One Sided Bootstrap Tests

Bloch, Lai, and Tubert-Bitter (2001) consider alternatives of the form HA : Aim > A2m for some m and lim > A2m - £m for all m i.e., treatment 1 is superior to treatment 2 on at least one of the endpoints and all of the other endpoints for treatment 1 are noninferior to those of treatment 2.

They consider the intersection of the rejection region for the likelihood ratio test of H0 (Hotelling's T2) with the rejection region for the non-inferiority region (a set of univariate tests). They show that this results in a level a test and generate its bootstrap distribution. Because they are using the bootstrap, the normality assumption required by many of the other tests is not needed. Although numerically intense, this formulation is shown to have high power and type I error close to alpha under various distributions, such as a mixture of normals and a normal-exponential mixture.

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