  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.
