Equivalence of regression curves

Abstract

This talk investigates the problem whether the difference between two parametric models m1, m2 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 for testing the hypothesis H0: d(m1, m2) ? ? versus H1: d(m1, m2) < ? to demonstrate equivalence between the two regression curves m1, m2, where d denotes a metric measuring the distance between m1 and m2 and ? a pre-specified relevance margin. Our approach is based on the asymptotic properties of a suitable estimate d (,) 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 with a simulation study. It is demonstrated that the new methods substantially improve currently available approaches with respect to power.