Scenario–model–parameter

Environment International 28 (2002) 247 – 261 www.elsevier.com/locate/envint Scenario–model–parameter: a new method of cumulative risk uncertainty analysis D.J. Moschandreas a,*, S. Karuchit b a Illinois Institute of Technology, Department of Chemical and Environmental Engineering, Perlstein Hall, Room 233, 10 West 33rd Street, Chicago, IL 60616-3783, USA b Suranaree University of Technology, School of Environmental Engineering, 111 University Avenue, Suranaree Subdistrict, Muang District, Nakhon Ratchasima 30000, Thailand Received 12 October 2001; accepted 27 March 2002 Abstract The recently developed concepts of aggregate risk and cumulative risk rectify two limitations associated with the classical risk assessment paradigm established in the early 1980s. Aggregate exposure denotes the amount of one pollutant available at the biological exchange boundaries from multiple routes of exposure. Cumulative risk assessment is defined as an assessment of risk from the accumulation of a common toxic effect from all routes of exposure to multiple chemicals sharing a common mechanism of toxicity. Thus, cumulative risk constitutes an improvement over the classical risk paradigm, which treats exposures from multiple routes as independent events associated with each specific route. Risk assessors formulate complex models and identify many realistic scenarios of exposure that enable them to estimate risks from exposures to multiple pollutants and multiple routes. The increase in complexity of the risk assessment process is likely to increase risk uncertainty. Despite evidence that scenario and model uncertainty contribute to the overall uncertainty of cumulative risk estimates, present uncertainty analysis of risk estimates accounts only for parameter uncertainty and excludes model and scenario uncertainties. This paper provides a synopsis of the risk assessment evolution and associated uncertainty analysis methods. This evolution leads to the concept of the scenario – model – parameter (SMP) cumulative risk uncertainty analysis method. The SMP uncertainty analysis is a multiple step procedure that assesses uncertainty associated with the use of judiciously selected scenarios and models of exposure and risk. Ultimately, the SMP uncertainty analysis method compares risk uncertainty estimates determined using all three sources of uncertainty with conventional risk uncertainty estimates obtained using only the parameter source. An example of applying the SMP uncertainty analysis to cumulative risk estimates from exposures to two pesticides indicates that inclusion of scenario and model sources increases uncertainty of risk estimates relative to those estimated using only the parameter source. Changes in uncertainty magnitude may affect decisions made by risk managers. D 2002 Published by Elsevier Science Ltd. Keywords: Cumulative risk; Aggregate risk; Uncertainty analysis; Variability; Monte Carlo simulation 1. Introduction 1. Exposures to a pollutant from multiple routes are usually treated as independent events associated with each The National Research Council (NRC) instituted the specific route (EPA, 1999a). Therefore, simultaneous expo- classical risk assessment paradigm, a multiple-step proce- sures experienced by one person from multiple routes over a dure that identifies a hazard and then relates population period of time are not considered. exposure to one agent with dose and risk (NRC, 1983). 2. Exposures to multiple chemicals are often treated as However, this conventional risk assessment practice is con- individual events and the combined toxicity effect(s) of strained by the following limitations that could lead to simultaneous exposures to multiple chemicals are not underestimation of risk. addressed. 3. Uncertainty analysis in conventional risk assessment considers only parameter uncertainty. Although both of the * Corresponding author. Tel.: +1-312-567-3040; fax: +1-312-567-8874. other two types of uncertainty (scenario and model) con- E-mail address: djm@iit.edu (D.J. Moschandreas). tribute to overall uncertainty, they are frequently assumed 0160-4120/02/$ - see front matter D 2002 Published by Elsevier Science Ltd. PII: S 0 1 6 0 - 4 1 2 0 ( 0 2 ) 0 0 0 2 5 - 9 248 D.J. Moschandreas, S. Karuchit / Environment International 28 (2002) 247–261 negligible or ignored (Fayerweather et al., 1999). Failure to new method that adds model and scenario uncertainty to the account for them could compromise the validity of the conventional parameter uncertainty analysis of the cumu- outcome and conclusions reached by current methods of lative risk assessment. We call this new inclusive method estimating risk assessment. the scenario –model – parameter (SMP) uncertainty analysis. The recently developed concepts of aggregate and This paper focuses on the development of the SMP uncer- cumulative risks respond to the first and second limitations, tainty analysis as an integral part of the cumulative risk respectively (EPA, 1999a, 2000). Risk assessment analysis assessment method. We begin with a review of essential is evolving as risk assessors formulate models that are more concepts involving exposure, dose, and risk, including the complex, identify many and more realistic scenarios of new aggregate and cumulative risk concepts, continue with exposure, and attain new insights that allow the practitioner a review of uncertainty classification and uncertainty anal- to estimate risks from exposures to multiple pollutants and ysis processes, and conclude by formulating the SMP multiple routes. This increase in complexity of the risk uncertainty analysis process. We demonstrate the applica- assessment process is likely to increase risk uncertainties. tion of this method with results from a related paper on the However, methods to estimate uncertainty associated with uncertainty of risk estimates from exposures to chlorpyrifos risk estimates have remained unchanged. Uncertainty anal- and diazinon using the National Human Exposure Assess- ysis of risk estimates accounts for only parameter uncer- ment Survey in Arizona (NHEXAS-AZ) database (Karuchit tainty and excludes model and scenario uncertainties. Risk and Moschandreas, 2001). analysts have not substantiated but assume that model and scenario uncertainties are smaller than parameter uncertain- ties. In a recent treatment of uncertainty assessment of 2. A synopsis of risk-related concepts chemical dose that the authors characterize as ‘‘introduc- tory,’’ Hertwich et al. (2000) address all three types of 2.1. Exposure and dose uncertainties. They conclude that scenario and model uncer- tainty analysis can change dose estimates by several orders Definitions of exposure, dose and related terms used in of magnitude. this paper are those established in the EPA document Currently, a specific procedure for a quantitative analysis ‘‘Guidelines for Exposure Assessment’’ (EPA, 1992a). The of scenario or model uncertainty is not available in the basic structure of the flow of an agent from the outer literature. A general suggestion regarding analysis of model boundary to the receptor target organ and associated defi- uncertainty is that risk assessors may use different models to nitions are illustrated in Table 1 (EPA, 1992a). The onset of estimate outputs (EPA, 1992a; Hoffman and Hammonds, the scheme is the contact of a chemical agent with the outer 1994). The range of outputs can be considered as represent- boundary, which establishes an exposure. The outer boun- ing the uncertainty range. A more focused approach that daries of the inhalation route are the mouth and nose, and deals specifically with scenario and model uncertainties is the outer boundary of the ingestion route is the mouth. In known as the distributional approach. This approach has this scheme, there is no outer boundary of the dermal route, been used in analyses of uncertainty from model structure since the skin is the place where absorption takes place, and and alternative assumptions or scenarios (Fayerweather et therefore it is an absorption barrier or exchange boundary, al., 1999; Evans et al., 1994a,b). The distributional approach not an outer boundary. The route-specific boundaries, with divides the risk assessment into a series of decision points corresponding chemical transfer process, are shown in Table called ‘‘nodes’’ that have alternatives. A combination of 2 (EPA, 1992a). alternatives from each node constitutes a ‘‘tree.’’ Each tree The intake process commences when the chemical has an assigned probability or ‘‘weight’’ based on expert moves through the opening of the outer boundary. The judgment. This weight is attributed to the risk estimate amount of the chemical after crossing the outer boundary resulting from each tree. Such results form the final risk is called a potential dose. Inhalation dose, oral dose and distribution. However, the integrity of the final distribution dermal dose are common names for route-specific potential relies heavily on the subjective nature of experts’ input. dose (EPA, 1992a). Potential dose is synonymous with There are also concerns that assigning probabilities to administered dose. The amount that reaches the exchange models, i.e., quantifying the possibility of a model to be boundary is called an applied dose (see Table 1). The ‘‘correct,’’ is inappropriate (Morgan and Henrion, 1990; uptake process takes place at the exchange boundary and Cullen and Frey, 1998). Although the literature does not involves absorption of the chemical through the skin or explicitly refer to scenario uncertainty, it is reasonable to exposed tissues. The amount of chemical absorbed is assume that approaches and comments on model uncertainty called an absorbed dose, while the amount of chemical are applicable to scenario uncertainty. transported to an individual organ and the amount that This paper responds to the need to account for changes in reaches it are called a delivered dose and a biologically uncertainty magnitude when two, not one, equally valid effective dose, respectively. models and two equally plausible scenarios are used to Although the above dose terms signify different quanti- estimate risk and uncertainty. The objective is to develop a ties, they all have the same unit. The unit of dose has three  D.J. Moschandreas, S. Karuchit / Environment International 28 (2002) 247–261 249 Table 1 Exposure and dose scheme (adapted from EPA, 1992a) different variations: mass of the chemical, mass of the 2.2. Risk and risk assessment chemical per time, and mass of the chemical per body weight per time. More importantly, the units are common Exposure to harmful chemical agents leads to risk—the across routes, which is a major advantage when evaluating probability of suffering adverse effect, e.g., harm or loss. risk from all routes of exposure, and when comparing The process of estimating that probability is called risk contribution of each route to the resulting risk. The generic analysis (LaGrega et al., 1994; Molak, 1997). Risk analysis unit of exposure (Concentration
Time) is usually used for applied to a particular situation constitutes a risk assess- inhalation route only. It is neither practical nor common to ment, which usually estimates the probability of occurrence use this unit with ingestion and dermal routes. Instead, of human health effects (Molak, 1997). The NRC defines exposures via these two routes are frequently expressed as risk assessment as a formalized and structured process that potential dose (see, for example, EPA, 1992b, 1993). The estimates the magnitude, likelihood and uncertainty of unit difference prohibits simple addition of exposure from environmentally induced health effects (NRC, 1983). Haz- all three routes. Addition of doses, however, is an estab- ard identification, dose – response assessment, exposure lished approach as is discussed later. assessment and risk characterization are the four elements or steps of risk assessment that constitute the risk assess- ment paradigm (NRC, 1983). Hazard Identification deter- Table 2 Route-specific boundaries and chemical transfer processes (EPA, 1992a) mines whether a particular chemical is causally linked to particular health effects. Dose –response assessment formu- Scheme Process Inhalation Ingestion Dermal boundary boundary boundarya lates a relation between the magnitude of exposure and the probability of occurrence of the health effects in question. (Hypothetical) Intake Mouth/nose Mouth – outer boundary Exposure assessment estimates the extent of human expo- Exchange boundary Uptake Lung Gastrointestinal Skin sure before or after application of regulatory controls. Risk (absorption barrier) tract characterization describes the nature and often the magni- a There is no intake process for dermal route, the skin is the exchange tude of human risk, including its uncertainty. (NRC, 1983). boundary where uptake process takes place (EPA, 1992a). Details on each element of the risk paradigm and the 250 D.J. Moschandreas, S. Karuchit / Environment International 28 (2002) 247–261 significance of exposure and risk assessment with respect to These two concepts are applied jointly in an aggregate risk scientific research are found in the literature (e.g., Sexton et assessment. For each individual, dose is estimated for all al., 1993; NRC, 1983). routes considered simultaneously, and then combined as an aggregate dose. The combination is based on the dose 2.3. Aggregate and cumulative risk assessment addition approach, which is explained in the next para- graph, along with the concept of cumulative risk. Aggre- The risk assessment paradigm estimates risks from gate doses, obtained from each individual, are used to exposure to one pollutant from multiple routes or multiple formulate the population distribution of aggregate dose. pollutants from one route. A paradigm shift was conceived Consequently, the population aggregate risk assessment is to enable risk assessors to estimate risks from exposures to based on this distribution. multiple pollutants from multiple routes. This shift led to the Although aggregate risk assessment addresses the issue cumulative risk assessment procedure. Thus, the risk assess- of exposure to multiple routes, it considers only one ment evolution begins with the risk assessment paradigm, chemical. The ‘‘aggregate’’ concepts do not address cumu- evolves with the notion of aggregate risk and ends with lative effects from exposure to multiple chemicals. Cumu- cumulative risk. lative risk assessment incorporates risks from both multiple Aggregate risk is the outcome of a three-concept routes and multiple chemicals. Concepts and methods of consolidation (EPA, 1999a): (1) Aggregate exposure is cumulative risk assessment are introduced in the EPA the amount of one chemical available at the biological document entitled ‘‘Proposed Guidance on Cumulative Risk exchange boundaries (e.g., respiratory tract, gastrointestinal Assessment of Pesticide Chemicals that Have a Common tract and skin) from multiple routes of exposure. (2) Mechanism of Toxicity’’ (EPA, 2000). Fundamentally, the Aggregate dose is the amount of a single substance cumulative risk assessment can be viewed as an extension available for interaction with metabolic processes at bio- of the aggregate risk assessment. It is defined as an assess- logically significant receptors from multiple routes of ment of risk from the accumulation of a common toxic exposure. (3) Aggregate risk is the likelihood of the effect from all routes of exposure to multiple substances occurrence of an adverse health effect resulting from all sharing a common mechanism of toxicity. Common toxic routes of exposure to a single substance. effect refers to the same toxic effect caused by different The term ‘‘aggregate’’ is the keyword used throughout substances in or at the same organ or tissue (EPA, 2000). several recently published EPA guidance documents. The Common mechanism of toxicity refers to substances that term ‘‘aggregate exposure’’ is not defined as the contact of cause a common toxic effect by the same sequence of an agent with the outer boundary of an