<p>Randomized clinical trials are usually designed to test whether a new treatment is equivalent to a reference treatment. To establish assay sensitivity and constancy, if ethically justifiable and practically feasible, the equivalence may be assessed through a three-arm trial, consisting of a new treatment, an active reference treatment and a placebo. In this article, we consider three-arm trials with multinomial outcome variables. Based on a constrained bootstrap approach, we develop a novel test for assessing the equivalence of reference and new treatments. We show that the proposed test is asymptotically of level <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha\)</EquationSource> </InlineEquation> and is consistent. Simulation studies demonstrate that the proposed test can control type I errors well and detect the equivalence effectively with moderate sample sizes.</p>