Dose-Response Models linear

Dose-Response Extrapolation Models. A dose-response model is simply a hypothetical mathematical relationship between dose-rate and probability of response. For example, the simplest form of such a model asserts that probability of tumor initiation is a linear multiple of dose-rate (provided the dosage is well below the organism s acute effect threshold for the substance in question). In general, we will express dose-response models as follows ... 

The most widely-accepted dose response model at the present time is the multi-stage model, which has great flexibility in curve-fitting, and also has a strong physiological justification. Although it is difficult to implement, there are already computer codes in existence that estimate the model parameters (13). The two most widely-used models, until recently, were the one-hit model and the log-probit model. They are both easy to implement, and represent opposite extremes in terms of shape - the former represents the linear non-threshold assumption, whereas the latter has a steep threshold-like curvature. In numerous applications with different substances it has been found that these three... 

For carcinogens a linear, no-threshold dose-response model (Figure 8.1) is assumed to apply at low dose, unless data are available in specific cases to demonstrate that such a model is inappropriate. 

The linear, no-threshold, dose-response model is accurate for very low exposures. 

The second step of the dose-response assessment is an extrapolation to lower dose levels, i.e., below the observable range. The purpose of low-dose extrapolation is to provide as much information as possible about risk in the range of doses below the observed data. The most versatile forms of low-dose extrapolation are dose-response models that characterize risk as a probability over a range of environmental exposure levels. Otherwise, default approaches for extrapolation below the observed data range should take into account considerations about the agent s mode of action at each tumor site. Mode-of-action information can suggest the likely shape of the dose-response curve at these lower doses. Both linear and nonlinear approaches are available. 

The BEIR III risk estimates formulated under several dose-response models demonstrate that the choice of the model can affect the estimated excess more than can the choice of the data to which the model is applied. BEIR III estimates of lifetime excess cancer deaths among a million males exposed to 0.1 Gy (10 rad) of low-LET radiation, derived with the three dose-response functions employed in that report, vary by a factor of 15, as shown in Ikble 6.1 (NAS/NRC, 1980). In animal experiments with high-LET radiation, the most appropriate dose-response function for carcinogenesis is often found to be linear at least in the low to intermediate dose range (e.g., Ullrich and Storer, 1978), but the data on bone sarcomas among radium dial workers are not well fitted by either a linear or a quadratic form. A good fit for these data is obtained only with a quadratic to which a negative exponential term has been added (Rowland et al., 1978). 

When the linear nonthreshold dose-response model is adjusted for background and survival, it becomes ... 

The nominal probability coefficient for radionuclides normally used in radiation protection is derived mainly from maximum likelihood estimates (MLEs) of observed responses in the Japanese atomic-bomb survivors. A linear or linear-quadratic dose-response model, which is linear at low doses, is used universally to extrapolate the observed responses at high doses and dose rates to the low doses of concern in radiation protection. The probability coefficient at low doses also includes a small adjustment that takes into account an assumed decrease in the response per unit dose at low doses and dose rates compared with the observed responses at high doses and dose rates. 

Fig. 3.6. Illustration of use of benchmark dose method to estimate nominal thresholds for deterministic effects in humans. The benchmark dose (EDio) and LEDi0 are central estimate and lower confidence limit of dose corresponding to 10 percent increase in response, respectively, obtained from statistical fit of dose-response model to dose-response data. The nominal threshold in humans could be set at a factor of 10 or 100 below LED10, depending on whether the data are obtained in humans or animals (see text for description of projected linear dose below point of departure).

NCRP (2001). National Council on Radiation Protection and Measurements. Evaluation of the Linear-Nonthreshold Dose-Response Model for Ionizing Radiation, NCRP Report No. 136 (National Council on Radiation Protection and Measurements, Bethesda, Maryland). 

Evaluation of the Linear-Nonthreshold Dose-Response Model for Ionizing Radiation (2001)... 

