for which the outcome can be considered abnormal. For example, a weight lower than 0.8 g might be considered abnormal for a teratology study in mice. Using the fitted model, one then calculates the dose-specific probability of falling into the abnormal region. The BMD is estimated as the dose corresponding to a specified increase in that probability, compared with the background probability. The BMDL is the corresponding 95% lower limit on that dose. Figure 7-1 illustrates the ideas behind the approach. The curve in the top panel represents the distribution of IQs in an unexposed population, and the curve in the lower panel has been shifted to the left in response to an exposure. Note that the mean IQ in the unexposed population is 100, and the standard deviation (SD) is 15. The shaded areas in the left tails of each distribution represent the proportion of the exposed and unexposed populations that fall below a specified cutoff point (we will refer to cutoff point as C), designated as the IQ level that indicates an adverse response. In Figure 7-1, we have used a value of C = 75, which represents the lower 5% of the control population. From the figure, it is easy to see that the further left we move the curve corresponding to the exposed group, the higher the percentage of the exposed population that falls below the cutoff point. Gaylor and Slikker's suggestion simply involves finding the exposure level that leads to a specific increase in the proportion of the population falling below the cutoff point. To be more precise, let Yi represent the outcome for the ith study subject, and suppose that a lowered outcome is considered to be adverse (e.g., as for IQ). Then, let P0 denote the probability that an unexposed individual falls below the value (C) that defines an adverse effect. The BMD is then defined as the dose, x, such that

Pr (Y < C | dose = x) − P0 = BMR,

where BMR denotes the “benchmark response” and refers to a specific risk increase above background risk. As in the quantal-response setting, BMR values of 0.1, 0.05, or possibly 0.01 are generally chosen. Later in the chapter, the committee focuses mostly on the case where P0 = 0.05 BMR = 10% of the children experiencing an adverse effect. Thus, these choices of P0 and BMR will result in a BMD that represents a doubling of the proportion of the population that falls into the adverse effect

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