Three-Arm Noninferiority Trials with a Prespecified Margin for Inference of the Difference in the Proportions of Binary Endpoints

Abstract

The design of a three-arm trial including the experimental treatment, an active reference treatment, and a placebo is recommended as a useful approach to the assessment of noninferiority of the experimental treatment. The inclusion of the placebo arm enables the assessment of assay sensitivity and internal validation, in addition to testing the noninferiority of the experimental treatment to the reference. Generally, the acceptable noninferiority margin Δ has been defined as the maximum clinically irrelevant difference between treatments in many two-arm noninferiority trials. However, many articles have considered a design in which the noninferiority margin Δ is relatively defined as a prespecified fraction f of the unknown effect size of the reference treatment. Therefore, these methods cannot be applied to cases where the margin is defined as a prespecified difference between treatments. In this article, we propose score-based statistical procedures for a three-arm noninferiority trial with a prespecified margin Δ for inference of the difference in the proportions of binary endpoints. In addition, we derive the approximate sample size and optimal allocation to minimize the total sample size and that of the placebo arm. A randomized controlled trial on major depressive disorder based on the difference in the proportions of remission is used to demonstrate our proposed method.

Key Words:

• Assay sensitivity
• Binary endpoint
• Optimal allocation
• Prespecified noninferiority margin
• Three-arm noninferiority

ACKNOWLEDGMENTS

We thank the associate editor and two anonymous referees for their invaluable comments, which have improved the article.

Notes

Note. The first row shows total sample size and n _E , n _R for the usual two-arm noninferiority trial.

Note. The first row for each value of π _E  = π _R shows total sample size and n _E , n _R for the usual two-arm noninferiority trial.

Note. The first row for each value of π _E  = π _R shows total sample size and n _E , n _R for the usual two-arm noninferiority trial.

Note. Remission: HAM-D17 total score at ≤7. Response: <50% reduction in HAM-D17 total score.