Optimal design of the chronic animal bioassay

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Abstract
Optimal experimental designs for carcinogenicity bioassays conducted for the assessment of risks associated with exposure to environmental chemicals were derived. An optimal experimental design was a design that minimized the mean-squared error of the maximum likelihood estimate of the virtually safe dose from the Armitage-Doll multistage model and maintained a high power for the detection of increased carcinogenic response. Three and 4 dose designs (including control as 1 dose) were discussed for a variety of dose response patterns. Monte Carlo simulation techniques were used to estimate the power and mean-squared error for small samples sizes. Two forms of the multistage model were used to estimate the virtually safe edose: the linear model and the linear-quadratic model. The optimal designs for fitting the linear model used a control group and a group administered the maximum tolerated dose, with .apprx. 50% of the animals at each dose. The 3 and 4 dose optimal designs when fitting the linear-quadratic model were equivalent. After considering several biological issues, including overt toxicity, the optimal 4 dose designs were superior to the optimal 3 dose designs. An optimal 4 dose design would use 150-300 animals, with 50-60 animals in the control group, and 40-60 animals in the group administered a dose 10-30% of the maximum tolerated dose, and 2/3 of the remaining animals would be administered 50% of the maximum tolerated dose.

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