Extrapolation modeling

This step utilizes either a safety factor approach or various extrapolation models. 

FiOyRE 5.57 Results of alternative extrapolation models for the same experimental data. (Reprinted with permission from Risk Assessment in the Federal Government. Copyright 1983 by the National Academy of Sciences. Courtesy of the National Academy Press, Washington, DC.)... 

To.xicity values for carcinogenic effects can be e.xprcsscd in several ways. The slope factor is usually, but not always, the upper 95th percent confidence limit of the slope of the dose-response curve and is e.xprcsscd as (mg/kg-day). If the extrapolation model selected is the linearized multistage model, this value is also known as the ql. That is ... 

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 ... 

Select the analysis (extrapolation) model(s) which will be used. 

The validity of the extrapolation model is likely to be better the more proven the procedures used and the smaller the degree of extrapolation. 

When extrapolation of measured data is carried out all the uncertainties become magnified, increasing as the degree of extrapolation is increased. Inevitably, extrapolations from accelerated tests to normal ambient conditions will be subject to enormous uncertainties, which is why the general advice for temperature is to extrapolate to 30-40 °C beyond the last data point at the very most. Additional to this, but generally not quantifiable, is the uncertainty of the validity of the extrapolation model. 

Regulatory officials nevertheless act on the basis of such hypothetical risks ( hypothetical definitely does not mean imaginary it means that the risk estimates are based on certain scientific hypotheses and that they have not been empirically tested). Such actions are in part based on legal requirements (Chapter 11) and in part on the prudence that is a traditional feature of public health policies. The scientific information, assumptions, and extrapolation models upon which risk assessments are based are considered sufficiently revealing on the question of human risk to prompt risk-control measures. To put off such actions until it is seen whether the hypothesized risks are real - to wait for a human body count - is considered to be an unacceptable course. 

Monte Carlo method, 210, 21 propagation, 210, 28] Gauss-Newton method, 210, 11 Marquardt method, 210, 16 Nelder-Mead simplex method, 210, 18 performance methods, 210, 9 sample analysis, 210, 29 steepest descent method, 210, 15) simultaneous [free energy of site-specific DNA-protein interactions, 210, 471 for model testing, 210, 463 for parameter estimation, 210, 463 separate analysis of individual experiments, 210, 475 for testing linear extrapolation model for protein unfolding, 210, 465. 

In the case of biological contamination, the identification of risk became obvious by experience, the risk assessment was made unambiguous by epidemiology, and the immediate and obvious effectiveness of the risk management decisions demonstrated their wisdom in the absence of elegant quantitative risk extrapolation models and projections of costs per case averted. Costs of water treatment and distribution became trivial relative to almost all other essential commodities, and in the public expectation the biological safety of drinking water became axiomatic. 

In contrast, nominal probability coefficients for chemical carcinogens are derived from upper 95 percent confidence limits of observed responses at high doses, mainly in studies in animals. In some studies, the difference between the upper 95 percent confidence limit and MLE of the observed responses at high doses is an order of magnitude or more. Furthermore, several models have been used to extrapolate the observed responses to the low doses of concern in health protection of the public, with the result that estimated probability coefficients at low doses can differ by several orders of magnitude depending on the extrapolation model chosen. 

The doses of hazardous substances at which responses can be observed in humans or animals are higher (sometimes by large factors) than doses relevant to waste disposal and other routine exposure situations. Therefore, most dose-response relationships at the low doses of interest in protection of human health are calculated rather than measured they are based not only on scientific data but also on various assumptions and extrapolation models which, while scientifically plausible, cannot yet be subjected to empirical study... 

Statistical models. A number of statistical dose-response extrapolation models have been discussed in the literature (Krewski et al., 1989 Moolgavkar et al., 1999). Most of these models are based on the notion that each individual has his or her own tolerance (absorbed dose that produces no response in an individual), while any dose that exceeds the tolerance will result in a positive response. These tolerances are presumed to vary among individuals in the population, and the assumed absence of a threshold in the dose-response relationship is represented by allowing the minimum tolerance to be zero. Specification of a functional form of the distribution of tolerances in a population determines the shape of the dose-response relationship and, thus, defines a particular statistical model. Several mathematical models have been developed to estimate low-dose responses from data observed at high doses (e.g., Weibull, multi-stage, one-hit). The accuracy of the response estimated by extrapolation at the dose of interest is a function of how accurately the mathematical model describes the true, but unmeasurable, relationship between dose and response at low doses. 

Dose corresponding to a given level of response. Presenting the dose corresponding to a given response can be useful, particularly when using nonlinear extrapolation models in which the response per unit dose depends on the dose. 

Low-dose extrapolation models are the backbone of dose-response assessments. Because they can play such a dominant role in the regulatory process, it is important to understand some of their characteristics. As shown in Figure 3.10, different extrapolation models usually fit the data in the observable dose region in animal tests about equally well (Krewski et al., 1989), but they often give quite different results in the unobserved low-dose region of interest in assessments of risk to human health. The results obtained by extrapolation of the most commonly used low-dose models usually vary in a predictable manner, because the models use different mathematical equations to describe the chemical s likely behavior in the low-dose region. 

Failure to adjust dose-response estimates by considering biological information. In many dose-response assessments, potentially important biological information is not taken into account in selecting an extrapolation model. Examples of information often not included when a model is selected are the types of tumors, time to onset, and whether the chemical is genotoxic. Some... 

Additional bioassays in animals do not seem necessary. Further research on dose-response relationships for the many biochemical effects of peroxisome proliferators leading to liver cancer in rodents, identification of specific thresholds, and potential reversibility, would be informative only if an extrapolation model for cancer was deemed appropriate in spite of profound differences between human and rodent responses. 

FIGURE 1.4 Illustration of range extrapolation from laboratory animal data (left) to potential responses in humans (right) and the influence of the extrapolation model on the choice of the virtual safe dose. 

Our current understanding of mixture extrapolation is based on simple pharmacodynamic concepts of noninteractive joint action, such as simple similar action and simple independent action, with the associated extrapolation models concentration addition and response addition. These models are used for various types of extrapolations. Although mode of action is important when considering possible mixture interactions and extrapolations, the concept of the ecological mode of action needs to be expanded, as was also concluded for extrapolation across levels of biological organization. Mixture extrapolation should consider environmental (matrix)-chemical... 

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