Rank-based methods for assessing equivalence/non-inferiority with assay sensitivity in a three-arm trial with ordinal endpoints

Various approaches have been developed to assess equivalence/non-inferiority with assay sensitivity in a three-arm trial with continuous or discrete endpoints. However, there is little work done on ordinal endpoints. Ordinal data do not have metric information, the method for analyzing metric endpoints can systematically lead to errors for ordinal observations. The win probability that a subject receiving one treatment achieves a better outcome (or "wins" against) compared to a subject receiving the other treatment, is developed to quantify the treatment effect. In this article, the equivalence/non-inferiority with assay sensitivity in a three-arm trial are assessed by the win probabilities from the perspective of simultaneous confidence intervals (SCIs). The proposed methods can be applied to studies with ordinal or continuous outcomes without making parametric assumptions. Empirical results show that the Fisher-z transformation-based SCI, the method of variance estimates recovery SCIs combing with logit transformation, logit with arcsinh transformation confidence limits perform well in the sense that their empirical coverage probabilities are pretty close to the nominal confidence level. Sample size determination for achieving the pre-specified power is also investigated according to the duality of hypothesis testing and interval estimation. An example taken from the study of prophylaxis of postoperative nausea and vomiting is used to illustrate the proposed methods.