In the Bayesian framework, the power priors have been increasingly used in the context
of the analysis of clinical trials and similar studies to incorporate external and past information, usually into the prior distribution of some treatment effect. Their use has been shown to be particularly effective in small sample size scenarios and when strong prior information is available. In a fully Bayesian approach, eliciting the initial distribution of the weight parameter controlling the amount of historical information remains a challenge, since it must be carefully chosen to reflect the available prior information accurately and not dominate the posterior inferential conclusions. We propose a novel preliminary method for eliciting the distribution of the weight parameter based on the Bayes factor, which allows the prior distribution will be updated based on the strength of the evidence the data provides.
