ABSTRACT
Each of the 23 target designs shown in Table 7 corresponds to the division of 50 animals among k = 3, 4, or 5 dose levels. The response probabilities corresponding to these doses are indicated by Q. For example, target design 20 consists of k = 5 dose levels, selected as the 10th, 30th, 50th, 70th, and 90th percentiles of the underlying dose-response distribution. Since the distribution parameters f30 and f31 are not known, f30 - 5 is arbitrarily set at 0 and f31 is arbitrarily set at 1 for purposes of comparing the target designs. The variable LI0DOSE corresponds to the common logarithm of the dose associated with the specified percentile for this standardized distribution. For each design two dose allocations are considered, an equal allocation and an unequal. The equal allocation places the same number of animals at each dose. The unequal allocation is specified by the variable N2. The rationale for the unequal allocation is that the expected number of nonresponders, N2(1 - Q/ 100), be constant at each dose in the design. For example, for design 20, N2(1 - Q/I00) = 2.7975 for all doses. This requires that larger numbers of animals be placed at the higher percentiles than at the lower and results in approximately equal coefficients of variation for estimation of each of the higher percentiles, no matter how far out in the upper tail they may be. Note that for planning purposes the sample sizes do not necessarily have to be integer valued; this is the case for the designs in Table 7.
