Dette, HolgerSchorning, Kirsten2015-10-122015-10-122015http://hdl.handle.net/2003/3427010.17877/DE290R-16347We 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%.enDiscussion Paper / SFB 823;40/2015similarity of regression curvesrobust designoptimal designconfidence band310330620working paper