organism, which is biochemical events (EPA, 2000). the conventional definition of exposure. Instead, it refers to Dose addition provides mechanisms and methods to applied dose—the amount that reaches the exchange boun- estimate both aggregate risk and cumulative risk. This dary. Thus, ‘‘aggregate exposure’’ is the applied dose in all approach is explained by the following quote (EPA, 2000): routes of exposure. This peculiar use of the term ‘‘expo- sure’’ is a concern related to its definition and usage. The application of dose addition is based on the Indeed, EPA occasionally uses the term ‘‘exposure’’ to assumption that the chemicals behave similarly in terms refer to dose (e.g., (EPA, 2000, 1992b)). Moreover, simple of the primary physiologic processes (absorption, interpretation of the term aggregate as ‘‘added’’ or metabolism, distribution, elimination), as well as the ‘‘summed’’ could lead to misconception about how aggre- toxicologic processes. In other words, the chemicals of gate risk is estimated. In fact, this term is used to denote interest are assumed to behave as if they were dilutions of essential concepts of the new risk assessment approach and each other. When applying dose addition methods, the deserves careful consideration. Since EPA does not appear Agency has generally assumed no interactions among the to provide an exact definition of this term, for the balance chemicals (i.e., simple additivity) when there is no of this paper a practical definition of the term ‘‘aggregate’’ adequate interaction information. is used to denote two concepts jointly: (1) simultaneous consideration of all routes of exposure and (2) ‘‘individual- The margin of exposure (MOE), aggregate risk index by-individual’’ assessment. The first concept is applied to (ARI), hazardous index (HI), relative potency factor (RPF) improve the current practice of risk assessment, which and toxicity equivalency factor (TEF) methods are among typically treats exposure from different routes as independ- the several metrics that help estimate cumulative risk (EPA, ent events (EPA, 1999a). Simultaneous consideration of all 1999a, 2000; Wilkinson et al., 2000). All methods are routes of exposure contributes to a more realistic risk similar in that they normalize doses of each substance to a assessment because a person may be simultaneously common scale (EPA, 2000). The normalized doses are then exposed to a chemical from multiple routes. The ‘‘individ- summed. All methods are considered valid approaches as ual-by-individual’’ assessment considers exposures that they are expected to give similar results when certain each individual actually experiences, and uses appropriate conditions are assumed and no single method is preferred information regarding time, location, and demographics. (EPA, 2000; Wilkinson et al., 2000).  D.J. Moschandreas, S. Karuchit / Environment International 28 (2002) 247–261 251 3. Conventional uncertainty analysis of risk estimates professional judgment are associated with defining appro- priate exposure schemes, selecting improper models or This section reviews the classification and prevailing determining unrepresentative conditions; and incomplete analysis of risk uncertainty before a new uncertainty anal- analysis denotes a source of errors from including or ysis procedure is developed. Uncertainty analysis is the excluding particular exposure scenarios. analysis of variation or imprecision of the outcome of an Model uncertainty refers to uncertainty from gaps in assessment (Iman and Helton, 1988). The uncertainty of the scientific theory that are necessary to make predictions outcome is caused by many sources; therefore, uncertainty based on causal inferences (EPA, 1997a). Its sources include is generally classified by its sources. Several different modeling errors and relationship errors (EPA, 1997a, classifications of uncertainty are suggested in the literature 1992a). Simplified representation of reality leads to model- (EPA, 1992a; Morgan and Henrion, 1990; Bogen, 1990; ing errors, while errors in correlation among model varia- Cullen and Frey, 1998; Finkel, 1990; IAEA, 1989). In bles result in relationship errors. general, there are two commonly used (and often not clearly separated) classifications: (1) scenario, model and parameter 3.2. U-V uncertainty and (2) uncertainty– variability (U-V). An analysis that deals with parameter uncertainty only 3.1. Scenario, model and parameter uncertainty uses the U-V classification. In this classification, uncertainty is classified as either U or V. V refers to the true hetero- The EPA classifies uncertainty involved in exposure and geneity, or interindividual variability, attributed to certain risk assessments into three types: parameter, scenario and characteristics of a population (EPA, 1997b). Other terms model uncertainty (EPA, 1992a, 1997a,b). The three types used for V in the literature include stochastic uncertainty, of uncertainty, their sources and examples are summarized aleatory uncertainty and Type A uncertainty (Cullen and below. Frey, 1998). All parameter uncertainty that is not V is Parameter uncertainty is the uncertainty regarding defined as U. parameters (EPA, 1997a). Sources of parameter uncertainty Most analysts prefer distinguishing variability from other are measurement errors, sampling errors, variability, and the types of uncertainty because of its characteristics and use of surrogate data (EPA, 1997a, 1992a). Measurement ramifications for decision-making in risk assessment. Vari- errors refer to random errors (imprecision) or systematic ability is usually not reducible by further measurement or errors (bias), while sampling errors are errors from small study, while uncertainty from other sources may be reduced sample size and/or nonrepresentative samples. Heterogene- by further measurement (Cullen and Frey, 1998; Burmaster ity in environmental and exposure-related data includes and Wilson, 1996; Haimes and Lambert, 1999). Therefore, seasonal variation, spatial variation, variation of human differentiating between variability and other types of uncer- activity patterns by age, gender and geographic location tainty in risk assessment helps decision-makers to focus on and leads to variability errors. Surrogate data refer to errors appropriate uncertainty reduction measures (EPA, 1997b). from the use of substitute data. The name of this classifica- Such distinction is fundamental to characterizing uncer- tion requires close attention. The term ‘‘parameter’’ is used tainty in the uncertainty analysis (Bogen, 1990; EPA, to reflect two concepts (EPA, 1997b). The first refers to the 1997b; MacIntosh et al., 1995; Rai et al., 1996; Haimes distribution parameter—the constants characterizing the and Lambert, 1999). Burmaster and Wilson (1996) discuss probability distribution of a variable (e.g., l or r). The the reason for separating V from U as follows: second refers to both distribution parameter and model variable, where model variable denotes a variable that is Since V and U arise from different sources, have different an element of a model, such as time, weight, concentration interpretations and have different consequences in or other variables in an exposure, dose or risk model. In our decision-making, many risk assessors have sought a opinion, the EPA uses the term ‘‘parameter uncertainty’’ way to encode and propagate them separately. At the end where ‘‘parameter’’ denotes both distribution parameter and of a long calculation, it is highly desirable for the risk model variable. This paper uses the term ‘‘distribution assessor to be able to segregate the total V from the total parameter’’ or ‘‘model variable’’ instead of ‘‘parameter’’ U so the risk manager could make appropriate decisions. to avoid possible confusion. In particular, the risk manager can do little to reduce the Scenario uncertainty refers to uncertainty associated with total V in an assessment, but she or he can often reduce missing or incomplete information needed to fully define the total U in an assessment by commissioning further the