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Issues in Risk Assessment (1993)

Chapter: 3.2 Range of Possible TD50 Values

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Suggested Citation:"3.2 Range of Possible TD50 Values." National Research Council. 1993. Issues in Risk Assessment. Washington, DC: The National Academies Press. doi: 10.17226/2078.
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correlation than the essentially linear one-stage model. The lowest correlation arises from the Weibull model. This is because, unlike the one-stage or multistage models, the Weibull model allows for supralinearity at low and moderate doses, and thus admits a greater range of TD50 values.

Crouch et al. (1987) commented on the absence of observations in the upper left and lower right triangular regions in scattergrams similar to those shown here in Figure 2. The absence of points in the upper left hand region is due to the lower limit on the number of tumors observed in the exposed groups in order to demonstrate a statistically significant increase in tumor occurrence. This implies that highly toxic chemicals of weak carcinogenic potency would likely go undetected in a standard bioassay, since such agents would not yield a measurable excess of tumors at the MTD. Crouch et al. (1987) attribute the absence of points in the lower right hand region to a lack of chemicals with extremely high potency relative to their MTDs. Reith & Starr (1989a) dispute this latter conclusion on the basis that experimental design constraints preclude the observation of potencies much larger than those shown in Figure 2. (This point is explored in greater detail in section 3.2 below.) Whether or not such "supercarcinogens" exist has been recently debated by the National Research Council (1992).

3.2 Range of Possible TD50Values

Bernstein et al. (1985) noted that TD50 values calculated from bioassay data vary within a limited range about the MDT as a function of the observed tumor response. To illustrate, suppose that the probability P(d) of a tumor occurring at dose d follows the one-stage model in (2.2), and the background tumor rate P(0) = 1 - e is known to be 0.10. Suppose further that 50 animals are exposed to a single dose D = MTD and that x of these animals develop the tumor of interest. Solving the equation

leads to the estimate

Suggested Citation:"3.2 Range of Possible TD50 Values." National Research Council. 1993. Issues in Risk Assessment. Washington, DC: The National Academies Press. doi: 10.17226/2078.
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The scientific basis, inference assumptions, regulatory uses, and research needs in risk assessment are considered in this two-part volume.

The first part, Use of Maximum Tolerated Dose in Animal Bioassays for Carcinogenicity, focuses on whether the maximum tolerated dose should continue to be used in carcinogenesis bioassays. The committee considers several options for modifying current bioassay procedures.

The second part, Two-Stage Models of Carcinogenesis, stems from efforts to identify improved means of cancer risk assessment that have resulted in the development of a mathematical dose-response model based on a paradigm for the biologic phenomena thought to be associated with carcinogenesis.

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