8

Uncertainty and Variability

Estimating potential human exposures to environmental concentrations resulting from emissions of waste-incineration facilities and estimating the risk of possible health effects of the exposures is a complex task. Such tasks involve the use of computational models coupled with large amounts of data to predict institutional performance, individual human behavior, engineered-system performance, contaminant transport in the environment, human contact with contaminants, and dose-response relationships. Comprehensive assessments also involve treatment of the variability and uncertainty associated with those data.1 This chapter addresses how, in the context of waste incineration, uncertainty and variability are defined, characterized, and treated in the risk-assessment and riskcommunication process. This process includes consideration of hazard identification, dose-response characterization, emission-source characterization, exposure assessment, risk characterization, and risk communication. Additional information on these issues can be found in NRC (1983, 1993, 1994, 1996), Morgan and Henrion (1990), Cullen (1995), and EPA (1999).

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Variability refers to the individual-to-individual differences in quantities associated with predicted risk. For example, actual human exposures vary according to individual differences in location, breathing rates, food consumption, activity patterns, and so forth. Uncertainty refers to the lack of precise knowledge as to what the truth is, whether qualitative or quantitative. There can be uncertainty in the magnitude of an individual quantity that can be measured (e.g., the imprecision of a stack emission rate measurement). Other uncertainties pertain to gaps in the scientific theory that is required to make predictions on the basis of causal inferences. For example, the appropriate model to use for predicting the relationship between the dose of a toxic substance and the health response.



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WASTE INCINERATION & PUBLIC HEALTH 8 Uncertainty and Variability Estimating potential human exposures to environmental concentrations resulting from emissions of waste-incineration facilities and estimating the risk of possible health effects of the exposures is a complex task. Such tasks involve the use of computational models coupled with large amounts of data to predict institutional performance, individual human behavior, engineered-system performance, contaminant transport in the environment, human contact with contaminants, and dose-response relationships. Comprehensive assessments also involve treatment of the variability and uncertainty associated with those data.1 This chapter addresses how, in the context of waste incineration, uncertainty and variability are defined, characterized, and treated in the risk-assessment and riskcommunication process. This process includes consideration of hazard identification, dose-response characterization, emission-source characterization, exposure assessment, risk characterization, and risk communication. Additional information on these issues can be found in NRC (1983, 1993, 1994, 1996), Morgan and Henrion (1990), Cullen (1995), and EPA (1999). 1   Variability refers to the individual-to-individual differences in quantities associated with predicted risk. For example, actual human exposures vary according to individual differences in location, breathing rates, food consumption, activity patterns, and so forth. Uncertainty refers to the lack of precise knowledge as to what the truth is, whether qualitative or quantitative. There can be uncertainty in the magnitude of an individual quantity that can be measured (e.g., the imprecision of a stack emission rate measurement). Other uncertainties pertain to gaps in the scientific theory that is required to make predictions on the basis of causal inferences. For example, the appropriate model to use for predicting the relationship between the dose of a toxic substance and the health response.

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WASTE INCINERATION & PUBLIC HEALTH The committee identified aspects of uncertainty and variability likely to have important scientific and policy implications for the potential health effects attributable to waste incineration. One overarching issue is how uncertainty and variability can influence the utility of estimates of health effects of waste incineration or of alternative technologies for waste management. As uncertainty and variability become larger, it becomes more difficult for interested or affected parties to decide how to interpret results and assign relevance to the magnitude of estimated risk. If the range is too large, different people might base their interpretation of the results on their prior opinion of waste incineration. That is, those who favor use of incineration technology might tend to focus on results in the middle range (for example, the median or mean of either variability or uncertainty distributions) of postulated effects. Those who oppose the technology might tend to focus on any results that suggest harmful effects (for example, the upper 5-10% of the possible range of outcomes). When the uncertainties or variabilities are large, there can be a large difference between those two parts of the range of possible outcomes. To give some perspective on how uncertain and variable information can influence the characterization of health impacts, Figure 8-1 provides a schematic of the major components that must be characterized to assess possible health effects. Listed next to each component are the major types of information or models needed to map the output from one logical stage of this system into the next. Two important issues are evident. First, there are large variations in the precision and accuracy2 of the information needed to characterize the sequence of steps as listed on the left of the figure. Second, this process is open, so that each component is not solely influenced by the previous one. For example, the concentration of dioxin congeners in the atmosphere near an incinerator is not linked solely to emissions from the incinerator, but may also be attributable to other sources in and out of the region. And a health effect might be connected to the facility, but understanding the etiology of any disease requires consideration of a variety of potential factors. As has been pointed out by Oreskes et al. (1994) such open-ended systems models—which are common in earth sciences, economics, engineering, and policy-making—cannot be fully verified or validated, because the operative processes are always incomplete. Nevertheless, such models can be confirmed and can be used to put bounds on the likely range of outcomes; in this sense, they offer something of value to the policy-making process. The following five factors determine the reliability of a health-risk assessment: specification of the problem (scenario development), formulation of the 2   Precision refers to the agreement among individual measurements of the same property of the sample. Accuracy refers to the agreement of a measurement (or an average of measurements of the same property) with an accepted reference or true value.

