Test Statistics and Confidence Intervals to Establish Noninferiority between Treatments with Ordinal Categorical Data

Abstract

The problem for establishing noninferiority is discussed between a new treatment and a standard (control) treatment with ordinal categorical data. A measure of treatment effect is used and a method of specifying noninferiority margin for the measure is provided. Two Z-type test statistics are proposed where the estimation of variance is constructed under the shifted null hypothesis using U-statistics. Furthermore, the confidence interval and the sample size formula are given based on the proposed test statistics. The proposed procedure is applied to a dataset from a clinical trial. A simulation study is conducted to compare the performance of the proposed test statistics with that of the existing ones, and the results show that the proposed test statistics are better in terms of the deviation from nominal level and the power.

Key Words:

• Noninferiority margin
• Shifted null hypothesis
• U-statistics
• Wilcoxon–Mann–Whitney test
• Z-type test.

ACKNOWLEDGEMENTS

The authors wish to thank the two referees and the editor for their valuable and useful comments leading to the improvement of the contents and presentation of the article.