Abstract
The Mann-Whitney-Wilcoxon test, often referred to as the Mann-Whitney U test or Wilcoxon rank-sum test, is a non-parametric statistical test used to compare two independent groups when the dependent variable is ordinal or continuous but not normally distributed. It's particularly useful for small sample sizes or when the assumptions of parametric tests, such as the t-test, are violated, including cases where the data is skewed. This study focuses on the Mann-Whitney-Wilcoxon test for ordinal data, which frequently arises in biomedical research when the proportional odds assumption does not hold. Currently, there are no optimal two-stage randomized clinical trial designs utilizing the Mann-Whitney-Wilcoxon test. To address this research gap, our study proposes optimal two-stage designs based on the Mann-Whitney-Wilcoxon test. We demonstrate the application of these designs through illustrative examples and evaluate their operating characteristics.