exposure and dose (EPA, 1997a). Its sources include studies. descriptive errors, aggregation errors, errors in professional judgment and incomplete analysis (EPA, 1997a, 1992a). Based on its uncertainty type, a model variable can be a U Descriptive errors are errors from incorrect or incomplete type, V type or both (Bogen, 1990; MacIntosh et al., 1995; information, while aggregation errors are spatial or temporal Burmaster and Wilson, 1996; Haimes and Lambert, 1999). approximations or homogeneity assumptions. Errors in The concept is best explained by examples. A U variable can 252 D.J. Moschandreas, S. Karuchit / Environment International 28 (2002) 247–261 represent the amount of pesticide on a child’s hand at a Parameter uncertainty analysis is the analysis conducted particular time. The amount of pesticide is not varying, but by most analysts at the present time. To analyze parameter the fixed, true amount is not known because of the lack of uncertainty, four approaches are typically employed: sensi- knowledge needed to make a perfect measurement. A V tivity analysis, analytical uncertainty propagation, probabil- variable can represent the grade point average (GPA) of each istic uncertainty analysis and classical statistical methods student in a class. The GPA is known exactly for each student (EPA, 1992a; Cox and Baybutt, 1981; Iman and Helton, but it varies from one student to another because it represents 1988; Seiler, 1987; Hamby, 1994; Cullen and Frey, 1998). heterogeneity in the population. An example of a U and V variable is a variable that represents the amount of pesticide on the hands of each student in a class. Its values are 4. A new uncertainty analysis of risk estimates uncertain because of the imperfect measurement, and varia- ble because of the heterogeneity in the population. Variables The new inclusive uncertainty analysis is called the SMP that have either U or V are sometimes referred to as ‘‘first- uncertainty analysis method. In this section, we present a order’’ random variables; while those that have both U and V step-by-step scheme to estimate cumulative risk and the are sometimes referred to as ‘‘second-order’’ random varia- SMP uncertainty. The flow chart of the scheme is illustrated bles (Burmaster and Wilson, 1996). The second-order ran- in Fig. 1; it consists of six steps: dom variable has a probability distribution that describes its variability, while the distribution parameters are themselves Step 1: Identify toxic effects and endpoints uncertain. Thus, each of the distribution parameters has a Step 2: Identify the exposure scenarios of concern specific probability distribution that describes its uncertainty. Step 3: Develop the dose models Step 4: Estimate exposure, dose and risk 3.3. Conventional uncertainty analysis: parameter uncer- Step 5: Perform uncertainty analyses tainty analysis Step 6: Characterize risk Uncertainty analysis focuses on model output. Generally, This step-wise scheme is based on fundamental princi- the objectives of an uncertainty analysis are: (1) to evaluate ples of risk assessment and methods suggested by the EPA the output uncertainty and (2) to find the relative contribu- (EPA, 1999a, 2000). Comparison with the four elements of tion of each model variable to the output uncertainty. The the early risk assessment paradigm indicates that the first second objective is commonly referred to as a sensitivity two elements of conventional risk assessment—hazard analysis (Iman and Helton, 1988; Hamby, 1994). Analysis identification and dose –response assessment—are included results make possible a more informed and sound decision- in the first step of the scheme. Exposure assessment and making process. There are two ways to analyze uncertainty: elements of risk assessment are found in Steps 2, 3 and 4. characterization and assessment (EPA, 1992a). Uncertainty Risk characterization is put together in the last three steps. characterization is a qualitative discussion that focuses on Certain steps of the scheme are explained with examples the determination of sources of uncertainty and their impact obtained from a study of the Arizona population risk assess- on the model results. Uncertainty assessment is a quantita- ment of exposure to pesticides using the NHEXAS-AZ tive analysis of uncertainty. database (Karuchit and Moschandreas, 2001). This risk Fig. 1. Flow chart of the scheme.  D.J. Moschandreas, S. Karuchit / Environment International 28 (2002) 247–261 253 assessment is an application of the risk assessment uncer- pollutants. When exposure measurement is not feasible, tainty estimating approach detailed in this paper. concentration and questionnaire data are combined to esti- mate exposures using the indirect method. Concentration 4.1. Identification of toxic effects and endpoints measurements are generally obtained from field studies. Subject information (e.g., time and frequency of contact, In the first step, information is gathered regarding toxic food consumption, and area of surfaces contacted) and other effects, toxic endpoints and dose – response relationship of exposure factors can be obtained from questionnaire data, the pollutants investigated. Toxic effects are defined as literature or assumptions. A typical assumption for the effects caused by exposure to a chemical that will or can estimation is that the subjects’ exposure to pollutant con- be expected to endanger one’s quality of life (EPA, 1999b). centrations in air, food and surfaces takes place according to Toxic endpoint is the quantitative presentation of a toxic each scenario defined over periods relevant for the mani- effect at a certain exposure level, e.g., NOAEL and RfD. By festation of a toxic effect. A concentration measured in a definition, cumulative risk assessment is only applicable to bulk medium is assumed homogeneous and not varying pollutants that have common toxic effects and common over the time of interest. For each subject and environment, mechanism of toxicity. medium sampling must take place at the same time and the exposure, dose and risk of pollutants assessed must have the 4.2. Identification of the exposure scenarios and exposure same mechanism of toxicity (EPA, 2000). models Usually, certain pollutant concentrations are censored values because they are assigned values below the limit of Exposure scenario is a set of facts, assumptions and detection (LOD) of their perspective measurement instru- inferences about how exposure takes place (EPA, 1992a). ment. Below LOD measurements are generally assigned one EPA’s ‘‘Standard Operating Procedures (SOPs) for Residen- of three values (zero, the LOD value or a value half the tial Exposure Assessments’’ (EPA, 1997c) contains informa- LOD value) or they can be assigned values using the robust tion about major exposure scenarios, which need to be method. The robust method generates ‘‘fill-in’’ values for adapted to the pollutants of interest. Not all the listed those below LOD values according to the distribution of the scenarios need to be included in the final assessment. To above-LOD values (Helsel, 1990; Moschandreas et al., perform a risk assessment that is focused and meaningful, the 2001). The ‘‘fill-in’’ values are then assigned randomly. included scenarios must be carefully selected. Criteria for This assignment is permanent for all analyses for a given excluding scenarios from a study are not definitive but database. include: scenarios that have very little possibility of happen- Cumulative risk can be estimated using either the deter- ing; scenarios that are likely to result in trivial amount of ministic or the probabilistic approach; each approach has subject pollutant dose; and scenarios that have inadequate advantages and limitations. We recommend both approaches information to perform an exposure assessment (EPA, to gain insights in the assessment and to make use of extant 1992a, 2000). Conventional and clear scenarios are identi- databases. The deterministic approach is the fundamental fied early in the risk assessment study and are called ‘‘base- estimation approach that is appropriate for the application of line.’’ Later in the SMP process, different assumptions are the ‘‘individual-by-individual’’ concept of the aggregate and made leading to ‘‘alternative’’ scenarios. Exposure duration cumulative risk assessment. In this approach, each subject’s is part of an exposure scenario; therefore, duration must be data are used with appropriate models to estimate pollutant both relevant to the toxic end and realistic. Exposure and route-specific dose, and then the risk metric. Therefore, duration is selected for each of the alternative scenarios. each risk metric is calculated using the dose estimates that For subpopulations of interest, an assessment uses the base- belong to one and the same subject. However, this approach line scenarios with only subjects from the subpopulation has two major limitations. First, it cannot provide as much groups that are likely to be exposed to pollutants of interest. information about the variation, i.e., uncertainty, of the Identification of models for estimating exposure and estimated results as the probabilistic approach. Second, the potential dose, Step 3, are pollutant dependent and are estimation can be performed only on those subjects with a developed on the basis of several existing examples found complete set of data—those who have exposure estimates in the literature. Dose models employ the indirect method of for all pollutants and all routes. In other words, subject exposure estimation, also known as the scenario estimation measurements must be available for all media (e.g., indoor approach. air, food, floor dust, sill wipe and yard soil) along with other relevant data needed for the dose estimations. In this study, 4.3. Estimation of exposure, dose and risk such subjects constitute the cumulative assessment group (CAG). Although this may be the case for a few databases Efforts in this step begin with estimating exposure to generated for research purposes, this is not generally the subject pollutants and continue with estimating dose and case for all subjects and all media for most databases that are risk caused by the exposure. While measurement of expo- medium specific. The probabilistic estimation approach is sure is possible for certain pollutants, it is not possible for all used to overcome these limitations. 254 D.J. Moschandreas, S. Karuchit / Environment International 28 (2002) 247–261 The probabilistic approach uses a probability distribution The cumulative HI of each of the CAG subject is to represent each model variable instead of a point estimate, estimated by: a single value. The estimation is performed using the Monte XX Carlo method—a statistical sampling method for obtaining HICAG ¼ HQr;p ¼ HIA;chlorpyrifos þ HIA;diazinon ð4Þ the probability distribution of the possible outcomes of a r p model (EPA, 1997b). The probability distribution of each variable is developed using all available subject data. Con- 4.3.2. Probabilistic method sequently, the information used in the assessment is not The primary purpose of probabilistic risk estimation is to limited only to the information from those subjects who analyze uncertainty and its sources as they associate with have a complete set of data. The other advantage of the risk estimates. The probabilistic analysis may be performed probabilistic approach relates to its greater potential and using the Monte Carlo method and one of several commer- ability to analyze uncertainty. The limitation of the proba- cial software packages such as the Crystal Ball (Sargent and bilistic approach relates to its inability to accommodate the Wainwright, 1996). Based on the deterministic dose and risk ‘‘individual-by-individual’’ assessment concept. The proba- estimation models, the first step in a probabilistic analysis is bilistic approach eliminates the identity of each subject in the formulation of a probability distribution for each model the simulation process because the probability distribution variable. of a variable is the distribution of the population, and Model variables can be classified into two classes: (1) individual subjects used to formulate the distribution are variables with measured values from field studies and (2) no longer discernible. Therefore, the dose and risk are not variables with assigned values, either surrogates or assumed. estimated for each sample subject, but for all that combine For the purpose of sensitivity analysis, variables estimated to represent possible outcomes. Although the estimation from submodels involving observed data and surrogate or does not conform to the strict cumulative risk assessment assumed data should be segregated in the probabilistic concept, it estimates the population distribution of the out- analysis models. In other words, each variable is substituted put, given that the probability distributions of the model by its submodel variables. Thus, a probability function is variables are good representation of the population. developed for such variables based on observed data with- out the effect of surrogate or assumed data. The segregation 4.3.1. Deterministic method has the benefit of improving the characterization of the input The deterministic method employs appropriate dose variables and the identification of significant contributors in models discussed in the previous step to estimate dose for model outputs. all routes, inhalation, dietary ingestion, dermal absorption To obtain credible outputs, significant correlation among and nondietary ingestion. To estimate aggregate risk and input variables must be taken into account in the Monte cumulative risk, the HI method is used in the NHEXAS-AZ Carlo simulation. Rank correlation coefficients are calcu- risk assessment of exposure to two pesticides: chlorpyrifos lated for each pair of input variables to determine if and diazinon. The application of this method is explained significant correlation exists. Selected significant correlation below (EPA, 1999a, 2000; Patrick, 1994; Mumtaz, 1995). coefficients are then specified in the simulations. When a The HI of each subject is the summation of the hazardous correlation between variables is defined, the simulation quotient (HQ) of the subject, which is calculated using the program (e.g., in Crystal Ball) generates random numbers following equation: for each variable from its probability distribution and uses the correlation coefficient to rearrange the numbers to Dr;p achieve the specified correlation. HQr;p ¼ ð1Þ RfDr;p 4.3.2.1. Monte Carlo methods in probabilistic uncertainty where r denotes exposure route, p denotes pesticide; Dr,p is analysis. The Monte Carlo method is a statistical sampling the estimated potential dose of pesticide p from route r for method for obtaining the probability distribution of the each subject; RfDr,p is the reference dose of pesticide p and possible outcomes of a model (EPA, 1997b). The Monte route r. Carlo simulation process is described as follows (Cox and The aggregate HI for each pesticide is the sum of its HQs Baybutt, 1981; Sargent and Wainwright, 1996). Let a1. . .am in all routes, and the cumulative HI is the sum of all HQs. be the input variables of a model. First, each of the Thus, the aggregate HI is estimated by: independent variables are assigned a probability distribu- tion. Second, the simulation process selects one value for X each variable based on its probability distribution. This step HIA;chlorpyrifos ¼ HQr;1 ð2Þ r is repeated a large number of times, N. Consequently, N sets of values (a1(i). . .am(i)), i = 1 to N, are obtained and the X corresponding model outputs, Y(i), i = 1 to N, are calculated. HIA;diazinon ¼ HQr;2 ð3Þ The distribution of N outputs represents the population r distribution. The uncertainty of the output can be examined  D.J. Moschandreas, S. Karuchit / Environment International 28 (2002) 247–261 255 Fig. 2. Illustration of the 2-D Monte Carlo simulation in Steps 1 and 2. using several statistics, including the standard error (S.E.) of that requires variability to be distinguished from other types the mean and the confidence interval (CI) of the mean or a of uncertainty (Bogen and Spear, 1987; IAEA, 1989; Hoff- specific percentile. Alternatively, the Monte Carlo method man and Hammonds, 1994; MacIntosh et al., 1995; Bur- can be described as a process where N sets of values are master and Wilson, 1996). Also known as ‘‘nesting’’ or obtained from a joint distribution of all of the input ‘‘double looping,’’ this simulation technique has an ability variables, and N corresponding model outputs are calculated to separately propagate the two types of uncertainty (Cullen (Cullen and Frey, 1998). and Frey, 1998). The two steps in the process are explained An advanced technique called the two-dimensional (2-D) using the following example. Let Y be the assessment Monte Carlo simulation is used with an uncertainty analysis endpoint, which is a function of three variables: a1 (a U Fig. 3. Illustration of the 2-D Monte Carlo simulation process (adapted from MacIntosh et al., 1995). 