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Equivalence of regression curves sharing common parameters

Author

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  • Kathrin Möllenhoff
  • Frank Bretz
  • Holger Dette

Abstract

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.

Suggested Citation

  • Kathrin Möllenhoff & Frank Bretz & Holger Dette, 2020. "Equivalence of regression curves sharing common parameters," Biometrics, The International Biometric Society, vol. 76(2), pages 518-529, June.
    • Handle: RePEc:bla:biomet:v:76:y:2020:i:2:p:518-529
    DOI: 10.1111/biom.13149
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    References listed on IDEAS

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    1. Long Feng & Changliang Zou & Zhaojun Wang & Lixing Zhu, 2015. "Robust comparison of regression curves," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 185-204, March.
    2. W. Liu & F. Bretz & A. J. Hayter & H. P. Wynn, 2009. "Assessing Nonsuperiority, Noninferiority, or Equivalence When Comparing Two Regression Models Over a Restricted Covariate Region," Biometrics, The International Biometric Society, vol. 65(4), pages 1279-1287, December.
    3. Holger Dette & Kathrin Möllenhoff & Stanislav Volgushev & Frank Bretz, 2018. "Equivalence of Regression Curves," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 711-729, April.
    4. F. Bretz & J. C. Pinheiro & M. Branson, 2005. "Combining Multiple Comparisons and Modeling Techniques in Dose-Response Studies," Biometrics, The International Biometric Society, vol. 61(3), pages 738-748, September.
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