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WASTE INCINERATION & PUBLIC HEALTH FIGURE 8-1 Schematic of major components included in assessment of possible health effects of waste incineration. Other important considerations such as social and economic impacts (see Chapter 7) are not included in this figure. conceptual model (the influence diagram), formulation of the computational model, estimation of input values, and calculation and interpretation of results, including uncertainties. Uncertainty analysis should be an iterative process, moving from the identification of generic uncertainties to more refined analyses for chemical-specific or facility-specific uncertainties (NRC 1994). The use of uncertainty analysis in health risk assessment for exposure to chemical contaminants became widespread in the 1980s (Bogen and Spear 1987).

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WASTE INCINERATION & PUBLIC HEALTH Uncertainty analysis must confront the distinction between variability and true uncertainty characterizing possible outcomes. Variability occurs in such factors as location (affecting such local properties as rainfall, soil characteristics, weather patterns), and human characteristics. Those factors are inherently variable (from person to person) and cannot be represented by single values. In contrast, true uncertainty refers to a factor that is not known beyond a certain degree of precision because of measurement or estimation error. CONFRONTING VARIABILITY AND UNCERTAINTY Risk-based management strategies often operate on the premise that, with sufficient funding, science and technology will ultimately provide an obvious and cost-effective solution to the problems of protecting human health and the environment. However, there are many sources of uncertainty and variability in assessing possible impacts on human-health (and ecological) risk assessment, and many of these uncertainties and variabilities are not reducible in a practical sense. Effective policies are possible under conditions of limited knowledge, but they must take the uncertainty and variability into account. For such technologies as waste incineration, it is rare to measure the magnitude of human exposure and the resulting health risks. Such aspects are often estimated by models that vary in complexity. Regardless of the model complexity, there are two approaches by which one can assess how model predictions are influenced by model reliability and data precision: uncertainty analysis and sensitivity analysis. To address sensitivity and uncertainty, one can think of a model as producing an output, that is a function of several inputs. For example, the output could be the dioxin concentration in human tissue, and the inputs could refer to dioxin emission source strengths, wind speed and direction, exposure factors, and uptake rates. Uncertainty analysis involves the determination of the variation or imprecision in the output based on the collective variation of the model inputs, whereas sensitivity analysis involves the determination of the size of the changes in model output as a result of changes of known size in individual model inputs. Data and Modeling Adequacy Uncertainty in model predictions arises from a number of sources, including specification of the problem, formulation of the conceptual model, formulation of the computational model, estimation of input values, and interpretation of the results. Of those, only uncertainties due to estimation of input values can be quantified in a straightforward manner using the usual methods of uncertainty propagation. Some of the uncertainties that arise from misspecification of the

