Self-Adapting Priors for Dynamic Borrowing in Three-Arm Non-Inferiority Trials With Pre-Specified Margin

Non-inferiority trials play a central role in clinical research by demonstrating that an experimental treatment is not unacceptably worse than an established reference treatment when superiority is unlikely, but the new treatment offers other advantages, such as reduced toxicity, easier administration, lower cost, or improved adherence. These trials are typically designed as active control studies, making historical data from previous clinical trials or real-world evidence readily available. A key challenge, however, is how to appropriately incorporate multiple heterogeneous historical datasets into the design and analysis of a non-inferiority trial, as each source may differ in relevance, quality, and similarity to the current study. Moreover, a conventional two-arm non-inferiority trial lacks a placebo or standard of care control, requiring the reference treatment effect to be justified using external evidence. When ethically and practically feasible, including a placebo arm allows assessment of assay sensitivity and provides internal validation of the reference treatment effect, thereby strengthening the credibility of the non-inferiority conclusion. In this article, we propose two novel Bayesian self-adapting priors, the Additive Self-Adapting Mixture (ASAM) prior and the Cumulative Self-Adapting Product (CSAP) prior, to incorporate information from multiple historical reference and placebo studies in three-arm non-inferiority trials. The ASAM prior constructs study-specific priors and combines them through an adaptively weighted mixture, whereas the CSAP prior uses a cumulative product formulation with adaptive study-specific weights. Both approaches dynamically borrow information by assigning greater weight to historical studies that are more compatible with the current trial while down-weighting less comparable studies, thereby mitigating the impact of between-study heterogeneity. Extensive simulation studies demonstrate that the proposed methods maintain appropriate control of the Type I error rate while achieving substantial gains in statistical power, providing a flexible and robust framework for Bayesian analysis of three-arm non-inferiority trials.