Equivalence of dose response curves

TL;DR

This paper develops statistical tests to determine whether two regression curves are practically equivalent, enabling pooled analysis, with improved accuracy and power through bootstrap methods, supported by simulations and real data examples.

Contribution

It introduces a novel bootstrap-based testing methodology for equivalence of dose-response curves, addressing small sample issues and improving upon existing methods.

Findings

Bootstrap test improves power over existing methods.

Method accurately controls the nominal level in simulations.

Application to real data demonstrates practical utility.

Abstract

This paper investigates the problem whether the difference between two parametric models $m_1,m_2$ describing the relation between a response variable and several covariates in two different groups is practically irrelevant, such that inference can be performed on the basis of the pooled sample. Statistical methodology is developed to test the hypotheses $H_0 : d(m_1,m_2)\geq \epsilon$ versus $H_1 : d(m_1,m_2) < \epsilon$ to demonstrate equivalence between the two regression curves $m_1,m_2$ for a pre-specified threshold $\epsilon$, where $d$ denotes a distance measuring the distance between $m_1$ and $m_2$. Our approach is based on the asymptotic properties of a suitable estimator $d(\hat{m}_1; \hat{m}_2)$ of this distance. In order to improve the approximation of the nominal level for small sample sizes a bootstrap test is developed, which addresses the specific form of the interval hypotheses. In particular, data has to be generated under the null hypothesis, which implicitly defines a manifold for the parameter vector. The results are illustrated by means of a simulation study and a data example. It is demonstrated that the new methods substantially improve currently available approaches with respect to power and approximation of the nominal level.