Dose-response models should have greater flexibility to fit the observed shape of the dose-response data such models should not be constructed to be forced to always be linearly decreasing at low doses... 

Let us specify some very low risk level as that which we would not like to see exceeded. Pick an extra lifetime probability of cancer of 0.00001 (1 in 100000). For purposes of this discussion, this risk will be considered tolerable. This probability is 10000 times smaller than the minimum risk for which we have dose—response data (0.1, see Figure 5). If we adopt hypothetical dose-response model A, the linear, nothreshold model, then we see that dose A produces an extra lifetime risk of 1/100000. Similarly, model B yields dose B as producing the same risk. 

The mouse study of Marrs et al. (1988a) indicated that Zn/HCE smoke causes alveolar carcinomas in mice. A generalized multistage linear dose-response model fitted to the data gave an upper limit of cancer risk of 0.086 mg ZnCL day. NRC (1997) derived a cancer potency factor for Zn/HCE smoke and determined that the possible cancer risk associated with the EEGLs and PEGL was approximately 1 in 10 . 

The totality of the scientific evidence for a causal default—a fundamental dose-response model, given the state-of-science—now discounts conjectural arguments (the linear, at low-dose, nonthreshold model) or arbitrary ones, such as those based on extrapolation (the threshold model) because both of them eliminate a very large number of experimentally observed health benefits. According to the EPA, the use of defaults is a subjective choice (EPA 2005). As the EPA states ... 

Figure 7.1 also depicts changes via behaviors, such as occupation, ambient exposure, and predisposition, such as genetic. Logically, it is correct regardless of the shape of the dose-response model. At low dose or at environmental (ambient) exposures, cancer risk assessment models used in regulatory law are either linear or linearized that is, each is a cumulative distribution function of lifetime cancer risk and thus is a monotonic function. Hormetic cancer dose-response models are also probabilistic however, they are nonmonotonic (they are relations). The EPA summarizes the reasons for using statistical and probabilistic methods in risk assessment as follows (EPA 2005) ... 

The LNT-based dose-response model for cancer, being a cumulative distribution function, begins at zero and is proportional to doses (i.e., is linear at low doses, resulting in the LNT hypothesis). The early form of the LNT model is the one-hit model ... 

The hormetic dose-response model can predict the occurrence of beneficial responses below the toxicological threshold. This can be seen with endpoints such as enhanced longevity, decreased disease incidence, and improved cognition, unlike the threshold and linear at low-dose (LNT) models. 

Chemical interactions can be accounted for. While threshold dose response model can only deal with chemical interactions for responses that exceed a threshold, the hormetic model also does this. These models differ where the interaction occurs in the hormetic stimulatory zone. In the case of the hormetic chemical interactions, the maximum response is still constrained to 30-60% above the control value a characteristic that the threshold and linear at low-dose models do not have. 

The first conclusion is that the factual and theoretical evidence points to replacing the classical causal regulatory defaults used to deal with low dose-response, the linear no-threshold, and the linear at low-dose-response models, or monotonic functions, with the J- and inverse J-shaped models—or relations. These models have been demonstrated to apply to toxicological and cancer outcomes for a very wide range of substances and diseases. The classical defaults may stiU be applicable on a case-by-case basis. The reasons for changing the defaults include the fact that the J-shaped class of models quantities a wide set of health benefits that are completely excluded from estimations that use monotonic models. We conclude that replacing both a conjecture and an arbitrary model with two theoretically and empirically sound ones leads to rational decision and does not exclude actually demonstrable benefits. Overall, the sum is positive for society. 

All of these considerations indicate that the biology behind the shape of the tumor dose-response curve is much more complex than a simple conclusion that mutagenic activity = linear dose-response. Ultimately, biologically based dose-response models and use of biomarker data may make it possible to extend the tumor dose-response curve to low doses based on biological data, rather than presumptions about the shape of the dose-response curve. In the shorter term, it is important to recognize that the biology is complex, and linear extrapolation from tumor data is a health-protective science policy decision. 

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