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 to a treatment effect. Their use is particularly effective in scenarios with small sample sizes and where robust prior information is actually 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. This parameter can be considered as either fixed or random. Although various strategies exist for its determination, eliciting the prior distribution of the weight parameter according to a full Bayesian approach remains a challenge. In general, this parameter should be carefully selected to accurately reflect the available prior information without dominating the posterior inferential conclusions. To this aim, we propose a novel method for eliciting the prior distribution of the weight parameter through a simulation-based calibrated Bayes factor procedure. This approach allows for the prior distribution to be updated based on the strength of evidence provided by the data: The goal is to facilitate the integration of historical data when it aligns 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.

翻译：在贝叶斯框架中，幂先验分布越来越多地被应用于临床试验及类似研究中，以整合外部及历史信息，通常用于为治疗效应相关的参数提供先验信息。该方法在小样本场景以及确实存在可靠先验信息的情况下尤为有效。该方法的一个关键组成部分是其权重参数，该参数控制着纳入当前分析的历史信息量。此参数可被视为固定值或随机变量。尽管存在多种确定该参数的策略，但根据完全贝叶斯方法来确定权重参数的先验分布仍是一个挑战。一般而言，应谨慎选择该参数，以准确反映可用的先验信息，同时避免主导后验推断结论。为此，我们提出了一种新方法，通过基于模拟的校准贝叶斯因子程序来确定权重参数的先验分布。该方法允许根据数据提供的证据强度更新先验分布：其目标是促进历史数据与当前信息一致时的整合，并在出现先验-数据冲突等差异时限制其影响。通过模拟研究测试了所提方法的性能，并将其应用于临床试验的真实数据。