Ratio of Means vs Difference of Means as Measures of Average Bioequivalence, Non-inferiority, and Superiority
Stella Grosser, FDA  *Wanjie Sun, FDA  Yi Tsong, US FDA CDER 

Keywords: average bioequivalence, non-inferiority, superiority, mean ratio, mean difference

Ratio of means and difference of means are often used for continuous data in an average bioequivalence (ABE), non-inferiority (NI), or superiority test to evaluate whether the test mean is equivalent , NI, or superior to the reference (active control or placebo) mean. Previous literature provided recommendations regarding how to choose between the two measures, mainly for superiority testing. In this paper, we evaluated the two measures from other perspectives focusing on the impact of different shifts (location, scale, or combined) in scoring systems on power of an ABE, NI, or superiority test for both measures. Conclusions: 1) For superiority, with the same margin, power remains the same if a location or scale or combined location and scale shift (not other transformations) is made to scoring systems for both measures; however, for NI and ABE, different shifts to scoring systems can change the power of the test significantly; 2) Direction of scores (larger or smaller value indicating desired effects) does not change power for mean difference for ABE, NI, or superiority, but it does change power for mean ratio, especially for NI and ABE. A larger value should be assigned to a better or desired effect. Otherwise, a study with a good active control (with a lower reference mean) would have a lower power to pass NI or ABE compared to a study with a bad active control but the same effect size. In summary, caution should be taken when choosing between the two measures especially for ABE and NI tests.