Recommended Distributions for Exposure Factors Frequently Used in Health Risk Assessment

Although there has been nearly complete agreement in the scientific community that Monte Carlo techniques represent a significant improvement in the exposure assessment process, virtually all state and federal risk assessments still rely on the traditional point estimate approach. One of the rate-determining steps to a timely implementation of Monte Carlo techniques to regulatory decision making is the development of "standard" data distributions that are considered applicable to any setting. For many exposure variables, there is no need to wait any longer to adopt Monte Carlo techniques into regulatory policy since there is a wealth of data from which a robust distribution can be developed and ample evidence to indicate that the variable is not significantly influenced by site-specific conditions. In this paper, we propose several distributions that can be considered standard and customary for most settings. Age-specific distributions for soil ingestion rates, inhalation rates, body weights, skin surface area, tapwater and fish consumption, residential occupancy and occupational tenure, and soil-on-skin adherence were developed. For each distribution offered in this paper, we discuss the adequacy of the database, derivation of the distribution, and applicability of the distribution to various settings and conditions.     

Mlonte Carlo Techniques for Quantitative Uncertainty Analysis in Public Health Risk Assessments

Most public health risk assessments assume and combine a series of average, conservative, and worst-case values to derive a conservative point estimate of risk. This procedure has major limitations. This paper demonstrates a new methodology for extended uncertainty analyses in public health risk assessments using Monte Carlo techniques. The extended method begins as do some conventional methods--with the preparation of a spreadsheet to estimate exposure and risk. This method, however, continues by modeling key inputs as random variables described by probability density functions (PDFs). Overall, the technique provides a quantitative way to estimate the probability distributions for exposure and health risks within the validity of the model used. As an example, this paper presents a simplified case study for children playing in soils contaminated with benzene and benzo(a)pyrene (BaP).     

Site-Specific Applications of Probabilistic Health Risk Assessment: Review of the Literature Since 2000

Whether and to what extent contaminated sites harm ecologic and human health are topics of considerable interest, but also considerable uncertainty. Several federal and state agencies have approved the use of some or many aspects of probabilistic risk assessment (PRA), but its site-specific application has often been limited to high-profile sites and large projects. Nonetheless, times are changing: newly developed software tools, and recent federal and state guidance documents formalizing PRA procedures, now make PRA a readily available method of analysis for even small-scale projects. This article presents and discusses a broad review of PRA literature published since 2000.     

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.     

On the Effect of Probability Distributions of Input Variables in Public Health Risk Assessment

A central part of probabilistic public health risk assessment is the selection of probability distributions for the uncertain input variables. In this paper, we apply the first-order reliability method (FORM)^(1–3) as a probabilistic tool to assess the effect of probability distributions of the input random variables on the probability that risk exceeds a threshold level (termed the probability of failure) and on the relevant probabilistic sensitivities. The analysis was applied to a case study given by Thompson et al. ⁽⁴⁾ on cancer risk caused by the ingestion of benzene contaminated soil. Normal, lognormal, and uniform distributions were used in the analysis. The results show that the selection of a probability distribution function for the uncertain variables in this case study had a moderate impact on the probability that values would fall above a given threshold risk when the threshold risk is at the 50th percentile of the original distribution given by Thompson et al. ⁽⁴⁾ The impact was much greater when the threshold risk level was at the 95th percentile. The impact on uncertainty sensitivity, however, showed a reversed trend, where the impact was more appreciable for the 50th percentile of the original distribution of risk given by Thompson et al. ⁴ than for the 95th percentile. Nevertheless, the choice of distribution shape did not alter the order of probabilistic sensitivity of the basic uncertain variables.     

Exposure Assessment: Then, Now, and Quantum Leaps in the Future

Health risk assessments have become so widely accepted in the United States that their conclusions are a major factor in many environmental decisions. Although the risk assessment paradigm is 10 years old, the basic risk assessment process has been used by certain regulatory agencies for nearly 40 years. Each of the four components of the paradigm has undergone significant refinements, particularly during the last 5 years. A recent step in the development of the exposure assessment component can be found in the 1992 EPA Guidelines for Exposure Assessment. Rather than assuming worst-case or hypothetical maximum exposures, these guidelines are designed to lead to an accurate characterization, making use of a number of scientific advances. Many exposure parameters have become better defined, and more sensitive techniques now exist for measuring concentrations of contaminants in the environnment. Statistical procedures for characterizing variability, using Monte Carlo or similar approaches, eliminate the need to select point estimates for all individual exposure parameters. These probabilistic models can more accurately characterize the full range of exposures that may potentially be encountered by a given population at a particular site, reducing the need to select highly conservative values to account for this form of uncertainty in the exposure estimate. Lastly, our awareness of the uncertainties in the exposure assessment as well as our knowledge as to how best to characterize them will almost certainly provide evaluations that will be more credible and, therein, more useful to risk managers. If these refinements are incorporated into future exposure assessments, it is likely that our resources will be devoted to problems that, when resolved, will yield the largest improvement in public health.     