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WASTE INCINERATION & PUBLIC HEALTH problem, model-formulation errors, and interpretation, can be assessed with more-complex processes, such as decision trees and event trees based on expert opinions. An additional uncertainty that can plague modeling efforts is straightforward quality assurance and quality control (QA/QC) problems in model implementation (so the results calculated are not the results of the intended computations)—these are in principle easy to correct, but may dominate other uncertainties. Influence of Uncertainty on Perception of Risk The decision to spend money to identify, estimate, and manage risk carries with it an implicit valuation of the risk being controlled. Because of the uncertainty inherent in risk characterization and risk management, it is important to consider how individuals and societies value uncertainty in knowledge of adverse consequences. One expects such valuations to be expressed in terms of relative preferences, economic preferences, or ethical constraints. In managing health risks, the results of a risk characterization are integrated with social, economic, and political considerations to provide input to the riskmanagement process. A variety of techniques have been proposed and used to apply the values held by different stakeholders to the evaluation of risks. Some of the commonly used techniques of risk valuation are the elicitation of individual and societal preferences, decision analysis, and application of theories of science policy, social-welfare economics, and ethics. Use of those valuation strategies can yield an important input to the risk-management decision. Exposure and dose-response estimates are important for understanding risks, but they fail to provide all of the tools used by individuals and societies to manage risk. As discussed in Chapter 7, it is also important to understand the process by which people perceive health risks and then decide how acceptable these risks are. Risk management decisions involving costs and benefits face the economic problem of individual and societal valuation of life —a problem which has been considered by Raiffa et al. (1977) among many others. For example, although it is difficult to set a value on a statistical year of life lost, some data have been compiled so as to make consideration of years of life lost more feasible (Murray and Lopez 1996). Because risk assessments and risk management decisions must be made in the absence of complete information, they implicitly involve judgments made with uncertainty. Psychologists have observed that when people are asked to make judgments involving uncertainty, they appear to adopt a number of heuristics, or rules of thumb, for decision-making. In particular, it appears that belief about the likelihood or severity of a given event is related to the ease with which previous occurrences of the event or a similar event can be recalled. Kahneman et al. (1982) proposed a number of interesting rules of thumb regarding the acceptability or trading of risks, among them that people prefer to reduce one

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WASTE INCINERATION & PUBLIC HEALTH risk to zero instead of lowering multiple risks, that gains and losses tend not to be valued the same, that people usually are not willing to trade gains against losses, and that people are usually not willing to make risk-risk tradeoffs. The limitations of risk-estimation methods make it clear that risk managers should be aware of the uncertainty in risk estimates and include this awareness in their decisions and in their communication of risk to the public. It should be recognized that as uncertainties become large and the range of possible outcomes (that is exposure or risk) becomes difficult to characterize precisely, the beliefs of the interested or affected parties regarding risk acceptability are likely to be as important, or even more important, than results of a risk assessment in a decision-making process (Kahneman et al. 1982; NRC 1982, 1989a). Performance Characteristics and Contaminant-Source Terms Characterizations of contaminant source terms for a waste-incineration facility are often derived from emission test-data of the facility itself or by extrapolating from similar ones, and from assumptions regarding the waste feed and incineration system performance. System performance includes both the operation of the combustor and the operation of the pollution-control equipment. Similar facilities may vary in emissions as a result of emission limitation requirements, control technologies, and operating practices, as well as more obvious differences. For example, older permits can be more lenient than those written more recently. In addition, some emission standards are different for different sizes of incinerators (See Chapter 6). To the extent that there is uncertainty regarding the performance of an incineration facility, there will be lack of precision in information on the magnitude and composition of emissions (for example, see Frey et al. 1999). Moreover, emissions from a single facility will vary with time, for example due to changes in operating conditions. Thus, assessment of health risk for waste-incineration facilities should include consideration of such variations, including emissions resulting from off-normal activities, in addition to routine stack and fugitive emissions. Because they involve unusual events on which there is little advance information, assessing the frequency of occurrence and progression of off-normal emissions is likely to be a highly uncertain process. Hazard Identification Hazard identification involves the determination that a health hazard is or might be associated with a chemical exposure or physical factor. It is a sine qua non in the risk-assessment process and can be based on simple screening methods, short- and long-term assays of living cells or multicellular organisms, or preliminary human health surveys. Such approaches generally cannot yield a yes or no answer, but a probability that approaches yes or no only as the probability

