Advances and Applications in Statistics
Volume 51, Issue 5, Pages 351 - 366
(November 2017) http://dx.doi.org/10.17654/AS051050351 |
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ASSESSING TEST SIZES FOR THE FARRINGTON-MANNING TEST
Félix Almendra-Arao and David Sotres-Ramos
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Abstract: Non-inferiority tests are frequently used in clinical trials to demonstrate that a new treatment (with minimum side effects or low cost) is not significantly inferior in efficacy to the gold standard treatment. The Farrington-Manning asymptotical test is a well known testing procedure for testing non-inferiority for two independent binomial proportions and it has been studied by several authors. It is believed that the test sizes of this test have good behaviour, and it is also believed that the exact test is too conservative; however, there are no studies calculating the exact test sizes for this test, only rough calculations have been performed. The goal of this work is to study the behaviour of the test sizes of the Farrington-Manning exact and asymptotical tests. The behaviour of the test sizes for the asymptotical test with a certain continuity correction is also analyzed. The conclusion is that the behaviour of the test sizes of the exact test is much better than the corresponding behaviour of the asymptotic tests. To show the use of the FM exact test, an example is analyzed that allows one to obtain very strong conclusions for the analyzed data which shows the great usefulness of the test in practice. |
Keywords and phrases: non-inferiority, proportion, exact test, asymptotic test, margin. |
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