Risk index, composite

Dept. Risk Index Relative Risk % Risk Index Composite Exposure ( X1000) Composite Dollars Risk ( x 1000) Rank... 

NCRP believes that a conceptually simple composite risk index for mixtures of hazardous substances can be developed that provides an adequate representation of risk for the purpose of waste classification. The composite risk index is written in terms of separate risk indexes for substances that induce stochastic (s) and deterministic (d) effects as ... 

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. 

In accordance with Equation 1.3 (see Section 1.5.1) and as indicated in Figure 1.2 (see Section 1.5.4), classification of waste would proceed in the following way. First, if the composite risk index is less than unity when the denominator represents a negligible risk and the numerator is evaluated using an exposure scenario appropriate to disposal of nonhazardous waste, the waste would be classified as exempt, but the waste would be nonexempt if the composite risk index is unity or greater. Then, for nonexempt waste, if the... 

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 ... 

Development of the Composite Risk Index for Multiple Substances... 

Hazardous waste generally can contain mixtures of substances that cause stochastic or deterministic responses. The composite risk index for any mixture of hazardous substances in a given waste can be represented as the sum of risk indexes for multiple substances that cause stochastic or deterministic responses given in Equations 6.4 and 6.5 ... 

Given the form of the deterministic risk index in Equation 6.5, which results in zero or integer values, the composite risk index for all hazardous substances in Equation 6.6 also can be expressed as the maximum of the separate risk indexes for multiple substances causing stochastic or deterministic responses ... 

If the risk index for all substances that cause deterministic responses in the waste (RId) in Equation 6.5 is zero (i.e., the doses of all substances that cause deterministic responses are less than the allowable values), classification is determined solely by the risk index for all substances that cause stochastic responses (RP) in Equation 6.4 the latter must be nonzero based on the assumption of a linear, nonthreshold dose-response relationship. On the other hand, if the risk index for all substances that cause deterministic responses is unity or greater, the calculated risk exceeds the allowable risk for the waste class of concern without the need to consider the risk posed by substances that cause stochastic effects. The only advantage of the form of the composite risk index in Equation 6.6 is that it indicates more explicitly that the total risk posed by a given waste is the sum of the risks posed by the two types of hazardous constituents, however approximate that representation may be. 

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... 

Table 6.1—Hypothetical values of risk indexes for individual substances and organs in first example calculation of a composite...

Based on the information given above, the composite risk index for the waste can be calculated and the resulting waste classification obtained. Substituting the values in Table 6.1 into Equation 6.8 results in the following ... 

Substances that cause deterministic responses (the first term in Equation 6.8) contribute a value of one to the composite risk index of 1.8, and substances that cause stochastic responses account for the remaining 0.8. Thus, the presence of the substances that cause deterministic responses alone would be sufficient to place this waste in Class 2. This result also would be indicated if the alternative form of the composite risk index in Equation 6.7 were used. 

As another example, suppose that each risk index for the individual hazardous substances given in Table 6.1 were a factor of two lower. Then, by the procedure described above, the composite risk index for the waste would be determined as follows ... 

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... 

The composite risk index for mixtures of substances that cause stochastic or deterministic effects is shown in its most general form in Equations 6.4, 6.5 and 6.6 (see Sections 6.4.1 and 6.4.2), and is restated in a simpler and more convenient form in Equation 6.7 (see Section 6.4.4). In calculating the risk index for mixtures of substances... 

To classify this mixed radioactive and hazardous chemical waste based on risk, a composite risk index giving the sum of the risk indexes for chemicals that cause deterministic effects, chemicals that cause stochastic effects, and radionuclides must be evaluated. The first two elements of the composite risk index were evaluated in Sections 7.1.7.4 and 7.1.7.5, respectively. In this Section, the stochastic risk index for 137Cs in the waste is computed. 

Calculation of the Composite Risk Index. The composite risk index for the chemical and radioactive components of electric arc furnace waste is given by ... 

We explain the method in detail below. It is imperative to fully understand the following parts of the contribution to risk in terms of (1) portfolio composition and (2) index composition. 

Composite Risk The composite risk, measured in dollars, for a department is the product of the composite exposure dollars and the percentage risk index. The composite risk represents the economic value of the relative risk for a department. 

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