An IM-based efficient test for non inferiority of the odds ratio between two independent binomial proportions

In drug development, non inferiority tests are often employed to determine the odds ratio between two independent binomial proportions. Some traditional test statistics for non inferiority based on different statistical schools of thought are available, but they can produce markedly different behaviors. Cornfield's exact conditional test is criticized for its conservativeness, while the Wald and score tests may be applicable for large samples but tend to be liberal with small samples. Although the mid-p value method has recently gained wide acceptance for its better behavior than those of other tests, it has almost no solid theoretical foundation attached to it. In the view of the fiducial school of thought, the fiducial test based on Fisher's fiducial argument also tends to perform unsatisfactorily for small samples. In this paper, we suggest an IM-based efficient test using the randomized plausibility function based on the Inferential Model. We prove that our new method is not only valid but also efficient, i.e., it maintains a nominal type I error rate, and we show, via simulations, that the proposed test also has satisfactory power when compared with those of other competing tests. A numerical example illustrates the proposed method.