256 D.J. Moschandreas, S. Karuchit / Environment International 28 (2002) 247–261 variable), a2 (a V variable) and a3 (a U and V variable). The to that value. The range is obtained from the M distribu- 2-D Monte Carlo simulation of this assessment is illustrated tions. in Figs. 2 and 3. Step 1: (1) A random value is selected for a1, a U- 4.4. Uncertainty analysis variable, from its probability distribution. (2) The U and V variable a3 has a probability distribution that describes its 4.4.1. Parameter uncertainty analysis variability, while its distribution parameters—the mean and Sensitivity analysis and probabilistic uncertainty analysis variance—are uncertain. A random value is selected for are two approaches used to analyze parameter uncertainty in each of the parameters from their probability distributions. this study. The former finds the relative contribution of each The selected pair of mean and variance characterizes a model input to the change in the output, while the latter distribution for a3. evaluates the variation or imprecision in the output. The Step 2: (1) A random value is selected for a2, a V flow chart for parameter uncertainty analysis is shown in variable, from its probability distribution. (2) A random Fig. 4. In the NHEXAS-AZ pesticide risk assessment, seven value is selected for a3 from its probability distribution, simulation modules with appropriate models are used: which is obtained from Step 1. (3) The value of a1 (selected in Step 1) and the values of a2 and a3 (both selected in Step Module 1: Chlorpyrifos inhalation dose (D1,1) estimation 2) are used to estimate one output value. Module 2: Chlorpyrifos ingestion dose (D2,1) estimation Fig. 2 illustrates the two steps. Step 2 is called an Module 3: Chlorpyrifos dermal dose (D3,1) estimation ‘‘inner’’ simulation. It is repeated a large number of times, Module 4: Diazinon inhalation dose (D1,2) estimation N. In each repetition, the value of a1 is fixed at the same Module 5: Diazinon ingestion dose (D2,2) estimation value selected in Step 1, only the values of a2 and a3 vary. Module 6: Diazinon dermal dose (D3,2) estimation The simulation that includes one run of Step 1 and N runs Module 7: Cumulative hazardous index (HICAG) estima- of Step 2 is called an ‘‘outer’’ simulation. It creates one tion output distribution of size N. A large number of outer simulation runs, M, are performed to create a family of All input variables in dose models are V types; their distributions (see Fig. 3). For the outer simulations, the values vary from one individual to another in any popula- value of a1 is different from one run to the other as a result tion of interest. The only input variable that is U type is the of Step 1 selection of each run. The uncertainty associated RfD variable for each case. A reference dose is a benchmark with a statistic (e.g., mean or percentile) of the outcomes dose level that applies to every individual in the population, can be estimated from its S.E., obtained from the family of but its true or rather ‘‘best’’ value is unknown for each M distributions. Furthermore, the uncertainty about the pollutant; such a variable is a U type. percentile associated with a certain output value can be Simulations of Modules 1 through 6 are performed using estimated from the range of the percentiles corresponding conventional Monte Carlo methods. The number of runs Fig. 4. The flow chart of the parameter uncertainty analysis.  D.J. Moschandreas, S. Karuchit / Environment International 28 (2002) 247–261 257 used for each simulation was 5000. Selection of the number the 90th percentile. For the outer simulation, the criterion for of runs in the simulation is usually based on the computing selecting the number of runs is based on the concept of limitation and acceptable level of precision for the most nonparametric tolerance limits used by Hoffman and Ham- concerned results (Cullen and Frey, 1998). In this study, we monds (1994). The concept provides a method to find the focus our attention on the high-end of the output distribu- sample size M needed to create an interval that contains at tions, particularly the 90th percentile values. Thus, the least a proportion q of the population, with a 1  a con- number of runs selected was based on the numerical fidence level (Conover, 1980; Montgomery and Runger, stability of this output. As the number of runs increases, 1999). Usually, the lower and upper tolerance limits are set the 90th percentile estimate stabilizes, i.e., closes in on to be the smallest and largest sample values, respectively. nearly constant values. The use of 5000 runs ensures that Using q = 0.99 and a = 0.05, a sample size of M = 473 runs numerical stability of the 90th percentile was achieved. was calculated for our example. Thus, with 500 outer For Modules 1 through 6, analyses of the variation of simulation runs, there is at least a .95 probability that at outputs used S.E. of the 90th percentile estimates that are least 99% of the population of the estimate is between the calculated using the nonparametric Bootstrap method (Efron smallest and largest values of the set of values obtained. and Tibshirani, 1993; Montgomery and Runger, 1999). Five Therefore, in the 2-D simulation, 500 distributions of the hundred bootstrap samples, each consisting of 5000 values, cumulative hazardous indexes (HICAG) were obtained. The are randomly sampled with replacement from the original mean and median of each percentile and their uncertainty set of 5000 output values. Then, the 90th percentile is were then estimated. estimated for each bootstrap sample, resulting in 500 values of the 90th percentile, from which one obtains the S.E. and 4.4.2. The SMP uncertainty analysis other statistics of the 90th percentile. The sensitivity anal- At present, there is no standard method for quantitatively ysis of each module is performed simultaneously with the analyzing these types of uncertainty. The SMP uncertainty Monte Carlo simulation using the rank correlation coeffi- analysis method presented in this section was developed to cient method. Model variables with high correlation values, incorporate scenario and model uncertainties in the uncer- R, have a significant impact on the corresponding model tainty analysis in risk assessment. The SMP uncertainty output. The model output and the rank correlation coeffi- analysis can be performed on any statistic of interest. The cient, R, between values of each variable and the output are process is best explained by an example. In the Arizona calculated simultaneously. Therefore, two outputs are pesticide risk assessment, the SMP analysis was performed obtained at the end of the simulation: a distribution of on the cumulative hazardous index, HICAG, of a subject 5000 output values and the coefficient values. The coeffi- population. It begins by dividing the analysis procedure cients of all input variables are ranked and compared to used to obtain HICAG into a series of decision points with identify the highly sensitive variables. alternatives. Two decision points, each with two alterna- 2-D Monte Carlo simulations are performed for estimat- tives, are identified and illustrated as a ‘‘decision tree’’ in ing the cumulative hazardous index of the CAG subjects Fig. 5. (HICAG), Module 7, which consists of U variables and V variables. The number of runs used is equal to 5000 and 500 4.4.2.1. Decision point #1. The first decision point is the for the inner and the outer simulation, respectively. For the selection of the method used to develop the probability inner simulation, 5000 runs ensure the numerical stability of distribution of model variables. Since the uncertainty in the Fig. 5. The ‘‘decision tree’’ of the SMP uncertainty analysis. 