# Equivalence of regression curves sharing common parameters

## TL;DR

This paper introduces a bootstrap test for comparing two regression curves sharing common parameters, demonstrating its effectiveness through theory, simulations, and a clinical trial example.

## Contribution

It develops a new bootstrap test for assessing the similarity of regression curves with shared parameters, improving power over traditional methods.

## Key findings

- Test controls level effectively
- Achieves higher power with shared parameters
- Validated through simulation and clinical trial example

## 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.