What to make of non-inferiority and equivalence testing with a post-specified margin?
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In order to determine whether or not an effect is absent based on a statistical test, the recommended frequentist tool is the equivalence test. Typically, it is expected that an appropriate equivalence margin has been specified before any data is observed. Unfortunately, this can be a difficult task. If the margin is too small, then the test's power will be substantially reduced. If the margin is too large, any claims of equivalence or non-inferiority will be meaningless. Moreover, it remains unclear how defining the margin afterwards will bias one's results. In this short article, we consider a series of hypothetical scenarios in which the margin is defined post-hoc or is otherwise considered controversial. We also review a number of relevant, potentially problematic actual studies from health research, with the aim of motivating a critical discussion as to what is acceptable and desirable in the reporting and interpretation of equivalence tests.
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