Risk index, deterministic responses

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. 

Risk Index for Mixtures of Hazardous Substances. For the purpose of developing a comprehensive and risk-based hazardous waste classification system, a simple method of calculating the risk posed by mixtures of radionuclides and hazardous chemicals is needed. The method should account for the linear, nonthreshold dose-response relationships for radionuclides and chemical carcinogens (stochastic effects) and the threshold dose-response relationships for noncarcinogenic hazardous chemicals (deterministic effects). 

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 ... 

NCRP believes that use of a risk index expressed in terms of dose is acceptable and desirable as long as (1) the units of the numerator and denominator are consistent at a conceptual level, (2) the assumptions embodied in the proportionality constants between dose and response for substances that cause stochastic responses are clearly stated, and (3) the allowable doses are adjusted when the proportionality constants between dose and response for substances that cause stochastic responses or the thresholds for substances that cause deterministic responses change significantly. 

Establishing Allowable Doses of Substances That Cause Deterministic Responses. The risk index for substances that cause deterministic responses normally should be expressed in terms of dose, rather than risk, given the assumption of a threshold dose-response relationship. The allowable dose of substances that cause deterministic responses in the denominator in Equation 6.3 should be related to thresholds for induction of deterministic responses in different organs or tissues. 

The implication of the difference described above is that the mathematical form of the risk index for the two types of hazardous substances must be different. Thus, while NCRP believes that it is appropriate to develop a single risk index that accounts for mixtures of substances that cause stochastic or deterministic responses, separate risk indexes for these two types of substances are formulated first. 

Section 6.3.2). Equation 6.4 is expressed in terms of dose, rather than risk, mainly because this form is consistent with the preferred form of the risk index for mixtures of substances that cause deterministic responses presented in the following section. Both ways of expressing the risk index are equivalent for substances that cause stochastic responses when a linear, nonthreshold dose-response relationship is assumed. 

Formulation of the risk index for mixtures of substances that cause deterministic effects is considerably more complex than in the case of substances that cause stochastic effects discussed in the previous section. The added complexity arises from the threshold dose-response relationship for these substances and the need to keep track of the dose in each organ or tissue at risk in evaluating whether the dose in each organ is less than the allowable dose in that organ. For substances that cause deterministic responses, the index T can refer not only to a specific organ or tissue (e.g., the liver or skin) but also to a body system that may be affected by a particular chemical, such as the immune or central nervous system. 

For each substance, the organ or organs (including tissues or body systems) in which deterministic responses can be induced are identified. If a substance can induce responses in more than one organ, all such organs are included in calculating the risk index. 

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. 

As in the case of the risk index for mixtures of substances that cause stochastic responses discussed in the previous section, the modifying factor (F) in Equation 6.5 generally can be substance-specific, but its value often would be the same for all substances in a given waste that cause deterministic responses. 

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. 

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. 

The second example illustrates the importance of identifying and keeping track of the specific organs at risk from exposure to substances that cause deterministic responses. If the deterministic risk indexes for each substance were simply summed without regard for the organs at risk, the risk index for all substances that cause... 

Use of the risk index in classifying waste requires that adequate data be available to allow estimation of dose-response relationships for substances that induce stochastic or deterministic responses. The availability of suitable data is a potential problem only for hazardous chemicals. If suitable data are not available for particular hazardous substances, there is no satisfactory approach that could be used to include these substances in classifying waste. However, this would be an important deficiency only if substances with inadequate data on dose-response posed an important hazard in the waste. NCRP does not expect that the most important hazardous substances in waste in regard to potential risks would be lacking information on the dose-response relationship. 

Finally, NCRP emphasizes that calculated risk indexes for substances that induce deterministic or stochastic responses are not intended to be used as predictors of the probability of a response for any actual or hypothetical exposure situation. The risk index is nothing more than a simple, dimensionless representation of the risk posed by hazardous substances in waste to be used for purposes of waste classification. 

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... 

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. 

Deterministic Risk Index for Hazardous Chemical Constituents. In accordance with Equation 6.5, the risk index for all substances in the waste that induce deterministic responses is... 

The results in Table 7.8 indicate that the organ- and endpoint-specific risk indexes are about 0.7 to 0.8 in all cases, due mainly to intakes of lead. The maximum risk index for any organ or endpoint is about 0.8. Truncating this result using the INTEGER function, as indicated in Equation 6.5, gives a risk index for all deterministic hazardous chemicals in the waste of zero. This result means that the calculated dose in all organs and for all endpoints due to exposure to all deterministic substances that cause deterministic responses in the waste is less than the assumed acceptable dose of 10 times RfDs. Therefore, based only on consideration of substances that... 

In the last twenty years, various non-deterministic methods have been developed to deal with optimum design under environmental uncertainties. These methods can be classified into two main branches, namely reliability-based methods and robust-based methods. The reliability methods, based on the known probabiUty distribution of the random parameters, estimate the probability distribution of the system s response, and are predominantly used for risk analysis by computing the probability of system failure. However, variation is not minimized in reliability approaches (Siddall, 1984) because they concentrate on rare events at the tail of the probability distribution (Doltsinis and Kang, 2004). The robust design methods are commonly based on multiobjective minimization problems. The are commonly indicated as Multiple Objective Robust Optimization (MORO) and find a set of optimal solutions that optimise a performance index in terms of mean value and, at the same time, minimize its resulting dispersion due to input parameters uncertainty. The final solution is less sensitive to the parameters variation but eventually maintains feasibility with regards probabilistic constraints. This is achieved by the optimization of the design vector in order to make the performance minimally sensitive to the various causes of variation. 

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