258 D.J. Moschandreas, S. Karuchit / Environment International 28 (2002) 247–261 model output is propagated from uncertainty in each of the The path with baseline decision for both decision points model variables, the probability distribution must be devel- is Path BB. For each analysis path, the 2-D Monte Carlo oped with appropriate methods. Two commonly used meth- simulation of Module 7 is performed using 5000 inner ods are parametric distributions, i.e., standard distributions simulation runs and 500 outer simulation runs. Therefore, that fit observations such as normal, lognormal and others, we obtained 500 distributions of HICAG estimates and 500 or empirical distributions, i.e., a histogram of study obser- 90th percentile estimates from each analysis path. Based on vations. The use of empirical distributions has certain these outputs, the uncertainty of 90th percentile estimates advantages and some limitations. Using parametric distri- was estimated and compared among different analysis paths. butions also has its benefits. With their own advantages and At this stage, uncertainty estimated for each analysis path is disadvantages, there is no general agreement as to which the parameter uncertainty only. method is preferred (EPA, 1997b). The use of different Four uncertainty analyses were established to investigate methods is likely to result in significantly different outputs the effect of inclusion of scenario or model uncertainty: and output uncertainties. Therefore, the decision made at this point is an important source of scenario uncertainty, and  Analysis P: Analysis that considers parameter uncertainty is considered as the first decision point of the SMP uncer- only tainty analysis. The alternatives of this decision point are the  Analysis SP: Analysis that considers scenario and empirical distribution method (baseline scenario) and the parameter uncertainties parametric distribution method (alternative scenario).  Analysis MP: Analysis that considers model and parameter uncertainties 4.4.2.2. Decision point #2. The second decision point is  Analysis SMP: Analysis that considers scenario, model the selection of a model for estimation of dose. Unlike and parameter uncertainties models for inhalation or ingestion route, dermal dose models are more complex and take different forms. Thus, Analysis P accounts for only parameter uncertainty and continuing with an explanation of the SMP method by ignores scenario and model uncertainties. It has only one example, we select as the baseline model that is suggested analysis path, Path BB. Analysis SP considers both scenario by the EPA in its publication entitled ‘‘Research Solicita- and parameter uncertainties; therefore, it has two analysis tion: Human Exposure Assessment’’ (EPA, 1993). It uses paths: BB and AB. In essence, this analysis assumes that the concentration data in three media (floor dust, sill wipe and two paths are equally suitable for the assessment, and assigns yard soil) and combines the data with subjects’ character- equal chance to each path to be used. In a similar fashion, istics to estimate dermal potential dose. However, the Scenario MP considers both model and parameter uncertain- model does not take into consideration information from ties, and assumes that Paths BB and BA have equal proba- hand wipe or dermal wipe. Dermal wipe data are available bility to be used in the assessment. Finally, Analysis SMP for both pesticides in the NHEXAS-AZ database. With the considers all three types of uncertainties, and assumes that all use of a general EPA dose model (EPA, 1992a), the dermal analysis paths are equally appropriate for the assessment. wipe data can be used to obtain different, but equally The scheme used to obtain estimates from each analysis is credible, estimates of dermal dose. These estimates are explained below. Analysis P is performed to obtain 500 independent of the floor dust, sill wipe or yard soil data. estimates of two statistics, the median and the 90th percen- The decision made regarding the model selection is an tile, using Path BB only. Analysis SP is performed to obtain important source of both scenario and model uncertainty, 250 estimates of the two statistics from each of the two and is considered as the second decision point of the SMP analysis Paths BB and AB. Analysis MP is performed to uncertainty analysis. The alternatives of this point are the obtain 250 estimates of the two statistics from each of the dermal model 1 (baseline model) and the dermal model 2 two analysis Paths BB and BA. Finally, Analysis SMP is (alternative model). The two models are summarized in performed to obtain 125 estimates of the two statistics from Appendix A. each of the four analysis paths. The distributions of each After establishing two alternatives for each of the two statistic are compared among analyses. The mean and decision points, four analysis paths must be considered for variance values estimated by each analysis are tested for estimating the SMP uncertainty (Fig. 5): equality. Ultimately, the relative change of risk uncertainty that accounts for only parameter uncertainty to risk uncer-  Path BB: Use empirical input distributions and dermal tainty that jointly accounts for scenario, model and parameter model 1 uncertainty is estimated using the 95% tolerance limits  Path BA: Use empirical input distributions and dermal range. model 2  Path AB: Use parametric input distributions and dermal 4.5. Risk characterization model 1  Path AA: Use parametric input distributions and dermal The findings from the risk assessment are integrated in Model 2 this final assessment step. Issues discussed in the risk  D.J. Moschandreas, S. Karuchit / Environment International 28 (2002) 247–261 259 characterization include risk estimates and associated uncer- food consumption, time budget and other pertinent informa- tainties, and comparisons of risks among subpopulations. tion. Most databases, however, are not as comprehensive Additionally, risk characterization identifies variables that and therefore are likely to result in larger uncertainties than significantly affect the outcomes in each simulation module, those found in this application. or alternatives in the assessment that could change the Analysis results obtained from the NHEXAS-AZ pesti- conclusions reached. Finally, risk characterization elaborates cide risk assessment indicate that inclusion of scenario on the results of the SMP uncertainty analysis and substan- uncertainty source into the process for estimating cumula- tiates all findings to assist and support the decision-making tive risk uncertainty increases overall uncertainty. The process. uncertainty of the 90th percentile estimate of HICAG—as measured by its 95% tolerance limits range—increases almost threefold compared to the output uncertainty that 5. Discussion considers only parameter uncertainty. Inclusion of the model uncertainty source increases the uncertainty of this statistic The SMP uncertainty analysis method is not intended to by 56%, and inclusion of both the scenario and model quantify all uncertainty that exists, i.e., uncertainty from all uncertainty sources increases uncertainty by nearly a factor imaginable scenarios and all published models. Instead, it of two. Similar results are obtained when the uncertainty is provides the mechanism that allows judiciously selected measured by the range of the 95% confidence level of the scenarios