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WASTE INCINERATION & PUBLIC HEALTH approaches 1 or zero. For example, one assay used to determine whether a chemical might be a human carcinogen is the Ames bacterial-revertant assay. A principal uncertainty associated with this assay is whether a positive response (or negative response) in the assay means that the chemical is capable (incapable) of producing cancer in humans. Other examples include epidemiologic studies of factors associated with the onset of respiratory or reproductive effects. Table 8-1 summarizes the utility of different types of information provided by assays used in hazard identification. Such assays are followed by qualitative extrapolations of various types from the assay to the human-exposure situations associated with incinerators. The extrapolations are smallest for the last assay listed in Table 8-1, and largest for the first. Even using the results of epidemiologic surveys generally requires qualitative (as well as quantitative) extrapolations, because various aspects of the exposure situations are usually different. From in vivo assays in other organisms, an additional interspecies extrapolation is required that may easily result in misclassifications of agents as hazardous or not hazardous, and the qualitative jump is even larger for the first two assays. It is important to also keep in mind that different approaches could be inconsistent (e.g., positive animal studies and negative epidemiologic studies). Environmental Transport and Human Exposure Some form of exposure assessment is required in a number of health-related assessments, including risk assessments, status and trends analyses, and epidemiologic studies. In assessing exposures to environmental concentrations resulting from the emission of contaminants from incineration facilities, a multimedia environmental approach is needed. In such an approach, all contaminant releases to the environment are traced through all environmental media—air, water, soil, sediment, vegetation, food, etc.—taking into account any changes in the form of the contaminants. Estimating the effects of human exposures resulting from incineration emissions generally require information on the following: The quantities of contaminants released to air or the concentrations measured or estimated in air, soil, plants, and water in the vicinity of the source. The transfer rates of contaminants onto (and out of) environmental media to which humans may be exposed. Such transfer rates must take account of contaminant degradation, partitioning, bioconcentration, dilution, and other physical, chemical, and biologic processes. The frequency, magnitude, and duration of human contact with the contaminated exposure medium.

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WASTE INCINERATION & PUBLIC HEALTH TABLE 8-1 Comparison of Uncertainties in and Reliability of Various Strategies for Hazard Identification Strategy Comments Predictions based on description of the chemical substituents, molecular weight, energy and molecular orbital calculations, structure-activity relationships or other factors that might predict toxicological characteristics These prediction methods are generally inexpensive and constitute a rapid screen. They can be applied to a large number of chemical agents. However, assessing the likely effects of mixtures is difficult. Validation is important for the overall reliability of the hazard measure. Predictions should be viewed as hypotheses that require more-detailed evaluation. In vitro assays, short-term assays, effects on cells in culture, analysis of effects on specific cellular functions Less expensive and more rapid than in vivo assays. These assays may be used to characterize a site and mechanism of action. They provide useful adjuncts to in vivo assays. The measure of effect is often sensitive to both the material used in the assay and the protocol used to assess damage. In vivo assays, toxic response to the agent, development of disease in exposed animals or humans These are generally more-expensive and time-consuming assays. They are thought to represent the most complete and biologically integrated assays for characterizing toxicity of a chemical. Despite their integrative nature, there can be considerable disagreement on the validity of animal data for use in assessing human hazards. Epidemiologic studies of health effects in response to chemical exposures, including cancer and reproductive, developmental, and immune disease In all epidemiologic studies, the focus of attention is on health effects in human populations. Uncertainties in these studies can refer to characterization of the exposure, the etiologic agent, confounding factors, and understanding causation in heterogeneous human populations. The dose-response relationships for the particular contaminants. Descriptions of such relationships must include the effect of time and intensity of exposure. The uncertainty and variability typical of these aspects have been assessed in a number of papers. McKone and Ryan (1989) considered the overall uncertainty in estimating the link between atmospheric concentrations and food concentrations for 2,3,7,8-tetrachlorodibenzo-p-dioxins (TCDD) and for metals. McKone (1993) compiled a list of the cross-media transfer coefficients typically incorporated in a multimedia exposure assessment and estimated the uncertainty

