Dose-response models, extrapolation

C Low dose effects usually not measurable directly In human or animal observations Need to extrapolate observed high dose effects to low or zero dose range by theoretical dose-response models ... 

Assumptions in Risk Extrapolation. Risk extrapolation cannot be performed as a mechanical exercise, due to the need for judgment in the selection of data and application of dose-response models. In particular, there are a number of implicit assumptions inherent in risk extrapolation. They may be summarized as follows ... 

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 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 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. 

K. Rai, and J. Van Rysin (1979), A generalized multihit dose/response model for low-dose extrapolation, Biometrics, 37, 341. 

If sufficient data are available to support the use of a biologically based dose-response model, it may represent the most appropriate method for using the observed data to extrapolate to exposure below the observed dose range. If data are not available for a biologically based model, which is the case for the majority of chemicals studied, a point of departure (POD) approach is recommended. The POD represents a dose within the range of observed data associated with a 10% extra tumor... 

As for PK, a solution to extrapolate PD from in vitro biological targets to a whole body in vivo is to develop integrative computational models. These models can be either very simple, like statistical dose-response models, or sophisticated and based on systems biology, according to the goal pursued and the data available. 

Second, in terms of experimental design, concentration data for PK should be systematically collected. That may not seem terribly exciting but forms the basis for correct extrapolation. Those data should be analyzed with pharmacokinetic models to quantify the in vitro PK and transpose it (using well-developed PBPK concepts) to the whole body. To relate cellular levels to effects, empirical (statistical) dose-response models can be used, but systems biology models are probably more interesting and fruitful in the long run. 

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 ... 

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. 

Krewski and Van Ryzin (40) examined the extrapolation characteristics of six of the more cbmmonly used dose-response models. They applied these models to 20 sets of toxic response data that were taken from the Report of the Scientific Committee of the Food Safety Council (15,16). The toxic responses were both carcinogenic and noncarcTnogenic in nature. Of the 19 data sets having... 

Figure 4. Comparison of high to low dose extrapolation for 6 dose-response models data from (41).

Figure 11. Extrapolation of Dose-Response Models to Low Doses of TCE. Adapted with permission from Ref. 21. Copyright 1984, Regul. Toxicol. Pharmacol.

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 ... 

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