Optimal designs for comparing curves

TL;DR

This paper develops optimal design strategies for comparing two regression curves, significantly reducing confidence band width and improving the accuracy of dose response relationship comparisons.

Contribution

It introduces a novel optimal design framework for comparing two regression curves, including explicit solutions for common dose response models.

Findings

Optimal designs reduce confidence band width by over 50%.

Explicit solutions are provided for standard dose response models.

Optimal comparison designs differ from individual model optimal designs.

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%.