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，幂先验分布日益广泛应用于临床试验及类似研究，以整合外部及历史信息——通常用于处理与治疗效果相关的参数。该方法在样本量较小且实际存在可靠先验信息的场景中尤为有效。该方法的关键组成部分在于其权重参数，该参数控制着历史信息在当前分析中的纳入比例。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，但依据完全贝叶斯方法确定权重参数的先验分布仍具挑战性。一般而言，该参数需审慎选择，以精确反映可用先验信息，同时避免主导后验推断结论。为此，我们提出一种通过基于模拟的校准贝叶斯因子程序来确定权重参数先验分布的新方法。该方法允许根据数据提供的证据强度更新先验分布：其目标在于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。