Robust incorporation of historical information with known type I error rate inflation

Bayesian clinical trials can benefit of available historical information through the elicitation of informative prior distributions. Concerns are however often raised about the potential for prior-data conflict and the impact of Bayes test decisions on frequentist operating characteristics, with particular attention being assigned to inflation of type I error rates. This motivates the development of principled borrowing mechanisms, that strike a balance between frequentist and Bayesian decisions. Ideally, the trust assigned to historical information defines the degree of robustness to prior-data conflict one is willing to sacrifice. However, such relationship is often not directly available when explicitly considering inflation of type I error rates. We build on available literature relating frequentist and Bayesian test decisions, and investigate a rationale for inflation of type I error rate which explicitly and linearly relates the amount of borrowing and the amount of type I error rate inflation in one-arm studies. A novel dynamic borrowing mechanism tailored to hypothesis testing is additionally proposed. We show that, while dynamic borrowing prevents the possibility to obtain a simple closed form type I error rate computation, an explicit upper bound can still be enforced. Connections with the robust mixture prior approach, particularly in relation to the choice of the mixture weight and robust component, are made. Simulations are performed to show the properties of the approach for normal and binomial outcomes.