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WASTE INCINERATION & PUBLIC HEALTH (measured as a coefficient of variation3) in these estimates. Table 8-2 lists McKone's (1993) estimates of uncertainties in correlation models for partition coefficients of organic chemicals between soil and plants, between air and plants, and between animal intake and animal food products. These early estimates of uncertainty include components that might be related to variability (for example, between soils or between locations) in a more modern assessment. Cullen (1995) has considered the degree to which the uncertainty of the results of a probabilistic risk assessment for waste incinerators is contingent on certain model assumptions. She found that the risk-assessment results are very sensitive to the selection of models for representing the fate and transport of incinerator contaminants, especially to their assumptions about gas-particle partitioning in the stack and downwind atmosphere. For lipophilic contaminants—such as dioxins, furans, and polychlorinated biphenyls—and for such metals as lead and mercury, exposures through food have been demonstrated to be major contributors to total dose in non-occupationally exposed populations (Travis and Hester 1991). Overall uncertainties in estimating potential doses through food chains are much larger than uncertainties associated with direct exposure pathways (McKone and Ryan 1989; McK-one and Daniels 1991). Intake of substances in food varies widely among individuals, among age groups, among regions of the country, and among seasons of the year (NRC 1993). It is possible that exposures via one environmental medium dominates the health concerns related to an emission source. Therefore, depending on the magnitude of error considered acceptable for a particular investigation, a focus on the medium of greatest exposure might be appropriate. Dose-Response Characterization Dose-response characterization is the process of defining the site of action in the body, the mechanism of action, and the dose-effect relationship, for a material causing adverse effects. In this process, a series of models usually are relied on. The models may be of various types, including statistical models and biologically based models (e.g., physiologically based pharmacokinetic or biologically based dose-response models). Each has limitations in representing the actual toxic or human-hazard effects and as a result each has associated various degrees of uncertainty (see Table 8-3). Model uncertainty (that is, being unsure about the true nature of the relationship between dose and response) is likely to be highly important in dose-response characterization. Despite the admitted large uncertainty, simple doseresponse models are the most commonly used for predicting human health effects 3   The coefficient of variation is the ratio of the standard deviation to the estimated arithmetic mean value of a parameter.

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WASTE INCINERATION & PUBLIC HEALTH TABLE 8-2 Summary of Methods for Estimating Intermedia Transfer Factors and Coefficient of Variation Associated with Estimation Errors Factor Description and Symbol Estimation Formula or Value Coefficient of Variation Unitsa Units Key References Octanol-water partition coefficient, Kow Chemical specific n/a kg (water)/kg (octanol) Lyman et al. 1982; Verschueren 1983; Howard 1990a,b, 1991 Organic-carbon partition coefficient, Koc 0.41 Kow 1 kg(water)/kg (carbon) Karickhoff (1981) Soil/soil-water partition coefficient, KD foc × Koc 1 kg(water)/kg (soil solids) Karickhoff (1981) Plant-soil partition coefficient for surface soil due to rainsplash, rain Kps 0.0034 1 1 kg(soil)/kg (plant FM)b Dreicer et al. (1984) Plant-soil partition coefficient from root-zone soil to above-ground plant parts, Kps 7.7 K -0.58ow 4 kg(soil)/kg (plant FM) Travis and Arms (1988) Plant-soil partition coefficient from root-zone soil to roots (used for protected produce), Kps (roots) 270 K -0.58ow 4 kg(soil)/kg (plant FM) Topp et al. (1986) Plant-air partition coefficient for gas-phase contaminant, Kgsap Riederer (1990) [0.5 + (0.4 + 0.01 × Kow) × (RT/H)] × 10-3 14 m3(air)/kg (plant FM) Bacci et al. (1990) Plant-air partition and coefficient for particle-bound contaminant, Kptap 3300 1.5 m3(air)/kg (plant FM) McKone and Ryan (1989) Biotransfer factor for meat concentration versus intake for beef cattle, Bt 2.5 × 10-8Kow 11 day/kg(meat) Travis and Arms (1988) Biotransfer factor for milk concentration versus intake for dairy cattle, Bk 7.9 × 10-9Kow 6 day/kg(milk) Travis and Arms (1988) Biotransfer factor for egg concentration versus intake for chickens, Be 1.6 × 10-6Kow 14 day/kg(eggs) McKone (1993) a A high coefficient of variation implies that the intermedia transfer factor is not well understood. b FM refers to fresh mass. Source: McKone 1993. Copyright 1993, Overseas Publishers AssociationN.V.; permission received from Gordon and Breach Publishers.

