Dose-response relationships stochastic responses

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). 

Two types of responses from exposure to hazardous substances, called stochastic or deterministic,5 are of concern in risk assessment. The two types of responses are distinguished by the characteristic features of the dose-response relationship, i.e., the relationship between the dose of a hazardous substance and the probability (or frequency) of a response. 

Dose-Response Relationships. The primary objective of this study is to set forth the foundations of a risk-based waste classification system that applies to hazardous chemicals and radionuclides. Most aspects of the risk assessment process that provide the basis for establishing this system are conceptually the same for chemicals and radionuclides, although the specific data (e.g., solubilities) may differ. One important exception is the assumed relationship of the probability of a response to a unit dose of a substance that causes stochastic effects, which is called the dose-response relationship There are important conceptual differences in the way this relationship has been defined and used for hazardous chemicals and radionuclides, and these differences could pose a major impediment to development of a risk-based waste classification system that applies to both types of substances on a consistent basis. These differences are elucidated in the following section. 

In general, the relationship between dose and response can be represented by a variety of functional forms. At low doses of substances that cause stochastic effects, the dose-response relationship usually is assumed to be linear and, thus, can be expressed as a single probability coefficient. This coefficient is frequently referred to as a risk (or potency factor or unit risk factor or slope factor) in the literature. However, it is really the response (consequence) resulting from a dose of a hazardous substance, and it should not be confused with risk as defined and used in this Report. 

UCL takes into account measurement uncertainty in the study used to estimate the dose-response relationship, such as the statistical uncertainty in the number of tumors at each administered dose, but it does not take into account other uncertainties, such as the relevance of animal data to humans. It is important to emphasize that UCL gives an indication of how well the model fits the data at the high doses where data are available, but it does not indicate how well the model reflects the true response at low doses. The reason for this is that the bounding procedure used is highly conservative. Use of UCL has become a routine practice in dose-response assessments for chemicals that cause stochastic effects even though a best estimate (MLE) also is available (Crump, 1996 Crump et al., 1976). Occasionally, EPA will use MLE of the dose-response relationship obtained from the model if human epidemiologic data, rather than animal data, are used to estimate risks at low doses. MLEs have been used nearly universally in estimating stochastic responses due to radiation exposure. 

Fig. 3.9. Biologically-based model of the cancer induction process used to estimate the dose-response relationship of chemicals causing stochastic effects (Andersen etal., 1987).

In spite of uncertainties in the dose-response relationship for radiation discussed above, it is generally believed that radiation risks in humans can be assessed with considerably greater confidence than risks from exposure to most hazardous chemicals that cause stochastic effects. The state of knowledge of radiation risks in humans compared with risks from exposure to chemicals that cause stochastic effects is discussed further in Section 4.4.2. 

The following sections present a comparison of approaches to estimating deterministic and stochastic dose-response relationships for radionuclides and hazardous chemicals. 

First, the dose-response relationships for radiation used for purposes of health protection and the probability coefficients derived from those relationships are intended to be MLEs. In contrast, the dose-response relationships and probability coefficients for chemicals that induce stochastic responses are intended to be upper-bound estimates (UCLs), although MLEs also are available. In animal data from which the probability coefficients for most chemicals that cause stochastic responses are obtained, UCL can be greater than MLE by a factor that ranges from 5 to 100 or more. 

The dose-response relationship for radionuclides is intended to be a best estimate, whereas the dose-response relationship for chemicals that cause stochastic effects is intended to be an upper-bound estimate (UCL). 

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. 

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. 

Approaches to Estimating Dose-Response Relationships for Substances That Cause Deterministic Responses. Most of the factors that must be considered in developing reasonably consistent approaches to estimating risk for radionuclides and chemicals that induce stochastic responses discussed in the previous section do not apply to substances that induce deterministic responses. For purposes of health protection, incidence generally is the appropriate measure of response for substances that cause deterministic responses. Furthermore, an accounting of deterministic responses... 

Dose-response relationships for substances that induce stochastic effects best estimates (MLE) for radionuclides but upper bounds (UCLs) for chemicals that induce stochastic effects ... 

The use of Monte Carlo and other stochastic analytical methods to characterize the distribution of exposure and dose-response relationships is increasing (IPCS, 2001a). The Monte Carlo method uses random numbers and probability in a computer simulation to predict the outcome of exposure. These methods can be important tools in risk characterization to assess the relative contribution of uncertainty and variability to a risk estimate. 

