There is an increasing number of clinical trials conducted in recent years with the objective to show that a test therapy is equivalent in efficacy to a standard or reference therapy. In this paper we consider therapeutic equivalence clinical trials where the clinical endpoints are ordered categorical. Some statistical procedures based on the Wilcoxon statistic or a proportional odds model are introduced in this paper. These procedures are illustrated and compared through the data from an equivalence clinical trial. conducted by a generic drug company in support of its application for marketing the generic copy of a brand name drug. The sample size determinations based on asymptotic two one-sided tests procedure are also discussed in this paper.