Calculation of the Risk Index

The risk index for any hazardous substance in Equation 1.1 or 1.2 (see Section 1.5.1) is calculated based on assumed exposure scenarios for hypothetical inadvertent intruders at near-surface waste disposal sites and a specified negligible risk or dose in the case of exempt waste or acceptable (barely tolerable) risk or dose in the case of low-hazard waste. Calculation of the risk index also requires consideration of the appropriate measure of risk (health-effect endpoint), especially for carcinogens, and the appropriate approaches to estimating the probability of a stochastic response per unit dose for carcinogens and the thresholds for deterministic responses for noncarcinogens. Given a calculated risk index for each hazardous substance in a particular waste, the waste then would be classified using Equation 1.3. 

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Stochastic Risk Index for Hazardous Chemical Constituents. Calculation of the risk index for all hazardous chemicals in the waste that cause stochastic effects is performed in the same manner as in the previous examples for radioactive wastes. The calculated risk for each such substance, based on the assumed exposure scenario, is summed and then divided by the acceptable lifetime risk of 10 3 for classification as low-hazard waste (see Table 7.1). The risk for each chemical is calculated by multiplying the arithmetic mean of the concentration in the waste given in Table 7.5 by the intake rate from ingestion, inhalation, or dermal absorption per unit concentration discussed in Section 7.1.7.3 and 10 percent of the appropriate slope factor in Table 7.7 (see Section 7.1.7.1) adjusted for the exposure time. Since the slope factors assume chronic lifetime exposure, they must be reduced by a factor of 70 based on the assumption that the exposure scenario at the hazardous waste site occurs only once over an individual s lifetime. In addition, a simplifying assumption is made that whenever more than one slope factor is given for a hazardous substance in Table 7.7, the higher value was applied to the total intake rate by all routes of exposure of about 4 X 10 8 mg (kg d) 1 per ppm. This assumption should be conservative. 

Taking the logarithm of both sides, this yields a number that can be directly inserted into the calculation of the risk index ... 

The basic definitions of exempt, low-hazard, and high-hazard waste shown in Figure 6.1 are considered in the following sections. Recommendations on approaches to calculating the risk from waste disposal in the numerator of the risk index and recommendations on specifying allowable risks in the denominator of the risk index for the purpose of classifying waste are discussed in Section 6.3. 

In general, calculation of the risk or dose from waste disposal in the numerator of the risk index in Equation 6.2 or 6.3 involves the risk assessment process discussed in Section 3.1.5.1. As summarized in Section 6.1.3, NCRP recommends that generic scenarios for exposure of hypothetical inadvertent intruders at waste disposal sites should be used in calculating risk or dose for purposes of waste classification. Implementation of models describing exposure scenarios for inadvertent intruders at waste disposal sites and their associated exposure pathways generally results in estimates of risk or dose per unit concentration of hazardous substances in waste. These results then are combined with the assumptions about allowable risk discussed in the previous section to obtain limits on concentrations of hazardous substances in exempt or low-hazard waste. 

The risk index defined in Equation 6.1 (see Section 6.2.1) is intended to provide a measure of the potential risk that arises from disposal of any waste that contains hazardous substances. In Section 6.3, the general definition of the risk index is elaborated and recommendations on suitable approaches to calculating the risk index for individual hazardous substances are presented. For purposes of developing a comprehensive and risk-based waste classification system, a simple method of calculating the risk from disposal of mixtures of hazardous substances is needed. The method must take into account that the allowable concentrations of particular hazardous substances in waste of a given class generally will be lower when multiple substances are present than when only a single substance is present. Such a method is presented and discussed in this Section. 

The order in which the summations over the responses (r) and substances (i) of concern are executed in the second and third steps above is arbitrary. However, these steps must be executed before the MAX and INTEGER functions are applied to the result. If the risk index for substances causing deterministic responses were based on calculations of health risk per se, rather than dose, the INTEGER function in Equation 6.5 would not be necessary, because the risk would be zero whenever a dose is below the threshold. Again, however, evaluation of the risk index for substances that cause deterministic responses based on dose is recommended when the dose-response relationship is assumed to have a threshold. The use of dose is supported by the observation that the dose-response relationship above the threshold generally is nonlinear. 

