  We consider two problems that are attracting increasing attention in clinical
dose finding studies. First, we assess the similarity of two non-linear
regression models for two non-overlapping subgroups of patients over a
restricted covariate space. To this end, we derive a confidence interval for
the maximum difference between the two given models. If this confidence
interval excludes the equivalence margins, similarity of dose response can be
claimed. Second, we address the problem of demonstrating the similarity of two
target doses for two non-overlapping subgroups, using again a confidence
interval based approach. We illustrate the proposed methods with a real case
study and investigate their operating characteristics (coverage probabilities,
Type I error rates, power) via simulation.
