Some Properties of Non Inferiority Tests for Two Independent Probabilities

On the Importance in Clinical Trials That Critical Regions for Comparing 2 Independent Proportions Must Be Barnard Convex Sets

“…These results by Frick 9 and Almendra-Arao and Sotres-Ramos 10 are of theoretical interest. However, we argue that NI tests with critical regions that fail to fulfill at least one of the conditions of a Barnard convex set do not make sense in the context of clinical trials and are not of interest in this context, as shown later.…”

“…For critical regions that fulfill only one condition of the Barnard convex set definition, Frick 9 generalized the theorem by Röhmel and Mansmann 8 considering also NI exact tests. Almendra-Arao and Sotres-Ramos 10 similarly established a theorem that generalized Frick’s theorem to exact and asymptotic tests.…”

“…Notably, the well-known Blackwelder and Hauck-Anderson tests do not satisfy the Barnard convexity condition for many sample sizes; for example, see Almendra-Arao and Sotres-Ramos. 10 If the critical region is not a Barnard convex set, is there anything we can do? Do we merely discard the test?…”

“…Almendra-Arao 18 obtained reasonably manageable representations for the first 2 derivatives of the power function, and this research made the calculation of test sizes for NI/S testing viable with Newton’s method and produced a significant reduction in computation time. Almendra-Arao and Sotres-Ramos 10 have provided many instances in which the critical regions for the Blackwelder and the Hauck-Anderson NI tests are not Barnard convex sets.…”