Eliciting prior information from clinical trials via calibrated Bayes factor

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.