A non-inferiority trial compares a test treatment to a control treatment of established effectiveness and seeks to show that the test treatment is not materially worse than or inferior to the control treatment. A non-inferiority trial seeks to show that any difference between the two treatments is small enough to allow a conclusion that the test treatment has at least some effect or, in many cases, an effect that is not significantly less than the active control. A non-inferiority trial may proceed under 21 CFR 50.24 if it meets the requirements of the regulation. 
For a non-inferiority trial to be informative, there would need to be clear data about the effectiveness of the control treatment (to make the non-inferiority study interpretable) and about known safety or other problems associated with the control treatment. Non-inferiority trials are generally used in situations where a placebo-controlled trial would be unethical and where there are no data to suggest the new treatment would be more effective than the standard treatment.