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WASTE INCINERATION & PUBLIC HEALTH TABLE 8-3 Aspects That Contribute to Uncertainty in Models Used for Dose-Response Characterization Model Description Aspects that Contribute to Uncertainty Statistical dose-effect models Dose-response characterizations are statistical descriptions of the relationship between dose and disease. The models contain little or no biologic insight. If the dose-effect models are derived from epidemiologic data, lack of biologic insight is of little concern. If they are derived from animal data, relevance might be a concern. Typically, large doses are given to experimental animals for statistical and predictive reasons. Therefore, it is necessary to scale the dose-response relationship across species by weight or surface-area adjustments. Toxicokinetic and toxicodynamic characteristics determine dose-response relationships. Does the observed dose-response relationship define the severity of disease, proportion of the population with the disease, or both? How does one correct for species differences in the dose-response relationship, surface area, or body weight? Biologic models Biologic models provide qualitative or quantitative descriptions of the site and mechanism of action. They attempt to define how and where an agent acts to produce disease, how sites and mechanisms differ across species, and what effect the differences have in the prediction of human disease. Is the parent compound or a metabolite responsible for the disease? What are the differences across species in toxicokinetics and toxicodynamics? Are there species differences in the physiologic factors that influence the response of different species to the agent (chemical or metabolite) associated with disease? What physiologic factors influence the chemical-disease relationship? What are the quantitative and qualitative descriptors of uncertainty and variability in dose-response characterization? Is the biologic model reasonably correct? in dose or exposure regions (usually low doses of exposures) that are not experimentally accessible. Such models have often been used in establishing policy. As use of risk assessment grows, the need for sophistication of the models and the accuracy or completeness of their representation of biologic processes is also likely to grow. For example, pharmacokinetic (PK) models provide tools to estimate the distribution of a chemical throughout the body and thus assists in evaluating the amount delivered to the target site. It is believed that such models can improve the procedures used to extrapolate to low doses or between species.

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WASTE INCINERATION & PUBLIC HEALTH UNCERTAINTY AND SENSITIVITY ANALYSES A Tiered Approach to Uncertainty and Variability Analyses An important, and often ignored, step in the risk-characterization process is the characterization of variability and uncertainty. This process has often been passed over in practice. To adequately confront variability and uncertainty in risk assessments, it is necessary to incorporate the treatment of both from the very beginning. One approach is to take a tiered approach to such analyses. Three tiers are involved, and may be applied separately to variability and uncertainty. First, the variation, and if possible the co-variation of all input values should be clearly stated, with clear separation between variation due to variability and that due to uncertainty. One approach might be to evaluate variances and covariances on suitable scales of measurement, or the components of such variances and covariances attributable to variability and uncertainty. More generally, the most-complete specifications available of joint variability and uncertainty distributions are needed. A clear assignment of the variation in input values to variability or uncertainty requires a careful and clear summary and justification of the assumptions used for each aspect of the modeling in which these input variables are used. Second, a sensitivity analysis may be used to assess how model predictions are affected by variation in input values. The goal of the sensitivity analysis is to rank input parameters on the basis of their contributions to variance in the output. The ranking should take account separately of the input-output sensitivity of the models, and the variability and uncertainty variances of the inputs (so that a highly variable or highly uncertain input might have high rank even if the input-output sensitivity is not high). Third, some form of variance-propagation methods (such as Monte-Carlo methods) should be used to map how the overall variability and uncertainty of risk estimates is tied to the variability and uncertainty associated with the models, inputs, and exposure scenarios. The sensitivity analysis may be used to limit the number of inputs for which full variability or uncertainty information is required, for example by retaining or demanding full distributional information only for the high rank inputs. Distributional information for lower-ranked inputs might be represented by approximations (e.g., using just constant estimates, or first and second moment estimates). Modern methods have now eliminated computer-program constraints and available computational power as limitations on retaining distributional information—if the information is available, it can now readily be used. The major limitation is now on gathering distributional

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WASTE INCINERATION & PUBLIC HEALTH information about the inputs, and a sensitivity analysis allows finding the inputs on which most resources should be expended. Methods for Representing and Propagating Parameter Variance Describing the uncertainty, variability, or both in a risk estimate obtained as an output from a model involves quantification of various statistics of that output. Such statistics might include its range, its arithmetic mean, its arithmetic or geometric standard deviation, and various percentiles, like the 5% and 95% percentile. Such information is encoded in, and may be presented by using the probability-density function or the cumulative-distribution function. Such functions of risk can be obtained only with usable estimates of the probability distributions of the input variables. What is usable depends on factors including the amount and quality of information available, the understanding of the appropriate biologic models, careful consideration of individual variations in susceptibility, population-wide confounders, and, of course, the needs of a particular analysis. Five main steps in an input uncertainty analysis (IAEA 1989) are described below, and very similar comments apply to analysis of variability: Identify the inputs that could contribute substantially to the uncertainty in the predictions of outcome by a model. Care should be exercised not to discard potentially important uncertainties without good cause. Construct for each input a probability-density function both to define the range of values that an input parameter can have and to reflect the belief that the parameter will take on the various values within that range. Account for dependencies (correlations) among the input data and how they affect uncertainty. Propagate the uncertainties through the model to generate a probability-density function of predicted outcome values. From the probability-density function of predicted values of the outcome variable, derive confidence limits and intervals to provide a quantitative statement about the effect of input uncertainty on the model predictions. The value of information derived from an input uncertainty or variability analysis depends heavily on the care given to the process of constructing input-parameter probability-density functions. One begins the process of constructing a probability-density function for a given input by assembling values from measurements. The values should be consistent with the model and its particular application. The values will vary as a result of spatial and temporal variability, measurement error, extrapolation of data from one situation to another, extent of knowledge, and so on. The process of constructing a probability-density function from limited and imprecise data can be highly subjective. The analyst must

