A fiducial test for assessing the non-inferiority of odds ratio in matched-pairs design

The non-inferiority of odds ratio in a matched-pairs design is a common question in medical research, and several different approaches are available to answer it. However, their performance is not always satisfactory. Some of the traditional approaches, such as the delta test and score test, do not perform well unless the sample size is large. The simulated significance level of the inferential model (IM) test is conservative, and its power is lower than that of the other tests. The results of the randomized IM test are satisfactory; however, since it is based on which is randomly generated, the plausibility function is not fixed. This paper describes a fiducial test that is based on Fisher's fiducial argument. Our simulation studies illustrated that the fiducial test can control Type I error, and its power appears to be very close to that of the score test. All of the test procedures are illustrated with a real example.