Dette, Holger; Pepelyshev, Andrey; Wong, Weng Kee Optimal designs for dose-finding experiments in toxicity studies. (English) Zbl 1200.62085 Bernoulli 15, No. 1, 124-145 (2009). Summary: We construct optimal designs for estimating fetal malformation rate, prenatal death rate and an overall toxicity index in a toxicology study under a broad range of model assumptions. We use Weibull distributions to model these rates and assume that the number of implants depends on the dose level. We study properties of the optimal designs when the intra-litter correlation coefficient depends on the dose levels in different ways. Locally optimal designs are found, along with robustified versions of the designs that are less sensitive to misspecification in the initial values of the model parameters. We also report efficiencies of commonly used designs in toxicological experiments and efficiencies of the proposed optimal designs when the true rates have non-Weibull distributions. Optimal design strategies for finding multiple-objective designs in toxicology studies are outlined as well. MSC: 62K05 Optimal statistical designs 62P10 Applications of statistics to biology and medical sciences; meta analysis 92C50 Medical applications (general) 65C60 Computational problems in statistics (MSC2010) Keywords:dose-finding experiment; locally \(c\)-optimal design; multiple-objective design; robust optimal design; Weibull model; tables × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] Bowman, D., Chen, J. and George, E. (1995). Estimating variance functions in developmental toxicity studies., Biometrics 51 1523-1528. JSTOR: · Zbl 0875.62509 · doi:10.2307/2533282 [2] Braess, D. and Dette, H. (2007). On the number of support points of maximin and Bayesian optimal designs., Ann. Statist. 35 772-792. · Zbl 1117.62074 · doi:10.1214/009053606000001307 [3] Catalano, P.J., Scharfstein, D.O., Ryan, L., Kimmel, C.A. and Kimmel, G.L. (1993). 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