Equivalence of regression curves sharing common parameters

Kathrin Möllenhoff (Corresponding author), Frank Bretz, Holger Dette

Research output: Contribution to journalArticleAcademicpeer-review

4 Citations (Scopus)


In clinical trials, the comparison of two different populations is a common problem. Nonlinear (parametric) regression models are commonly used to describe the relationship between covariates, such as concentration or dose, and a response variable in the two groups. In some situations, it is reasonable to assume some model parameters to be the same, for instance, the placebo effect or the maximum treatment effect. In this paper, we develop a (parametric) bootstrap test to establish the similarity of two regression curves sharing some common parameters. We show by theoretical arguments and by means of a simulation study that the new test controls its significance level and achieves a reasonable power. Moreover, it is demonstrated that under the assumption of common parameters, a considerably more powerful test can be constructed compared with the test that does not use this assumption. Finally, we illustrate the potential applications of the new methodology by a clinical trial example.

Original languageEnglish
Pages (from-to)518-529
Number of pages12
Issue number2
Publication statusPublished - Jun 2020
Externally publishedYes

Bibliographical note

© 2019 The Authors. Biometrics published by Wiley Periodicals, Inc. on behalf of International Biometric Society.


  • dose-finding studies
  • equivalence testing
  • nonlinear regression
  • parametric bootstrap
  • similarity of regression curves


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