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7.1 Introduction

As applied to hazardous agents in food, health-risk assessment is a quantitative evaluation of information on potential health hazards from exposure to various agents and involves four inter-related steps discussed earlier, namely, (i) hazard identification; (ii) hazard characterization; (iii) exposure assessment, and; (iv) risk characterization. There are many sources of both uncertainty and variability in the process of human health-risk assessment (Covello and Merkhofer, 1993; Finkel, 1990; IAEA, 1989; Morgan and Henrion, 1990; NRC, 1983, 1993, 1994). While effective risk management policies are possible under conditions of both uncertainty and variability, such policies must take both into account.

An uncertainty analysis is an important component of risk characterization. It provides a quantitative estimate of value ranges for an outcome, such as estimated numbers of health effects. The ranges in the outcome are attributable to the variance and uncertainties in data and the uncertainties in the structure of any models used to define the relationship between exposure and adverse health effects. This section addresses the problems of defining, characterizing, and propagating uncertainty and variability in risk characterization. The nature of variance and uncertainties in data and models are considered, and variability (heterogeneity) and true uncertainty (lack of precise knowledge) in data and models are distinguished. Methods for addressing uncertainties in data, the relationship between the true uncertainty and variability inherent in models and data, and the nature of the uncertainties likely to be confronted at each stage of the risk assessment process are identified.

7.2 Uncertainty versus variability

One of the issues in uncertainty analysis that must be confronted is how to distinguish between the relative contribution of variability (i.e., heterogeneity) and true uncertainty to the characterization of predicted population risk. Variability refers to quantities that are distributed within a defined population, such as: food consumption rates, exposure duration, and expected lifetime. These are inherently variable and cannot be represented by a single value, so that we can only determine their moments (e.g., mean, variance, skewness, etc.) with precision. In contrast, true uncertainty or model-specification error (e.g., statistical estimation error) refers to a parameter that has a single value, which cannot be known with precision due to measurement or estimation error. Variability and true uncertainty may be formally classified as follows: (i) Type A uncertainty that is due to stochastic variability with respect to the reference unit of the assessment question, and; (ii) Type B uncertainty that is due to lack of knowledge about items that are invariant with respect to the reference unit of the assessment question. There are situations in which true (Type B) uncertainty is negligible relative to variability (Type A uncertainty). In these situations, the outcome of a variance propagation analysis represents the expected statistical variation in dose or risk among the exposed population. When neither variability nor uncertainty are negligible, the shape of the distributional curve representation of variability is unknown because of uncertainties.

7.3 Model uncertainty versus input (parameter) uncertainty

Uncertainty in model predictions arises from a number of sources, including specification of the problem, formulation of conceptual and computational models, estimation of input values, and calculation, interpretation, and documentation of the results. Of these, only uncertainties due to estimation of input values can be quantified with variance propagation techniques. Uncertainties that arise from mis-specification of the model can be assessed using decision trees and event trees based on elicitation of expert opinions. In some cases, using methods such as meta-analysis, model specification errors can be handled using simple variance propagation methods.

7.3.1 Nature of models

Because the magnitude of chemical or microbial risks attributable to food can rarely be measured, such outcomes are estimated using models or projections from historical data. Exposure-effect models range from simple "rule-of-thumb" models to complex stochastic models. The reliability of these models is determined by the precision of the inputs and the accuracy with which the model captures the relevant biological, chemical, and physical processes. Uncertainty analysis can be used to assess how model predictions are impacted by model reliability and data precision.

7.3.2 Methods for addressing model uncertainty

When there is uncertainty about the appropriate scenario or model, techniques can be used to assess the implication of alternate models on the predicted outcome. Methods such as probability trees, event trees, and fault trees can be used to portray the multiple events leading to the outcome of interest. An event tree starts with some initiating event and contains all the possible outcomes. The probability associated with each event may be represented by a probability distribution. The strengths of this approach include the visual portrayal of all the potential scenarios and the use of probability distributions as interpretations of relevant evidence.

7.3.3 Methods for representing and propagating input variance

Describing uncertainty in the risk involves quantification of the arithmetic mean value, the arithmetic or geometric standard deviation, and upper and lower quantile values of risk. Convenient tools for presenting such information are the probability density function or the cumulative distribution function for risk. However, the probability density function or cumulative density function of risk can often only be obtained when there are meaningful estimates of the probability distributions of the input variables used to estimate risk. There are five steps in an uncertainty analysis:

  1. identify inputs that could contribute to uncertainty in the predictions of a model;
  2. construct a probability density function to define the values that an input parameter can take;
  3. account for dependencies (correlations) among input parameters;
  4. propagate the uncertainties through the model to generate a probability density function of the outcome values; and,
  5. derive confidence limits and intervals from the probability density function of predicted values of the outcome variable.

The relationship between variance in model parameter inputs and the variance in the model predictions are estimated using variance propagation methods. Exact analytical, approximate analytical, and statistical simulation methods are available that can be used to propagate variance.

