Non-inferiority test based on transformations for non-normal distributions

Non-inferiority trials are becoming very popular for comparative effectiveness research. These trials are required to show that the effect of an experimental treatment is not worse than that of a reference treatment by more than a specified margin. Hence non-inferiority trials are of great importance, when superiority cannot be claimed. A three-arm non-inferiority trial consists of a placebo, a reference treatment, and an experimental treatment is considered. However unlike the traditional choices, it is assumed that the distributions of the end points corresponding to these treatments are unknown and suggested test procedures for a three-arm non-inferiority trial based on monotone transformations in conjunction with a normal approximation. The resulting test procedures are flexible and robust. Theoretical properties of the proposed methods are also investigated. The performance of the suggested test procedures is compared to their counterparts using simulations. In terms of type I error and power, the proposed methods perform better than their counterparts in most cases. The usefulness of the proposed methods is further illustrated through an example.