This Section provides example calculations of the composite risk index for a simple, hypothetical waste that contains a mixture of substances that cause stochastic or deterministic effects. Application of the risk index in classifying real wastes is considered in Section 7.1. 

For the purpose of illustrating how the composite risk index in Equation 6.6 would be used to classify a hypothetical waste, it is helpful to simplify Equations 6.4 and 6.5. This is done by assuming that the summation over all responses (index r) has been calculated, that only one waste classification boundary represented by the index j is being considered (i.e., the boundary between exempt and low-hazard waste, based on a negligible risk, or the boundary between low-hazard and high-hazard waste, based on an acceptable risk), and that the modifying factor (F) is unity. Further, the calculated dose in the numerator of the risk index is denoted by D and the allowable dose in the denominator is denoted by L. Then, the composite risk index for all hazardous substances in the waste, expressed in the form of Equation 6.6, can be written as ... 

Calculation of the composite risk index for the purpose of waste classification based on the simplified Equation 6.8 is illustrated using the hypothetical data given in Table 6.1. Consistent with the form of the risk index in Equations 6.3 and 6.8, risk indexes for individual hazardous substances in Table 6.1 are expressed as the ratio of a... 

For substances that cause stochastic effects, the risk index can be expressed in terms of risk, rather than dose. In this case, the risk per unit dose would be incorporated in the calculated risk in the numerator, based on the assumed exposure scenario, rather than in the denominator. However, the effective dose provides a convenient surrogate for risk for radionuclides, because all organs at risk and all stochastic responses of concern are taken into account, and the use of dose for all substances that cause stochastic effects is consistent with the form of the risk index for substances that cause deterministic effects, which generally should be expressed in terms of dose based on the assumption of a threshold dose-response relationship. 

The boundaries between different waste classes would be quantified in terms of limits on concentrations of hazardous substances using a quantity called the risk index, which is defined in Equation 6.1. The risk index essentially is the ratio of a calculated risk that arises from waste disposal to an allowable risk (a negligible or acceptable risk) appropriate to the waste class (disposal system) of concern. The risk index is developed taking into account the two types of hazardous substances of concern substances that cause stochastic responses and have a linear, nonthreshold dose-response relationship, and substances that cause deterministic responses and have a threshold dose-response relationship. The risk index for any substance can be expressed directly in terms of risk, but it is more convenient to use dose instead, especially in the case of substances that cause determinstic responses for which risk is a nonlinear function of dose and the risk at any dose below a nominal threshold is presumed to be zero. The risk index for mixtures of substances that cause stochastic or deterministic responses are given in Equations 6.4 and 6.5, respectively, and the simple rule for combining the two to obtain a composite risk index for all hazardous substances in waste is given in Equation 6.6 or 6.7 and illustrated in Equation 6.8. The risk (dose) that arises from waste disposal in the numerator of the risk index is calculated based on assumed scenarios for exposure of hypothetical... 

An important issue in developing a risk-based hazardous waste classification system is the degree of conservatism in protecting public health that should be embodied in the foundations and framework of the system and its implementation. The specific issues are, first, the extent to which calculations of risk in the numerator of the risk index should deliberately overestimate expected risks that arise from disposal of hazardous waste and, second, the extent to which the... 

In many respects, the foundations and framework of the proposed risk-based hazardous waste classification system and the recommended approaches to implementation are intended to be neutral in regard to the degree of conservatism in protecting public health. With respect to calculations of risk or dose in the numerator of the risk index, important examples include (1) the recommendation that best estimates (MLEs) of probability coefficients for stochastic responses should be used for all substances that cause stochastic responses in classifying waste, rather than upper bounds (UCLs) as normally used in risk assessments for chemicals that induce stochastic effects, and (2) the recommended approach to estimating threshold doses of substances that induce deterministic effects in humans based on lower confidence limits of benchmark doses obtained from studies in humans or animals. Similarly, NCRP believes that the allowable (negligible or acceptable) risks or doses in the denominator of the risk index should be consistent with values used in health protection of the public in other routine exposure situations. NCRP does not believe that the allowable risks or doses assumed for purposes of waste classification should include margins of safety that are not applied in other situations. 

Risk indices are single numbers or a tabulation of numbers correlated to the magnitude of risk. Some risk indices are relative values with no specific units, which only have meaning within the specific context of the risk index calculation methodology. Risk indices are easy to explain and present, but contain less information than other, more complex measures of risk. 