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WASTE INCINERATION & PUBLIC HEALTH often apply judgment to the process, and so requires expertise and wisdom. The process is likely to become more objective as the amount of data on a given input increases. However, a large set of data does not necessarily imply easy construction of a suitable probability-density function for any particular application. UNCERTAINTIES IN THE COMMUNICATION OF RISK INFORMATION Most risk assessment documents for waste-incineration facilities have been assembled mainly to comply with regulatory requirements and guidelines. There is even now an EPA document that attempts to formalize some of the requirements for risk assessments for hazardous-waste incinerators (EPA 1998a). However, if regulatory requirements or guidelines are the only motivation for investing time and energy in these a risk assessment document, the result is usually badly presented. Such documents are difficult to use as a basis for interacting with affected communities, and it is hard to argue that the documents provide much in the way of public service. If an important goal of a risk assessment is to address the effect of a process or facility on public health and to address the concerns of the affected community, there is a need to provide information that can be used to support informed debate on community health issues. However, in many risk-assessment documents, much of the information related to those issues is not readily accessible in the text, equations, tables, and appendixes. The sense of incomprehensibility and exclusion that is experienced by affected communities can result in unnecessary polarization. One way to avoid that is to include early in the risk-assessment process a summary of the local-community concerns and a brief description of how they are addressed in the risk assessment. Failure to express community concerns in a risk assessment leaves one with the impression that the concerns of the regulators are all that matter. CONCLUSIONS There are many reasons for uncertainty and variability in the information used to assess possible health effects of waste incineration. There are large variations from facility to facility with regard to types of waste combusted, operating practices, allowable emission levels, emission-control technologies, types of chemicals emitted, environmental characteristics, proximity to other sources of contaminant exposure, frequency of off-normal emissions, and the biologic and behavioral characteristics of the people who might be exposed to the contaminants in the environment. Some uncertainties are peculiar to incineration, and some are inherent in any activity that releases contaminants into the environment. Some of the uncertainties and variabilities can be reduced or better accounted for; others, by their nature, remain unchanged. Nonetheless, there is a need to make decisions concerning the siting, design, operation, and regulation of incin-

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WASTE INCINERATION & PUBLIC HEALTH eration facilities. The most effective decisions are the ones that take uncertainty and variability fully into account. When key uncertainties become very large, quantitative estimates of risk may do little to change the previously held beliefs of interested or affected parties. Those who favor the use of incineration technology tend to focus on results in the middle range, and those who are opposed to incineration tend to focus on scenarios associated with the high exposures. RECOMMENDATIONS Decisionmakers should coordinate with risk assessors in identifying the uncertainties and variabilities associated with estimating the health risks of waste incineration that are likely to have the greatest impact on the specific decision to be made. Decisionmakers should consider individual and societal values regarding uncertain adverse consequences by eliciting individual or societal preferences, using decision analysis, and applying theories of science policy, social-welfare economics, and ethics. Assessments of public-health risk posed by waste incineration should consider, through the use of sensitivity analyses or otherwise, the importance of emissions resulting from off-normal activities in addition to routine stack emissions or fugitive emissions. Incinerator risk assessments should include the following components of uncertainty and variability analyses: An estimate of the variability and uncertainty distributions of all input values and their effect on final estimates. A sensitivity analysis to assess how model predictions are related to variations in input data. Variance-propagation models that show how the variability and uncertainty of final results are tied to the uncertainties and variabilities associated with various models, their inputs, and assumptions used throughout the risk assessment. Risk assessments should provide information that can be used to support informed debate on the various issues of concern regarding the health of community members. Assessments should include a summary of local community concerns and a description of how they have been or will be addressed in the risk-assessment process.