American Statistical Association New York City Metropolitan Area Chapter Mailman School of Public Health Columbia University Department of Biostatistics Colloquium

Equivalence trials are experiments which attempt to show that one intervention is not too much inferior to another on some quantitative scale. The cutoff value is commonly denoted as Delta. For example, one might wish to show that the hazard ratio of disease-free survival among patients given an experimental chemotherapy versus a currently approved regimen is Delta = 1.3 or less, especially if the former is thought to be less toxic than or otherwise advantageous over the latter.

Naturally, a lot of attention is given to choice of Delta. In addition to this, I assert that even more than in superiority clinical trials the _scale_ of Delta in equivalence trials must be carefully chosen. Since null hypotheses in superiority studies generally imply no effect, they are often identical or at least compatible when formulated on different scales. However, nonzero Deltas on one scale usually conflict with those on another. For example, the four hypotheses of arithmetic or multiplicative differences of either survival or hazard in general all mean different things unless Delta = 0 for differences or 1 for ratios. This can lead to problems in interpretation when the clinically natural scale is not a statistically convenient one.