Doseresponse Modeling

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The goal of dose-response modeling is to make a quantitative evaluation of the incidence of an adverse effect (such as cancer or systemic toxicity) that would be expected in a human population as a result of exposure to a particular amount of an environmental contaminant. From the perspective of scientific accuracy, this quantitative evaluation would ideally be based on evidence of adverse health effects arising from similar conditions of exposure and would be summarized in a mathematical relationship that expressed the fractional response of a population as a function of the dose received by that population. However, environmental exposures to chemical and radiological contaminants are often over long periods at low dose rates. Direct data on human health impacts are extremely limited for such exposures, since the effects may be statistically indistinguishable from the natural variability of the effect. Consequently, the quantitative estimation of human health effects due to environmental exposures usually requires two critical (and often controversial) extrapolations. If reliable data on health effects in human populations are not available from adequate epidemiological studies, dose-response relationships for humans must be inferred from animal studies, with the implicit assumption that animals are adequate models of human toxicological response. For stochastic responses, particularly those that have very low or nonexistent thresholds, a second extrapolation is required, which is potentially even more problematic. This is the extrapolation of effects at very high doses or dose rates to the very low doses or dose rates characteristic of environmental exposures.

Many dose-response analyses lack a firm foundation in biologically based models. The models that do exist are often highly simplified abstractions of the actual physiological processes involved in contaminant toxicity. In practice, such considerations dictate that effects be extrapolated from tests with similar durations and routes of exposure. If the dose rates or routes of contaminant exposure are substantially different from those used to develop dose-response data, the data must either be adjusted to reflect the changed conditions of exposure or the risk estimates must reflect the uncertainties associated with the extrapolation.

262 DOSE-RESPONSE AND RISK CHARACTERIZATION 11.4.1 Animal-to-Human Extrapolation

Due to the large differences in size between humans and test animals, a given mass of contaminant does not have the same effect in humans as it does in animals. This is because the response is typically proportional to the concentration of a contaminant in a target tissue, not to the total amount of the contaminant in the organism. This necessitates the adjustment of the doses administered to laboratory animals to an equivalent human dose. The equivalent human dose is the dose that yields the same level of effect in human populations as that in animal populations. The methods that can be used to infer an equivalent human dose from an animal dose range from simple scaling laws to pharmacokinetic models that explicitly model the metabolism of the substance. If sufficient data are available, a pharmacokinetic model is the preferred method for scaling between humans and animal doses. These models are capable of providing a more accurate estimate of the equivalent human dose by determining the administered dose necessary to produce the same effective dose at the target organ in the test species and in humans.

Frequently, however, such models do not exist. In these cases, there are a variety of simple scaling relationships available for inferring equivalent human doses from animal doses, although there is considerable debate as to which relationship is most generally appropriate. The simplest relationship is based on body weight scaling. Early studies indicated that the LD50 was approximately equal in humans and animals when the mass of contaminant taken into the body was divided by the body weight. This observation led to the traditional chemical dose unit of mass of contaminant per unit body weight (BW), which is typically expressed in units of mg/kg (Dedrick 1973; Rhomberg and Wolff 1998). However, this relationship does not always hold true. The LD50 values are frequently found to be more nearly equal among species when a relationship based on body surface area is used. A mass scaled dose (in mg/kg) can be converted to a surface area scaled dose by noting that surface area is proportional to BW2/3. Another simple scaling relationship endorsed by the U.S. EPA is based on relative metabolic rate, which is proportional to BW3/4 (EPA 1992a). These relationships are reflected in the following general expression for estimating the equivalent human daily dose (Dhuman) corresponding to an animal daily dose (Danimal):

where BW is the body weight in kilograms, D the dose in mg/(kg • d), and n the scaling factor. For surface area scaling, n = 1/3; for metabolic rate scaling, n = 1/4. These simple scaling relationships can be seen as highly simplified models of contaminant metabolism that are based on simple assumptions (e.g., that the most relevant physiological parameters are relative metabolic rates or surface areas of exchange boundaries) and require only readily available data (e.g., body weight).

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