and/or model uncertainty sources to be included in mean of the 90th percentile HICAG. the analysis. Ultimately, the SMP uncertainty analysis Clearly, this result confirms that the scenario and model compares the uncertainty based on all selected uncertainty uncertainty sources are significant contributors to overall sources with that based on parameter uncertainty alone to uncertainty of the outcome of the assessment. When both are ascertain if ignoring certain sources of errors would change ignored, the 90th percentile of HICAG is not likely to be near the conclusions reached. This method, therefore, allows the the level of concern: 95% of the estimates are between 0.22 risk assessor to be all-inclusive and consider all appropriate and 0.70. When the scenario uncertainty source is included, sources of uncertainty. If the SMP estimate is significantly i.e., the use of parametric distribution is considered an larger than the conventional estimate, the decision may be equally appropriate alternative as the use of empirical dis- affected. Conversely, if the SMP result is not significantly tribution, the abovementioned conclusion about the 90th larger than that of the conventional analysis, it is reassuring percentile of HICAG changes substantially. Both analysis to know that the uncertainty estimate is not sensitive to the scenarios that include the scenario uncertainty yield tolerance additional uncertainty sources included in the SMP analysis. limits range that extend more than 1.50, which means that the Selection of alternative models and scenarios as sources 90th percentile HICAG could exceed the level of concern. of uncertainty is the nucleus of the SMP analysis process; it Thus, the cumulative risk assessment process that includes must focus on realistic and practicable alternatives. Clearly, two different but realistic scenarios with two different but exposure scenario selection depends on the population, equally feasible models may lead to risk estimates that have pollutant, subject population and relevant information about substantively different uncertainty from that estimated with the population. Recall that cumulative risk requires that the conventional estimating risk uncertainty methods. pollutants share a common toxic end and the same mech- anism of adverse effect. Such information and associated factors can be obtained from the literature. The models Appendix A. Two dermal dose models selected for use and their alternatives depend on the expo- sure route. It is important to note that the literature contains A.1. Dermal dose model 1 many additional models, making the appropriate choice of alternative models a critical concern. The baseline dermal models for estimating potential dose Performance of the SMP uncertainty analysis requires are as follows (Moschandreas et al., 2001): performance of a risk assessment study. Therefore, it requires identification of one or more databases, information Dose : PDder;t ¼ Eder;t
BW1
103 ðA:1Þ on the subject population and subpopulations, selection of model and scenario uncertainty sources and factors that will be used in the performance of the research. In the work Exposure : Eder;t ¼ Eder;r þ Eder;y ðA:2Þ presented in the related paper, the SMP uncertainty method was applied using NHEXAS-AZ database. It is one among X the very few multiple pollutant, multiple route exposure, Eder;r ¼ ½CDs
Aps
Tps
ð1  DOps Þ ðA:3Þ s risk studies sponsored by a consortium of federal agencies led by the EPA. NHEXAS-AZ consists of comprehensive X subject information obtained from a multiple stage survey Eder;r ¼ ½CSs
ððSps
SAps Þ  SOps Þ
M ðA:4Þ using six different questionnaires on demographic, housing, s 260 D.J. Moschandreas, S. Karuchit / Environment International 28 (2002) 247–261 PDder,t is the total dermal potential dose of the exposure duration is assumed 24 h per day. Therefore, the pesticide of each subject (ng/kg day) total potential dose is the potential dose integrated over the Eder,t is the total dermal exposure to a pesticide of 1-day duration and the averaging time used in the model is 1 each subject (Ag/day) day. Furthermore, it is assumed that the pesticide mass is BW is the body weight of the subject (kg) distributed uniformly over the exposed body surface area Eder,r is the dermal exposure to the pesticide in and is represented by the dermal wipe concentration. There- dislodgeable surface residue of each subject fore, the total potential dose is estimated by the dermal wipe (Ag/day) concentration times the exposed body surface area: Eder,y is the dermal exposure to the pesticide in soil of each subject (Ag/day) s is the type of surfaces contacted per day. Total Potential Dose ¼ Chand
SAps
103 ðA:6Þ Dislodgeable surfaces residue data in the NHEXAS database were obtained from two surfaces: floor surface and window sill Chand is the pesticide concentration in the dermal surface. The latter is assumed representative wipe sample (Ag/m2) of residue from ‘‘nonfloor’’ surfaces, i.e., SAps is the body surface area of the subject exposed surfaces other than the floor in the house, to surface s (m2) such as furniture surfaces. For Eq. (A.3), s = 1 for floor surface and s = 2 for nonfloor sur- face. For Eq. (A.4), s = 1 for yard soil surface. CDs is the pesticide concentration of dislodgeable References surface residue on surface s (Ag/m2) Bogen KT. Uncertainty in environmental health risk assessment. Garland As is the surface area of surface s contacted by Publishing; 1990. the subject (m2/day) Bogen KT, Spear RC. Integrating uncertainty and interindividual variability Tps is the transfer proportion of surface s by the in environmental risk assessment. Risk Anal 1987;7:427 – 36. subject, proportion Burmaster DE, Wilson AM. An introduction to second-order random var- DOps is the proportion of dislodgeable residue of iables in human health risk assessments. Hum Ecol Risk Assess 1996; 2(4):892 – 919. surface s transferred to oral route by the Conover WJ. Practical nonparametric statistics. 2nd ed. Wiley; 1980. subject via hands, food and objects; Cox DC, Baybutt P. Methods for uncertainty analysis: a comparative sur- proportion vey. Risk Anal 1981;1(4):251 – 8. CSs is the pesticide concentration in soil surface s Cullen CA, Frey HC. Probabilistic techniques in exposure assessment: a (Ag/g) handbook for dealing with variability and uncertainty in models and inputs. New York: Plenum; 1998. Sps is the soil from surface s covering on skin of Efron B, Tibshirani RJ. An introduction to the bootstrap. Monographs on the subject (g/m2 day) statistics and applied probability, vol. 57. New York: Chapman and SAps is the body surface area of the subject exposed Hall; 1993. to surface s (m2) EPA, US Environmental Protection Agency. Guidelines for exposure as- SOps is the amount of soil from surface s covering sessment, 1992a. EPA, US Environmental Protection Agency. Dermal exposure assessment: on skin that is transferred to oral route by the principles and application, 1992b. subject (g/day) EPA, US Environmental Protection Agency. Research solicitation: human M is the matrix effect of soil, proportion exposure assessment. Office of Research and Development, 1993. EPA, US Environmental Protection Agency. Exposure factors handbook, 1997a. A.2. Dermal dose model 2 EPA, US Environmental Protection Agency. Guiding principles for Monte Carlo analysis, EPA/630/R-97/001, 1997b. The general EPA dose model calculates the average daily EPA, US Environmental Protection Agency. Standard operating procedure (SOPs) for residential exposure assessments. Draft, The Residential potential dose, ADDpot, by (EPA, 1992a,b, 1997a): Exposure Assessment Work Group, Office of Pesticide Programs, 1997c. EPA, US Environmental Protection Agency. Guidance for performing ag- ADDpot ðng=kg dayÞ gregate exposure and risk assessments, 1999a. Total Potential Dose ðngÞ EPA, US Environmental Protection Agency. Guidance for identifying pes- ¼ ðA:5Þ ticide chemicals and other substances that have a common mechanism Body Weight ðkgÞ
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