7.4 Uncertainty and variability in hazard identification

The hazard identification step involves the determination that a health hazard is or may be associated with a biological, chemical, or physical agent present in foods. The step is generally based on screening methods and short and long-term cell or animal assays. Some examples and assay systems include quantitative structure-activity relationships, short-term bioassays, and animal bioassays. This step provides a dichotomous answer - that is, the factor is or is not thought to be a human health hazard. The uncertainty involves the correct classification of the agent (i.e., it is or is not a human health hazard) and performance of the assay in classification of the agent. If the agent is evaluated in the assay multiple times, it is predicted to be either positive or negative with a certain degree of precision that is related to the performance of the assay. For example, one assay used to determine if a chemical is a mutagen is the Ames bacterial revertant assay. Uncertainty associated with the analysis of a chemical in this assay derives from knowing whether the assay is actually capable of predicting whether a positive response (or negative response) means that the chemical is capable (or incapable) of producing cancer in humans. The performance of the assay involves determining how the same chemical is characterized if analyzed in this assay system at several different times and in different assay systems.

Three issues are considered potentially significant contributions to uncertainty and variability in hazard identification. First, is the misclassification of an agent - either identification of an agent as a hazard when it is not or the reverse. Second, is the issue of the reliability of the screening method both for appropriately identifying a hazard and the reliability of the assays to give the same result each time the assay is performed. Third, is the issue of extrapolation because all screening methods are used to extrapolate the information provided by the test to predict human hazards. Epidemiological studies are used to predict the impact of exposures on human populations in the future. As an example, in epidemiological studies, the extent of the extrapolation needed to predict health hazards for future human populations is generally minimal; whereas, other assays have substantially greater need for extrapolation to produce predictions of potential adverse health effects for human populations.

7.5 Uncertainty and variability in hazard characterization

Hazard characterization is the process of defining the site, mechanism of action and at minimum the dose-response (proportion responding or severity of response) relationship. In this step, it is likely that a series of models may be developed. The models vary from purely mathematical representations to biologically-based representations. As a result, each has varying degrees of representation of the actual human disease process and as a result varying degrees of uncertainty.

Model uncertainty is likely to be an important issue in the hazard characterization step. Mathematical dose-response relationships have the greatest uncertainty in actual representation of the biological processes. Despite the admitted large uncertainty, dose-response models are currently the most commonly used methods for predicting human health effects and have often proved useful in establishing policy. As interest in risk assessment has grown, the sophistication of the models, including the accuracy and completeness of their representation of the biological processes, has also grown.

An important issue of both variability and uncertainty that arises in hazard characterization is in the variance in the dose-response at the dosage levels for the species studied. To increase power and the value of a negative study, typically large exposures are used in bioassays. These exposures are generally substantially greater than usual human exposures. That means that models including exposure response information gathered at high exposures may not be accurate at the low exposure levels of concern for human risk assessment. In addition, there is variance by animals in response at a given dose, despite the fact that most experimental animals are generally inbred and expected to be genetically identical. If outbred animals are used, the variability in the dose response relationship is expected to be larger, and if humans are exposed, the variance is also expected to be large.

Another issue of both uncertainty and variability that arises in hazard characterization is the need to extrapolate between species. Approaches used for extrapolation between species include both uncertainty about the appropriate model for performing the extrapolation as well as variability in the parameters used for extrapolation.

7.6 Uncertainty and variability in exposure assessment

Any model used to represent exposure should include several pieces of information:

  1. the level of an agent measured in a commodity or the levels measured in soil, plants, or animals that supply this commodity;
  2. the depletion/concentration ratio which defines changes in the level of an agent as a result of processing, preparation, and dilution;
  3. the frequency and magnitude of human intake of a commodity;
  4. the duration of contact or the fraction of a lifetime during which an individual is exposed to a commodity; and,
  5. the averaging time for the type of health effects under consideration to be clinically detectable.

These factors typically converge in the process of defining the distribution of population exposure.

The population at risk for exposure refers to the population that consumes food containing the hazard. An exposure assessment is the key input to the assessment of dose, which reflects the amount of the agent delivered to the target organ or tissue, where the adverse effect can be induced

Defining exposure pathways is an important component of the exposure assessment. An exposure pathway is the course a biological, chemical, or physical agent takes from a known source to an exposed individual. In the case of agents in food, concentrations of chemicals and/or organisms (microbes, parasites, etc.) can change between what is measured in soil, plants, animals and raw food and what is ingested by an individual. In the case of chemicals, there can be some increases of contaminant concentration due to process (i.e. distillation), but more likely the storage, processing and preparation of the food product will result in a reduction of contaminant concentration. For organisms, there might be significant increases of microbe or contaminant concentration due to replication under favorable environmental conditions. Thus, significant uncertainties might be expected in the ratio of the concentration of a bacterial agent in food at the time of consumption to the concentration measured in raw foods or measured in animals, plants, or soil.

7.7 Uncertainty and variability in risk characterization

Once hazard characterization and exposure information have been collected, risk characterization is carried out by constructing a model for the distribution of individual or population risk. This is done by summing the effect over all exposure routes. Because of the uncertainties and variabilities involved in its constituent steps, the overall process of risk characterization might involve potentially large uncertainties.

An important final step in the risk characterization process is the characterization of uncertainties. In order to directly characterize uncertainties in risk assessments, it is necessary to take a tiered approach to uncertainty analysis. Three tiers can be used. First, the variance of all input values should be clearly stated and the impact of these variances on the final estimates of risk assessed. Second, a sensitivity analysis should be used to assess how model predictions are impacted by model reliability and data precision. The goal of a sensitivity analysis is to rank the input parameters on the basis of their contribution to variance in the output. Finally, variance propagation methods should be used to carefully map how the overall precision of risk estimates is tied to the variability and uncertainty associated with the models, inputs, and scenarios.

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