FIGURE 7-1 Hypothetical IQ distribution in an exposed and unexposed population.

region. Two broad approaches are available for BMD calculations that are based on continuous outcomes. As described above, one option is to fix P0 at a specified percentile of performance in the unexposed population (e.g., 0.05 or 0.10). Assuming that the data follow a linear model (Yi = a0 + a1X i + εi, where X i represents the exposure level for the ith subject, a0 and a1 are unknown regression coefficients, and εi is random error, assumed to be normally distributed with variance σ2), specifying a fixed P0 is equivalent to setting the cutoff value at a specified number of SDs below the mean in the unexposed group:

C = a0 + σΦ-1 (P0),

where Φ (×) represents the normal cumulative distribution function (i.e., the area under a standard normal curve up to and including the value ×). When P0 = 0.05, for example, the value of C is a0 −1.645 σ (i.e., 1.64 SDs below the control mean). Alternatively, one can choose the cutoff

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