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

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.