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Robustness of design in dose-response studies. (English) Zbl 1411.62323
Summary: We construct experimental designs for dose-response studies. The designs are robust against possibly misspecified link functions; for this they minimize the maximum mean-squared error of the estimated dose required to attain a response in 100\(p\)% of the target population. Here \(p\) might be one particular value – \(p=0.5\) corresponds to \(\mathrm{ED}_{50}\)-estimation – or it might range over an interval of values of interest. The maximum of the mean-squared error is evaluated over a Kolmogorov neighbourhood of the fitted link. Both the maximum and the minimum must be evaluated numerically; the former is carried out by quadratic programming and the latter by simulated annealing.

MSC:
62P10 Applications of statistics to biology and medical sciences; meta analysis
62K05 Optimal statistical designs
62F12 Asymptotic properties of parametric estimators
62G20 Asymptotic properties of nonparametric inference
62G35 Nonparametric robustness
62J12 Generalized linear models (logistic models)
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