In the Bayesian framework power prior distributions are increasingly adopted in clinical trials
and similar studies to incorporate external and past information, typically to inform the parameter
associated with a treatment effect. Their use is particularly effective in scenarios with small sample
sizes and where robust prior information is available. A crucial component of this methodology
is represented by its weight parameter, which controls the volume of historical information
incorporated into the current analysis. Although this parameter can be modeled as either fixed
or random, eliciting its prior distribution via a full Bayesian approach remains challenging. In
general, this parameter should be carefully selected to accurately reflect the available historical
information without dominating the posterior inferential conclusions. A novel simulation-based
calibrated Bayes factor procedure is proposed to elicit the prior distribution of the weight
parameter, allowing it to be updated according to the strength of the evidence in the data.
The goal is to facilitate the integration of historical data when there is agreement with current
information and to limit it when discrepancies arise in terms, for instance, of prior-data conflicts.
The performance of the proposed method is tested through simulation studies and applied to real
data from clinical trials.
