Dose: extrapolation

There have been a number of recent survey articles and theoretical papers describing the available models for low-dose extrapolation. Through a literature review the most prominent models have been selected and discussed below. However, there are other models, less commonly used, that were not mentioned here for the sake of brevity. The models addressed below represent a good cross-section of the different features and capabilities that are pertinent to carcinogenic risk estimation. 

H.A. Guess and K.S. Crump. "Low Dose Extrapolation of Data from Animal Carcinogenicity Experiments - Analysis of a New Statistical Technique." Math. Biosciences, 32, 1976, pp. 15-36. 

Resmethrin (I) Likely to be carcinogenic to humans based on increased incidences of benign and malignant liver tumors in female rats and male mice. A low-dose extrapolation approach was applied to the experimental animal data in order to estimate human cancer risk [100]. No oncogenic effects were seen [101]. 

Several methods are available for developing OELs analogy, correlation, safety and uncertainty factors, and low-dose extrapolation (Table 14.5). The appropriate method must be selected on the basis of the appropriateness of the available data. For example, low-dose extrapolation may be appropriate only if sufficient pharmaco-... 

Trend Analysis, Low-Dose Extrapolation, and NOEL Estimation... 

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. 

Used to derive acute inhalation Minimal Risk Level (MRL) of 0.05 ppm (50 ppb) animal dose extrapolated to human dose according to method of EPA (1989d) values of blood/air partition coefficients assumed to be equal for animals and humans dose adjusted for 1 ess-than-continuous exposure (8 hours/24 hours), and divided by an uncertainty factor of 100 (10 for extrapolation from animals to humans, and 10 for human variability). 

These three commonly encountered problems in dealing with the dose-response step of the risk assessment process (and there are others as well) are respectively referred to as the problems of (1) high-to-low dose extrapolation (2) extrapolation across exposure durations ... 

Figure 8.1 Dose-response curves for carcinogens and illustration of low-dose extrapolation using linear, no-threshold model. Benchmark dose (BMD) is also illustrated.

So when this approach is used for carcinogens, it takes into account the no-threshold hypothesis (it predicts a risk at all exposures greater than zero), but there should be no pretense that we have arrived at an accurate prediction of risk. The LNT is the default used for carcinogens for low-dose extrapolation. 

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... 

High-low Dose Extrapolation. The Corley model was designed to facilitate extrapolations from high doses (similar to those used for chronic rodent studies) to low doses that humans may potentially be exposed to at home or in the workplace. 

High-low Dose Extrapolation. No high-low dose extrapolation was specifically addressed by the Gearhart model. 

High-low Dose Extrapolation. For tap-water concentrations below 100 mg/L, the model predicted a linear relationship between potential dose (i.e., amounts present in the drinking water, inhaled in a shower, or skin surface contact) and the cumulative metabolized dose. At tap-water concentrations greater than... 

The outcome of low-dose extrapolation is the resulting lifetime cancer risk associated with estimated exposure for a particular population. A wide range of models have been developed for low-dose extrapolation of animal data to calculate a tolerable intake for an acceptable risk, often set at one extra cancer per million exposed persons (see Section 6.2.4 for acceptable risk). 

In view of the considerable uncertainties in the extrapolation of results over several orders of magnitude, specification of risks in terms of predicted incidence or numbers of excess cancers per unit of the population implies a degree of precision that is considered misleading by some. Larsen (2006), e.g., noted that the model most often used in low-dose extrapolation is a linear extrapolation from the observable range, and the apparent precision of the calculations does not reflect the uncertainty in the risk estimate the results are therefore open to misinterpretation because the numerical estimates may be regarded as quantification of the actual risk. 

The most widely used of the many mathematical models proposed for extrapolation of carcinogenicity data from animal studies to low-dose human exposures (i.e., low-dose extrapolation) is the LMS model. This has, in effect, become the default approach for quantitative risk assessment and has been used by, e.g., the US-EPA for many years as well as by the WHO in relation to derivation of drinking-water guideline values for potential carcinogens (WHO 1996) (see Section 9.2.1.2 for drinking-water guideline values). 

The linear component of the LMS model, qi (i.e., one of the parameters of the polynomial), is approximately equivalent to the slope at low doses of the dose-response relationship between the tumor incidence and the dose. This linearity at low dose is a property of the formulation developed for the multistage model and is considered by proponents to be one of its important properties. This linear component of the polynomial, qi, is used to carry out low-dose extrapolation. The linear response at low doses is considered to be conservative with regard to risk, as the dose-response relationship at low doses may well be sublinear. Although supralinearity at low doses cannot be excluded, it is usually considered to be unlikely. 

According to WHO/IPCS (1999), any model that fits the empirical data well is likely to provide a reasonable estimation of the TD5. Choice of the model may not be critical since estimation is within the observed dose range, thereby avoiding the numerous uncertainties associated with low-dose extrapolation. 

Previously the LMS model (Section 6.2.1.2) was the most widely adopted approach for low-dose extrapolations for data from studies in experimental animals. More recently, an MOE approach has... 

In order to account for differences in metabolic rates between experimental animals and humans, a surface area to body weight correction (Section 5.3.2.2) is sometimes applied to quantitative estimates of cancer risk derived by low-dose extrapolation. The WHO stated that incorporation of this factor increases the risk by approximately one order of magnitude, depending on the species upon which the estimate is based, and increases the risk estimated on the basis of studies in mice relative to that in rats. The WHO considered incorporation of this factor to be overly conservative, particularly in view of the fact that linear extrapolation more likely overestimates risk at low doses. Therefore, the guideline values for carcinogens were developed on the basis of quantitative estimates of risk that were not corrected for the ratio of surface area to body weight. 

The major change from the previous guidelines in terms of the quantitative risk assessment is that the LMS model no longer is the recommended default approach for low-dose extrapolation. Instead, an MOE approach is recommended based on curve fitting within the range of observation with extrapolation from a UED (the 95% lower confidence limit on a dose associated with an extra tumor risk) chosen to be representative of the lower end of the observed range. 

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. 

Radiation-induced genomic instability and bystander effects are now well-established consequences of exposure of living cells to ionizing radiation. Cells not directly traversed by radiation may still exhibit radiation effects. This phenomenon, known as bystander effect, has become a major activity in radiation biology and in some cases has challenged the conventional wisdom. An example is the currently accepted models used for low-dose extrapolation of radiation risks. The currently used models assume that cells in an irradiated population respond individually rather than collectively. If bystander effects have implications for health risks estimates from exposure to ionizing radiation, then the question of whether this is a general phenomenon or solely a characteristic of a particular type of cell and the radiation under test becomes an important issue. 

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