TY - JOUR

T1 - Constructing tests to compare two proportions whose critical regions guarantee to be Barnard convex sets

AU - Almendra-Arao, Félix

AU - Castro-Alva, José Juan

AU - Reyes-Cervantes, Hortensia

PY - 2016/12/1

Y1 - 2016/12/1

N2 - © 2016 Elsevier B.V. In both statistical non-inferiority (NI) and superiority (S) tests, the critical region must be a Barnard convex set for two main reasons. One, being computational in nature, based on the fact that calculating test sizes is a computationally intensive problem due to the presence of a nuisance parameter. However, this calculation is considerably reduced when the critical region is a Barnard convex set. The other reason is that in order for the NI/S statistical tests to make sense, its critical regions must be Barnard convex sets. While it is indeed possible for NI/S tests’ critical regions to not be Barnard convex sets, for the reasons stated above, it is desirable that they are. Therefore, it is important to generate, from a given NI/S test, a test which guarantees that the critical regions are Barnard convex sets. We propose a method by which, from a given NI/S test, we construct another NI/S test, ensuring that the critical regions corresponding to the modified test are Barnard convex sets, we illustrate this through examples. This work is theoretical because the type of developments refers to the general framework of NI/S testing for two independent binomial proportions and it is applied because statistical tests that do not ensure that their critical regions are Barnard convex sets may appear in practice, particularly in the clinical trials area.

AB - © 2016 Elsevier B.V. In both statistical non-inferiority (NI) and superiority (S) tests, the critical region must be a Barnard convex set for two main reasons. One, being computational in nature, based on the fact that calculating test sizes is a computationally intensive problem due to the presence of a nuisance parameter. However, this calculation is considerably reduced when the critical region is a Barnard convex set. The other reason is that in order for the NI/S statistical tests to make sense, its critical regions must be Barnard convex sets. While it is indeed possible for NI/S tests’ critical regions to not be Barnard convex sets, for the reasons stated above, it is desirable that they are. Therefore, it is important to generate, from a given NI/S test, a test which guarantees that the critical regions are Barnard convex sets. We propose a method by which, from a given NI/S test, we construct another NI/S test, ensuring that the critical regions corresponding to the modified test are Barnard convex sets, we illustrate this through examples. This work is theoretical because the type of developments refers to the general framework of NI/S testing for two independent binomial proportions and it is applied because statistical tests that do not ensure that their critical regions are Barnard convex sets may appear in practice, particularly in the clinical trials area.

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U2 - 10.1016/j.stamet.2016.08.005

DO - 10.1016/j.stamet.2016.08.005

M3 - Article

SP - 160

EP - 171

JO - Statistical Methodology

JF - Statistical Methodology

SN - 1572-3127

ER -