Equivalence of dose response curves

Abstract

This paper investigates the problem if the difference between two parametric models m₁,m₂ describing the relation between the response and covariates in two groups is of no practical significance, such that inference can be performed on the basis of the pooled sample. Statistical methodology is developed to test the hypotheses H₀ :d(m₁,m₂) ≥ ε versus H₁ : d(m₁,m₂) < ε of equivalence between the two regression curves m₁;m₂, where d denotes a metric measuring the distance between m₁ and m₂ and ε is a pre specified constant. Our approach is based on an estimate d(m̂₁,m̂₂)) of this distance and its asymptotic properties. 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 vector of parameters. The results are illustrated by means of a simulation study, and it is demonstrated that the new methods yield a substantial improvement with respect to power compared to all currently available tests for this problem.