Establishing Non-Inferiority of a New Treatment in a Three-Arm Trial: Apply a Step-Down Hierarchical Model in a Papulopustular Acne Study and an Oral Prophylactic Antibiotics Study

Abstract

Clinical trials comparing a test treatment with an active control therapy have become very popular in drug and medical device development in the last decade. An active controlled trial without a placebo, however, exhibits some major challenges in design, analysis, and interpretation, such as the determination of the non-inferiority margin or the assumption of constancy condition. When there are no ethical concerns, the comparison of a test drug with placebo usually provides the most convincing proof of the efficacy of a new treatment. Therefore, it may be advisable to conduct a three-arm trial — including placebo, active control, and the new treatment — if it is ethically justifiable such as a papulopustular acne study and an oral prophylactic antibiotics study. In this paper, we propose a statistical methodology for a three-arm non-inferiority trial with binary outcomes. We adapt the step-down hierarchical hypotheses and give a three-step testing procedure which is more realistic in conducting a clinical trial. We derived an optimal sample size allocation rule in an ethical and reliable manner to minimize the total sample size and hence to shorten the duration of the trials. Real examples from a papulopustular acne study and an oral prophylactic antibiotics study are used to demonstrate our methodology.