The individual tolerance concept has some unrealistic properties (Kooijman 1996 Newman and McCloskey 2000). Most importantly, if there is a distribution in sensitivities, this would imply that the survivors from an experiment are the less sensitive individuals. Experiments with sequential exposure show that this prediction fails (at least as the dominant mechanism) (Newman and McCloskey 2000 Zhao and Newman 2007). There is sufficient reason to conclude that the individual threshold model is not sufficient to explain the observed dose-response relationships, and that mortality is a stochastic process at the level of the individual... 

For radiation protection purposes, the biological effects of ionizing radiation are grouped into two main categories, the stochastic and deterministic effects. In both cases, the effects are related to the absorbed doses. Therefore, the knowledge on the dose-response relationships is essential for risk assessment. 

Stochastic responses are those for which the probability, but not their severity, is a function of dose, without threshold. Because of the long latency period between exposure and the expression of a stochastic response, the existence of a causal relationship between dose and response can only be inferred on statistical grounds based, for example, on knowledge of the background incidence of the response of concern in unexposed populations. Severe hereditary (genetic) and many carcinogenic (e.g., genotoxic) responses are considered to be stochastic. 

Dose-Response Assessment for Chemicals That Cause Stochastic Effects. For hazardous chemicals that do not have a threshold in the dose-response relationship, which is currently believed to... 

Although dose-response assessments for deterministic and stochastic effects are discussed separately in this Report, it should be appreciated that many of the concepts discussed in Section 3.2.1.2 for substances that cause deterministic effects apply to substances that cause stochastic effects as well. The processes of hazard identification, including identification of the critical response, and development of data on dose-response based on studies in humans or animals are common to both types of substances. Based on the dose-response data, a NOAEL or a LOAEL can be established based on the limited ability of any study to detect statistically significant increases in responses in exposed populations compared with controls, even though the dose-response relationship is assumed not to have a threshold. Because of the assumed form of the dose-response relationship, however, NOAEL or LOAEL is not normally used as a point of departure to establish safe levels of exposure to substances causing stochastic effects. This is in contrast to the common practice for substances causing deterministic effects of establishing safe levels of exposure, such as RfDs, based on NOAEL or LOAEL (or the benchmark dose) and the use of safety and uncertainty factors. 

In all studies of the relationship of radiation-induced stochastic responses to dose, the derivation of MLEs (mean values) of the dose-response relationships has been emphasized (NAS/NRC, 1988b 1990). Furthermore, for purposes of radiation protection, MLEs of the dose-response relationships, rather than UCLs, have been emphasized in extrapolating the observed dose-response data to lower doses beyond the range of observation (NCRP, 1975 1999b). 

The use in radiation protection of MLEs of the relationships of stochastic responses to dose, rather than UCLs, is justified on the grounds that the probability of a response in most individuals is not likely to be significantly underestimated. Even if the probability were underestimated, the current framework for radiation protection... 

Stochastic Responses. A basic principle of health protection for both radionuclides and hazardous chemicals is that the probability of a stochastic response, primarily cancers, should be limited to acceptable levels. For any substance that causes stochastic responses, a linear dose-response relationship, without threshold, generally is assumed for purposes of health protection. However, the probability coefficients for radionuclides and chemicals that induce stochastic responses that are generally assumed for purposes of health protection differ in two potentially important ways. 

The acceptable risks for substances that induce stochastic responses discussed in this Section are values in excess of unavoidable risks from exposure to the undisturbed background of naturally occurring agents that cause stochastic responses, such as many sources of natural background radiation and carcinogenic compounds produced by plants that are consumed by humans. This distinction is based on the assumption of a linear, nonthreshold dose-response relationship for substances that cause stochastic responses and the inability to control many sources of exposure. Risk management can address exposures to naturally occurring substances that induce stochastic responses, but only when exposures are enhanced by human activities or can be reduced by reasonable means. 

Stochastic responses from exposure to radionuclides and hazardous chemicals generally are of concern in health protection of the public and in classifying waste. Of the three differences in approaches to dose-response assessment identified above, the most important is the use of a best estimate (MLE) of the dose-response relationship for radionuclides but upper-bound estimates (UCLs) for hazardous chemicals that cause stochastic effects. UCL in the dose-response relationship for chemicals that cause stochastic effects normally exceeds MLE by a factor of 5 to 100 or more. If this difference... 

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