Residential House and Zone Volumes in the United States: Empirical and Estimated Parametric Distributions

This research reports empirical distributions and estimated univariate parametric probability distributions for house volume and certain zone volumes within households for residential structures in the United States. The author derived the distributions from two separate databases. The volumes were found to be exceptionally well fit by lognormal distributions (adjusted R² >> 0.95) in almost all cases. In addition, data from one database indicates that the correlation between house volume and air changes per hour is very weak.     

First-Order Reliability Analysis of Public Health Risk Assessment

This paper demonstrates a new methodology for probabilistic public health risk assessment using the first-order reliability method. The method provides the probability that incremental lifetime cancer risk exceeds a threshold level, and the probabilistic sensitivity quantifying the relative impact of considering the uncertainty of each random variable on the exceedance probability. The approach is applied to a case study given by Thompson et al. ⁽¹⁾ on cancer risk caused by ingestion of benzene-contaminated soil, and the results are compared to that of the Monte Carlo method. Parametric sensitivity analyses are conducted to assess the sensitivity of the probabilistic event with respect to the distribution parameters of the basic random variables, such as the mean and standard deviation. The technique is a novel approach to probabilistic risk assessment, and can be used in situations when Monte Carlo analysis is computationally expensive, such as when the simulated risk is at the tail of the risk probability distribution.     

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.     

Quantitative Risk Assessment Relating to Adventitious Presence of Allergens in Food: A Probabilistic Model Applied to Peanut in Chocolate

Peanut allergy is a public health concern, owing to the high prevalence in France and the severity of the reactions. Despite peanut-containing product avoidance diets, a risk may exist due to the adventitious presence of peanut allergens in a wide range of food products. Peanut is not mentioned in their ingredients list, but precautionary labeling is often present. A method of quantifying the risk of allergic reactions following the consumption of such products is developed, taking the example of peanut in chocolate tablets. The occurrence of adventitious peanut proteins in chocolate and the dose-response relationship are estimated with a Bayesian approach using available published data. The consumption pattern is described by the French individual consumption survey INCA2. Risk simulations are performed using second-order Monte Carlo simulations, which separately propagates variability and uncertainty of the model input variables. Peanut allergens occur in approximately 36% of the chocolates, leading to a mean exposure level of 0.2 mg of peanut proteins per eating occasion. The estimated risk of reaction averages 0.57% per eating occasion for peanut-allergic adults. The 95% values of the risk stand between 0 and 3.61%, which illustrates the risk variability. The uncertainty, represented by the 95% credible intervals, is concentrated around these risk estimates. Children have similar results. The conclusion is that adventitious peanut allergens induce a risk of reaction for a part of the French peanut-allergic population. The method developed can be generalized to assess the risk due to the consumption of every foodstuff potentially contaminated by allergens.     

Parametric Distributions for Soil Ingestion by Children

This note presents parameterized distributions of estimates of the amount of soil ingested by children based on data collected by Binder et al. (1986). Following discussions with Dr. Binder, we modified the Binder study data by using the actual stool weights instead of the 15 g value used in the original study. After testing the data for lognormality, we generated parameterized distributions for use in risk assessment uncertainty analyses such as Monte Carlo simulations.     

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.     

Quantifying the Distribution of Inhalation Exposure in Human Populations: 2. Distributions of Time Spent by Adults, Adolescents, and Children at Home, at Work, and at School

Using distributions of time spent at various ventilation levels, ranges of inhalation exposure in the population can be established. Distributions of exposure time were determined using results of a study by the California Air Resources Board (CARB) which focused on time spent by humans participating in various activities and the locations where the activities occurred. The daily at-home activities from the CARB study were assigned to one of three ventilation levels, generating aggregate time periods. Distinct age and gender populations were identified, and distributions for aggregate time were established for these populations at each of the ventilation levels. In addition to aggregate time spent at home, distributions for various ages and genders were established for aggregate time spent at school and work. By combining distributions of aggregate time with corresponding ventilation rates, the distribution of inhalation rates can be established for at home, at work, and at school exposures.     

