estimates for LD employed the exponential and beta-Poisson models. With an exposure of 10 colony-forming units (CFU) (retained dose), the QMRA model predicted a mild infection risk of 0.4 (as evaluated by seroprevalence) and a clinical severity LD case (e.g., hospitalization and supportive care) risk of 0.0009. The calculated rates based on estimated human exposures for outbreaks used for the QMRA model validation are within an order of magnitude of the reported LD rates. These validation results suggest the LD QMRA animal model selection, dose-response modeling, and extension to human risk projections were appropriate.     

Summary of the Workshop on Issues in Risk Assessment: Quantitative Methods for Developmental Toxicology

This report summarizes the proceedings of a conference on quantitative methods for assessing the risks of developmental toxicants. The conference was planned by a subcommittee of the National Research Council's Committee on Risk Assessment Methodology ⁴ in conjunction with staff from several federal agencies, including the U.S. Environmental Protection Agency, U.S. Food and Drug Administration, U.S. Consumer Products Safety Commission, and Health and Welfare Canada. Issues discussed at the workshop included computerized techniques for hazard identification, use of human and animal data for defining risks in a clinical setting, relationships between end points in developmental toxicity testing, reference dose calculations for developmental toxicology, analysis of quantitative dose-response data, mechanisms of developmental toxicity, physiologically based pharmacokinetic models, and structure-activity relationships. Although a formal consensus was not sought, many participants favored the evolution of quantitative techniques for developmental toxicology risk assessment, including the replacement of lowest observed adverse effect levels (LOAELs) and no observed adverse effect levels (NOAELs) with the benchmark dose methodology.     

Quantitative Risk Assessment from Farm to Fork and Beyond: A Global Bayesian Approach Concerning Food-Borne Diseases

A novel approach to the quantitative assessment of food-borne risks is proposed. The basic idea is to use Bayesian techniques in two distinct steps: first by constructing a stochastic core model via a Bayesian network based on expert knowledge, and second, using the data available to improve this knowledge. Unlike the Monte Carlo simulation approach as commonly used in quantitative assessment of food-borne risks where data sets are used independently in each module, our consistent procedure incorporates information conveyed by data throughout the chain. It allows "back-calculation" in the food chain model, together with the use of data obtained "downstream" in the food chain. Moreover, the expert knowledge is introduced more simply and consistently than with classical statistical methods. Other advantages of this approach include the clear framework of an iterative learning process, considerable flexibility enabling the use of heterogeneous data, and a justified method to explore the effects of variability and uncertainty. As an illustration, we present an estimation of the probability of contracting a campylobacteriosis as a result of broiler contamination, from the standpoint of quantitative risk assessment. Although the model thus constructed is oversimplified, it clarifies the principles and properties of the method proposed, which demonstrates its ability to deal with quite complex situations and provides a useful basis for further discussions with different experts in the food chain.     

A Quantitative Risk Assessment of Waterborne Cryptosporidiosis in France Using Second-Order Monte Carlo Simulation

A pragmatic quantitative risk assessment (QRA) of the risks of waterborne Cryptosporidium parvum infection and cryptosporidiosis in immunocompetent and immunodeficient French populations is proposed. The model takes into account French specificities such as the French technique for oocyst enumeration performance and tap water consumption. The proportion of infective oocysts is based on literature review and expert knowledge. The probability of infection for a given number of ingested viable oocysts is modeled using the exponential dose-response model applied on published data from experimental infections in immunocompetent human volunteers challenged with the IOWA strain. Second-order Monte Carlo simulations are used to characterize the uncertainty and variability of the risk estimates. Daily risk of infection and illness for the immunocompetent and the immunodeficient populations are estimated according to the number of oocysts observed in a single storage reservoir water sample. As an example, the mean daily risk of infection in the immunocompetent population is estimated to be 1.08 x 10(-4) (95% confidence interval: [0.20 x 10(-4); 6.83 x 10(-4)]) when five oocysts are observed in a 100 L storage reservoir water sample. Annual risks of infection and disease are estimated from a set of oocyst enumeration results from distributed water samples, assuming a negative binomial distribution of day-to-day contamination variation. The model and various assumptions used in the model are fully explained and discussed. While caveats of this model are well recognized, this pragmatic QRA could represent a useful tool for the French Food Safety Agency (AFSSA) to define recommendations in case of water resource contamination by C. parvum whose infectivity is comparable to the IOWA strain.     

Quantitative Risk Assessment of Vibrio parahaemolyticus in Finfish: A Model of Raw Horse Mackerel Consumption in Japan

The aim of this study was to evaluate the effects of implemented control measures to reduce illness induced by Vibrio parahaemolyticus (V. parahaemolyticus) in horse mackerel (Trachurus japonicus), seafood that is commonly consumed raw in Japan. On the basis of currently available experimental and survey data, we constructed a quantitative risk model of V. parahaemolyticus in horse mackerel from harvest to consumption. In particular, the following factors were evaluated: bacterial growth at all stages, effects of washing the fish body and storage water, and bacterial transfer from the fish surface, gills, and intestine to fillets during preparation. New parameters of the beta‐Poisson dose‐response model were determined from all human feeding trials, some of which have been used for risk assessment by the U.S. Food and Drug Administration (USFDA). The probability of illness caused by V. parahaemolyticus was estimated using both the USFDA dose‐response parameters and our parameters for each selected pathway of scenario alternatives: washing whole fish at landing, storage in contaminated water, high temperature during transportation, and washing fish during preparation. The last scenario (washing fish during preparation) was the most effective for reducing the risk of illness by about a factor of 10 compared to no washing at this stage. Risk of illness increased by 50% by exposure to increased temperature during transportation, according to our assumptions of duration and temperature. The other two scenarios did not significantly affect risk. The choice of dose‐response parameters was not critical for evaluation of control measures.     

A Hint of Risk: Tradeoffs Between Quantitative and Qualitative Risk Factors

Risk-perception research plays an active role in discussions of risk-management alternatives. However, little guidance is provided regarding how public concerns should be weighed against other sources of cost and benefits. This paper reports the results of two experiments that measure tradeoffs among cost (in dollars), a quantitative risk measure (number of deaths or injuries), and several qualitative characteristics associated with perceived risk. Most subjects were willing to make the requested trade. However, the perceived risk information led others to reject the proposed technology.     

Attribution of Human VTEC O157 Infection from Meat Products: A Quantitative Risk Assessment Approach

To address the risk posed to human health by the consumption of VTEC O157 within contaminated pork, lamb, and beef products within Great Britain, a quantitative risk assessment model has been developed. This model aims to simulate the prevalence and amount of VTEC O157 in different meat products at consumption within a single model framework by adapting previously developed models. The model is stochastic in nature, enabling both variability (natural variation between animals, carcasses, products) and uncertainty (lack of knowledge) about the input parameters to be modeled. Based on the model assumptions and data, it is concluded that the prevalence of VTEC O157 in meat products (joints and mince) at consumption is low (i.e., <0.04%). Beef products, particularly beef burgers, present the highest estimated risk with an estimated eight out of 100,000 servings on average resulting in human infection with VTEC O157.