This module consists on the presentation of results obtained from the completion of remaining modules the risk calculation in each risk dimension, the global risk of each pipeline section and the ranking of the sections under a risk hierarchy and the results analysis too. In relation to the presentation of obtained residts, it is basically an numerical and a graphical presentation of the risk index, both in each criterion of risk as in multi-attribute analysis for each section of pipeline. 

Wilkinson et al. (2000) used the information in Table 10.2, chose compound IV as the index compound (TFF= 1), assigned TEF values to compounds I (0.05), II (0.01), and III (0.2) and calculated the total compound IV equivalent exposure (TEQ) to 0.042 mg/kg bw/day. When this TEQ was compared to the RfD of compound IV (0.05 mg/kg bw/day), a value of 0.84 was obtained, representing a kind of combined HQs that indicates that 84% of the risk cup was filled. This risk estimate will be the same regardless which compound is selected as the index compound, provided that the AF for each member in the group is the same (Table 10.2, scenario A). 

Use of the composite risk index in classifying waste. Given the risk indexes for mixtures of substances causing stochastic or deterministic effects calculated using Equations 1.5 and 1.6, respectively, the composite risk index for all hazardous substances is calculated using Equation 1.4. This procedure assumes that induction of stochastic effects is independent of exposures to substances causing deterministic effects, and vice versa. 

Limits on amounts of hazardous substances in each waste class would be calculated based on values of the so-called risk index for each hazardous substance in the waste and the composite risk index for mixtures of hazardous substances. For the purpose of describing the recommended framework for a risk-based hazardous waste classification system, the risk index is generally defined as ... 

The modifying factor in the risk index represents any considerations of importance to waste classification other than those that are directly incorporated in the calculated risk from disposal and the specified allowable risk. The modifying factor can take into account, for example, the probability of occurrence of assumed exposure scenarios used in classifying waste, uncertainties in the assessment of risk from disposal and in the data required to evaluate the risk index, levels of naturally occurring hazardous substances in surface soil and their associated health risks to the public, and the costs and benefits of different means of waste disposal. The modifying factor is discussed further in Section 6.3.3. 

NCRP assumes that the risk from disposal of any hazardous substance in waste can be described by means of a dimensionless risk index. The risk index for the ith hazardous substance is defined as the calculated risk from disposal of that substance, based on an assumed exposure scenario, relative to a specified allowable risk for the assumed type of disposal system. Based on this definition, the risk index is written as ... 

The risk index in Equation 6.2 is expressed in terms of risk (i.e., the probability that an adverse response will occur during an individual s lifetime). This definition is consistent with the fundamental objective of developing a risk-based hazardous waste classification system. However, the use of health risk per se in calculating the risk index presents some difficulties because risk is not proportional to dose for substances that cause deterministic effects. For this type of substance, the risk is presumed to be zero at any dose below a nominal threshold. Since the allowable dose should always be less than the threshold in order to prevent the occurrence of adverse responses, expressing the risk index in terms of risk would result in an indeterminate value and, more importantly, a lack of distinction between doses near the nominal thresholds and lower doses of much less concern. For any hazardous substance, including carcinogens for which risk is assumed to be proportional to dose without threshold, it is generally useful to express the risk index as the ratio of a calculated dose [e.g., sieverts, mg (kg d)-1] to an allowable dose that corresponds to an allowable risk ... 

Establishing Allowable Risks or Doses of Substances That Cause Stochastic Responses. Given the assumption of a linear dose-response relationship for substances that cause stochastic responses without threshold, either risk or dose may be used to calculate the risk index. The following two sections discuss suitable approaches to establishing negligible and acceptable risks or doses of substances that cause stochastic responses. 

The modifying factor in the risk index in Equation 6.2 or 6.3 represents any factors deemed important in classifying waste other than those explicitly accounted for in the calculated risk or dose from waste disposal in the numerator or the allowable risk or dose for the waste class of concern in the denominator. The modifying factor generally can be substance- or waste-specific. 

Therefore, for waste that contains mixtures of substances that cause stochastic responses, the risk index in Equation 6.4 generally can be reduced to a single summation over all such substances (i) of the ratio of a calculated dose to an allowable dose. The risk index for such mixtures of substances thus is in the form of a simple sum-of-fractions rule. An example calculation is described in Section 6.4.4. 

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