Biedermann, Stefanie, Dette, Holger and Zhu, Wei
Optimal designs for dose-response models with restricted design spaces.
Journal of the American Statistical Association, 101, (474), . (doi:10.1198/016214505000001087).
In dose-response studies, the dose range is often restricted due to concerns over drug toxicity and/or efficacy. We derive optimal designs for estimating the underlying dose-response curve for a restricted or unrestricted dose range with respect to a broad class of optimality criteria. The underlying curve belongs to a diversified set of link functions suitable for the dose
response studies and having a common canonical form. These
include the fundamental binary response models -- the logit and
the probit as well as the skewed versions of these models. Our methodology is based on a new geometric interpretation
of optimal designs with respect to Kiefer's $\Phi_p$-criteria in regression models with two parameters, which is of independent interest. It provides an intuitive illustration of
the number and locations of the support points of $\Phi_p$-optimal designs. Moreover, the geometric results generalize the classical characterization of $D$-optimal designs by the minimum covering ellipsoid [see Silvey (1972) or Sibson (1972)] to the class of Kiefer's $\Phi_p$-criteria. The results are
illustrated through the re-design of a dose ranging trial.
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