Equivalence of regression curves sharing common parameters
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Date
2019
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Abstract
In clinical trials the comparison of two different populations is a frequently addressed
problem. Non-linear (parametric) regression models are commonly used to
describe the relationship between covariates as the 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 level and
achieves a reasonable power. Moreover, it is demonstrated that under the assumption
of common parameters a considerable more powerful test can be constructed compared
to the test which does not use this assumption. Finally, we illustrate potential
applications of the new methodology by a clinical trial example.
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Keywords
similarity of regression curves, dose finding studies, nonlinear regression, parametric bootstrap, equivalence testing