Quantitative Assessment of Exposure to the Mycotoxin Ochratoxin A in Food

This article presents the methodology and the simulation results concerning the quantitative assessment of exposure to the fungus toxin named Ochratoxin A (OA) in food, in humans in France. We show that is possible to provide reliable calculations of exposure to OA with the conjugate means of a nonparametric-type method of simulation, a parametric-type method of simulation, and the use of bootstrap confidence intervals. In the context of the Monte Carlo simulation, the nonparametric method takes into account the consumptions and the contaminations in the simulations only via the raw data whereas the parametric method depends on the random samplings from distribution functions fitted to consumption and contamination data. Our conclusions are based on eight types of food only. Nevertheless, they are meaningful due to the major importance of these foodstuffs in human nourishment in France. This methodology can be applied whatever the food contaminant (pesticides, other mycotoxins, Cadmium, etc.) when data are available.     

On Modeling Correlated Random Variables in Risk Assessment

Monte Carlo methods in risk assessment are finding increasingly widespread application. With the recognition that inputs may be correlated, the incorporation of such correlations into the simulation has become important. Most implementations rely upon the method of Iman and Conover for generating correlated random variables. In this work, alternative methods using copulas are presented for deriving correlated random variables. It is further shown that the particular algorithm or assumption used may have a substantial effect on the output results, due to differences in higher order bivariate moments.     

Estimated Distributions for Average Daily Consumption of Total and Self-Caught Fish for Adults in Michigan Angler Households

Fish consumption rates play a critical role in the assessment of human health risks posed by the consumption of fish from chemically contaminated water bodies. Based on data from the 1989 Michigan Sport Anglers Fish Consumption Survey, we examined total fish consumption, consumption of self-caught fish, and consumption of Great Lakes fish for all adults, men, women, and certain higher risk subgroups such as anglers. We present average daily consumption rates as compound probability distributions consisting of a Bernoulli trial (to distinguish those who ate fish from those who did not) combined with a distribution (both empirical and parametric) for those who ate fish. We found that the average daily consumption rates for adults who ate fish are reasonably well fit by lognormal distributions. The compound distributions may be used as input variables for Monte Carlo simulations in public health risk assessments.     

Measures of Compounding Conservatism in Probabilistic Risk Assessment

Concern about the degree of uncertainty and potential conservatism in deterministic point estimates of risk has prompted researchers to turn increasingly to probabilistic methods for risk assessment. With Monte Carlo simulation techniques, distributions of risk reflecting uncertainty and/or variability are generated as an alternative. In this paper the compounding of conservatism⁽¹⁾ between the level associated with point estimate inputs selected from probability distributions and the level associated with the deterministic value of risk calculated using these inputs is explored. Two measures of compounded conservatism are compared and contrasted. The first measure considered, F , is defined as the ratio of the risk value, R _d, calculated deterministically as a function of n inputs each at the j th percentile of its probability distribution, and the risk value, R _j that falls at the j th percentile of the simulated risk distribution (i.e., F=R_d/R_j). The percentile of the simulated risk distribution which corresponds to the deterministic value, R_d , serves as a second measure of compounded conservatism. Analytical results for simple products of lognormal distributions are presented. In addition, a numerical treatment of several complex cases is presented using five simulation analyses from the literature to illustrate. Overall, there are cases in which conservatism compounds dramatically for deterministic point estimates of risk constructed from upper percentiles of input parameters, as well as those for which the effect is less notable. The analytical and numerical techniques discussed are intended to help analysts explore the factors that influence the magnitude of compounding conservatism in specific cases.     

Body Weight Distributions for Risk Assessment

Precise age-specific average body weight estimates are necessary for deterministic risk assessments, and an accurate body weight distribution is equally important in probabilistic risk assessments. Age-specific body weight distributions for U.S. residents are estimated using NHANES (National Health and Nutrition Examination Survey) data collected in four surveys over the last 24 years. The weighted mean and standard deviation of natural log-transformed body weights are computed for single-year age groups and population age-specific weight patterns further described using piece-wise polynomial spline functions and nonparametric age-smoothed trend lines. These functions are used to compare distributional changes in age-specific body weight in the United States from the first NHANES survey in 1976-1980 to the most recent in 1999-2002. Analysis demonstrates that age- and sex-specific average body weight changes over this time period are not uniform. Use of these functions to compute body weight distributions for selected child-age categories is demonstrated.     

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.