Efficient and easy-to-use sample size formulas in ratio-based non-inferiority tests

Abstract

In many biomedical applications, tests for the classical hypotheses based on the difference of treatment means in a one-way layout can be replaced by tests for ratios (or tests for relative changes). This approach is well noted for its simplicity in defining the margins, as for example in tests for non-inferiority. Here, we derive approximate and efficient sample size formulas in a multiple testing situation and then thoroughly investigate the relative performance of hypothesis testing based on the ratios of treatment means when compared with differences of means. The results will be illustrated with an example on simultaneous tests for non-inferiority.

Keywords:

• relative margin
• sample size
• multivariate t
• normal approximation

Acknowledgements

The authors thank the anonymous referee and the editor for providing valuable comments. We also thank Professor Ludwig A. Hothorn for discussions on an earlier version of the manuscript. We would like to express our sadness that our co-author Dr. Volker Guiard passed away while this manuscript was under review. We are indebted to him as our mentor, whom we valued as a very considerate, sociable and skillful person. This way, we want to thank him post hum for his collaboration and guidance throughout many years.

Additional information

Notes on contributors

Volker Guiard

Deceased