Optimal design of the chronic animal bioassay

Optimal experimental designs for carcinogenicity bioassays conducted for the assessment of risks associated with exposure to environmental chemicals are derived. For our purposes, an optimal experimental design is a design that minimizes the mean-squared error of the maximum likelihood estimate of the virtually safe dose from the Armitage-Doll multistage model and maintains a high power for the detection of increased carcinogenic response. Three- and four-dose designs (including control as one of the doses) are discussed for a variety of dose response patterns. Monte Carlo simulation techniques are used to estimate the power and mean-squared error for small samples sizes. Two forms of the multistage model are used to estimate the virtually safe dose: 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 about 50% of the animals at each dose. The three- and four-dose optimal designs when fitting the linear-quadratic model were found to be equivalent. However, after considering several biological issues, including overt toxicity, the optimal four-dose designs would use between 150 and 300 animals, with 50 to 60 animals in the control group, and 40 to 60 animals in the group administered the maximum tolerated dose. One-third of the remaining animals would be administered a dose between 10 and 30% of the maximum tolerated dose, and two-thirds of the remaining animals would be administered 50% of the maximum tolerated dose.