The Annals of Statistics

Optimal designs for comparing curves

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 $50\%$.

Article information

Source
Ann. Statist., Volume 44, Number 3 (2016), 1103-1130.

Dates
Revised: September 2015
First available in Project Euclid: 11 April 2016

https://projecteuclid.org/euclid.aos/1460381688

Digital Object Identifier
doi:10.1214/15-AOS1399

Mathematical Reviews number (MathSciNet)
MR3485955

Zentralblatt MATH identifier
1338.62162

Subjects
Primary: 62K05: Optimal designs

Citation

Dette, Holger; Schorning, Kirsten. Optimal designs for comparing curves. Ann. Statist. 44 (2016), no. 3, 1103--1130. doi:10.1214/15-AOS1399. https://projecteuclid.org/euclid.aos/1460381688

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