Dose: extrapolation estimation, 116 threshold

Such low-dose extrapolation is typically only conducted for tumors believed to be caused by a genotoxic effect, which some, but by no means all, scientists believe have no threshold. For other types of tumors and for many nonneoplastic endpoints a threshold cannot be estimated directly from data at a limited number of dose levels a no observed effect level (NOEL) can be estimated by finding the highest dose level at which there is no significant increase in effects. 

A simple example might make this clearer. Suppose it were known that a 100 mg dose of chemical Z produced an extra 10% incidence of liver tumors in rats. Suppose further that we studied the pharmacokinetics of compound Z and discovered that, at the same 100 mg dose, 10 mg of the carcinogenic metabolite of Z was present in the liver. The usual regulatory default would instruct us to select the 100 mg dose as the point-of-departure for low dose extrapolation, and to draw a straight line to the origin, as in Figure 8.1. We are then further instructed to estimate the upper bound on risk at whatever dose humans are exposed to - let us say 1 mg. If the extra risk is 10% at 100 mg, then under the simple linear no-threshold model the extra risk at 1 mg should be 10% 100 = 0.1% (an extra risk of... 

For food allergens, validated animal models for dose-response assessment are not available and human studies (double-blind placebo-controlled food challenges [DBPCFCs]) are the standard way to establish thresholds. It is practically impossible to establish the real population thresholds this way. Such population threshold can be estimated, but this is associated with major statistical and other uncertainties of low dose-extrapolation and patient recruitment and selection. As a matter of fact, uncertainties are of such order of magnitude that a reliable estimate of population thresholds is currently not possible. The result of the dose-response assessment can also be described as a threshold distribution rather than a single population threshold. Such distribution can effectively be used in probabilistic modeling as a tool in quantitative risk assessment (see Section 15.2.5)... 

Once a dose metric is selected and estimated, a dose extrapolation model can be applied to estimate cancer risk. The choice of the model will be driven by the likely mechanism of action of the chemical or agent. For example, if the substance is a genotoxic material, such as radiation, a linear model would be used. A threshold model or nonlinear model might be used if the chemical or agent is not genotoxic (Paustenbach 2002 Williams and Paustenbach 2002). The general theory behind both models is discussed below. 

Quantitative risk assessment requires extrapolation from results of experimental assays conducted at high dose levels to predicted effects at lower dose levels which correspond to human exposures. The meaning of this high to low dose extrapolation within an animal species will be discussed, along with its inherent limitations. A number of commonly used mathematical models of dose-response necessary for this extrapolation, will be discussed. Other limitations in their ability to provide precise quantitative low dose risk estimates will also be discussed. These include the existence of thresholds incorporation of background, or spontaneous responses modification of the dose-response by pharmacokinetic processes. 

Hazard characterization is a quantitative or semi-quantitative evaluation of the nature, severity, and duration of adverse health effects associated with biological, physical, or chemical agents that may be present in food. The characterization depends on the nature of the toxic effect or hazard. Eor some hazards such as genotoxic chemicals, there may be no threshold for the effect and therefore estimates are made of the possible magnitude of the risk at human exposure level (dose-response extrapolation). 

This model tends to approach a zero probability rapidly at low doses (although it never reaches zero) and thus is compatible with the threshold hypothesis. Mantel and Bryan, in applying the model, recommend setting the slope parameter b equal to 1, since this appears to yield conservative results for most substances. Nevertheless, the slope of the fitted curve is extremely steep compared to other extrapolation methods, and it will generally yield lower risk estimates than any of the polynomial models as the dose approaches zero. 

My research eventually convinced me (and a great many others) that radon in homes is very much less harmful than the widely publicized estimates that were based on extrapolating from the number of excess cancers seen in uranium miners who had very high radon exposures. Those estimates were (and are) based on the assumption that the cancer risk from radiation is proportional to the dose, the so-called linear-no threshold theory (LNT). 

The extrapolation from high to low doses will depend on the type of primary toxic effect. If this is a carcinogenic effect, then a threshold normally cannot be assumed, and a mathematical model is used to estimate the risk at low doses (see above). If the primary toxic effect is noncarcinogenic, then it will normally be assumed that a threshold exists. 

The linearized multistage model (used by the EPA). This determines the cancer slope factor, which can be used to predict cancer risk at a specific dose. It assumes a linear extrapolation to a zero-dose threshold (Fig. 2.10). This factor is an estimate (expressed in mg/kg/day) of the probability that an individual will develop cancer if exposed to the chemical for 70 years. 

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. 

Based on inhalation data for agent GB, McNamara et al. (1973) calculated the no-effect dose for VX-indnced tremors in hnmans to be 0.34 g/kg. Carnes et al. (1986) suggested that the threshold for muscular tremors in sensitive snbpopnlations, such as infants, may be 0.16 g/kg. McNamara et al. (1973) estimated that the human LD50 and no-death levels for VX were 7.5 pg/kg and 0.94 g/kg, respectively. These estimates were based on extrapolations of LCtso data for GB. 

The existing methods available for scientifically defensible risk characterization are not yet ideal since each step has an associated uncertainty resulting from data limitation and incomplete knowledge on exact mechanism of action of the toxic chemical on the human body. For noncancer end points, safety factors or uncertainty factors are applied since these effects are assumed to have a threshold below which no adverse effect is expected to be observed. US EPA has used the concept of a reference concentration (RfC) to estimate acceptable daily human exposure from HAPs. The RfC was adapted for inhalation studies based on a reference dose (RfD) method previously used for oral exposure assessment. The derivation of the RfC differs from that for the RfD in the use of dosimetric adjustment to extrapolate the exposure concentration for animals to a human equivalent concentration. Both are estimates, with uncertainty spaiming perhaps an order of magnitude, of a daily exposure to the human population, including sensitive subgroups, which would be without appreciable risk of deleterious effects over a lifetime. 

The Cramer classification scheme can be used to make a threshold of toxicological concern (TTC) estimation. TTC is a concept that aims to establish a level of exposure for all chemicals below which there would be no appreciable risk to human health the threshold is based on a statistical analysis of the toxicological data from a broad range of different and/or structurally related chemicals and on the extrapolation of the underlying animal data to a no-effect dose considered to represent a negligible risk to human health. 

How the problems of selecting the appropriate animal result for dose—response extrapolation across species and of estimating the threshold dose for a broad human population are resolved in the risk assessment process will be explored in the next chapter. What has been covered here sets the stage for that discussion. 

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