Optimal designs for comparing curves
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Date
2015
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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 the-
orems, 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 ex-
amples 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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Keywords
similarity of regression curves, robust design, optimal design, confidence band