Dose-response relationship INDEX

Risk is not always a useful measure of health impact in evaluating the risk index, because risk is not proportional to dose when a hazardous substance is assumed to have a threshold dose-response relationship. For this type of substance, the risk is presumed to be zero at any dose below a nominal threshold. Since the allowable dose of such substances 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 when the dose is below the threshold 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, a generally useful form of risk indexes (Rid is in terms of dose ... 

Adding risk indexes (RR) for noncarcinogenic substances and combining risk indexes (RR) for carcinogenic and noncarcinogenic substances requires care, however, due to the assumed forms of the dose-response relationships. The evaluation of Equation 1.3 for mixtures of hazardous substances is described in Section I.5.5.4. 

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). 

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. 

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. 

Risk Index for Multiple Substances That Cause Stochastic Responses. The risk index for mixtures of substances that cause stochastic responses (radionuclides and chemicals) is based on an assumption of a linear, nonthreshold dose-response relationship. This risk index takes into account the stochastic risk in all organs or tissues, and it assumes that the risk in any organ is independent of risks in any other organs. Based on these conditions, and expressing the risk index for a single hazardous substance in terms of dose (see Equation 6.3), the risk index for mixtures of substances that cause stochastic responses, denoted by RIS, can be expressed as ... 

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. 

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. 

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. 

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. 

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... 

Once a drug s dose-response relationship for lethality has been established there are several ways in which this information can be utilized. For example, from the data in Figure 7.2 we can obtain a numerical index of toxicity analogous to the way we obtained a numerical index of effectiveness in Chapter 6. If you remember, we... 

The dose-response relationship therefore allows the toxicologist to establish a threshold, the dose at which there is no adverse effect, which is vital for the proper assessment of risL Information from the dose-response relationship is used to determine the therapeutic index and the margin of safety for drugs, which indicate how safe the drug is. The greater the value the greater the difference between the dose at which there are adverse effects and the therapeutic dose. This is used as part of the risk assessment process. 

Using the Cd concentration in rice as an index of exposure and the prevalence of proteinuria with glucosuria as an index of health effect, a significant dose-response relationship was demonstrated between the two indices. The allowable values of Cd concentration in rice were estimated to be in the range of 0.05-0.20 mg/kg, representing values lower than the 0.4 mg/ kg provisionally adopted by the Japanese government [84]. 

Therapeutic index (TI) Dose-response relationship/curve... 

The relationship of Pb exposure and anemia in terms of dose—response relationships and thresholds indexed by various exposure markers has been recorded. In children, the thresholds in the older literature for onset of Pb-derived anemia with reference to Hb reduction are lower, i.e., <40 pg/dl than it is in adults, s40—50 p-g/dl. At levels above these thresholds, studies typically identified an inverse relationship with PbB levels in children (Pueschel et al., 1972) and Pb workers (Baker et al., 1979). Several Pb worker epidemiological studies evaluated the percentage population response for a selected Hb reduction at varying levels of PbB. In the U.S. study of smelter workers by Baker et al. (1979), employing an Hb level <14.0 g/dl, 5% of workers had a Hb reduction at 40—59 pg/dl PbB, 14% at 60—79 pg/dl PbB, and 36% at s80 p-g/dl PbB. A similar analysis by Grandjean (1979), however, showed much higher frequencies at a somewhat different Hb cutoff of <14.4 g/dl 17% showed an Hb reduction at <25 pg/dl PbB, 26% at... 

The dose—response relationships for EP change with Pb exposure, including thresholds, are logarithmic and appear to show that children are more sensitive than adults, while women are somewhat more sensitive than men (Table 16.6). For children, the dose—response relationship persists down to a threshold in blood lead on the order of 15—20 xg/dl, and in adults across gender, 25—35 p-g/dl. The dose—response relationship of EP and PbB is affected by the time course of EP s accumulation with increase in Pb exposure indexed through PbB. 

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