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June 2016 Optimal designs for comparing curves
Holger Dette, Kirsten Schorning
Ann. Statist. 44(3): 1103-1130 (June 2016). DOI: 10.1214/15-AOS1399

Abstract

We consider the optimal design problem for a comparison of two regression curves, which is used to establish the similarity between the dose response relationships of two groups. An optimal pair of designs minimizes the width of the confidence band for the difference between the two regression functions. Optimal design theory (equivalence theorems, efficiency bounds) is developed for this non-standard design problem and for some commonly used dose response models optimal designs are found explicitly. The results are illustrated in several examples modeling dose response relationships. It is demonstrated that the optimal pair of designs for the comparison of the regression curves is not the pair of the optimal designs for the individual models. In particular, it is shown that the use of the optimal designs proposed in this paper instead of commonly used “non-optimal” designs yields a reduction of the width of the confidence band by more than $50\%$.

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Holger Dette. Kirsten Schorning. "Optimal designs for comparing curves." Ann. Statist. 44 (3) 1103 - 1130, June 2016. https://doi.org/10.1214/15-AOS1399

Information

Received: 1 June 2015; Revised: 1 September 2015; Published: June 2016
First available in Project Euclid: 11 April 2016

zbMATH: 1338.62162
MathSciNet: MR3485955
Digital Object Identifier: 10.1214/15-AOS1399

Subjects:
Primary: 62K05

Keywords: Confidence band , optimal design , robust design , Similarity of regression curves

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 3 • June 2016
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