With the robust uptick in the applications of Bayesian external data borrowing, eliciting a prior distribution with the proper amount of information becomes increasingly critical. The prior effective sample size (ESS) is an intuitive and efficient measure for this purpose. The majority of ESS definitions have been proposed in the context of borrowing control information. While many Bayesian models can be naturally extended to leveraging external information on the treatment effect scale, very little attention has been directed to computing the prior ESS in this setting. In this research, we bridge this methodological gap by extending the popular ELIR ESS definition. We lay out the general framework, and derive the prior ESS for various types of endpoints and treatment effect measures. The posterior distribution and the predictive consistency property of ESS are also examined. The methods are implemented in R programs available on GitHub: https://github.com/squallteo/TrtEffESS.

翻译：随着贝叶斯外部数据借用应用的快速增长，如何设定具有适当信息量的先验分布变得日益关键。先验有效样本量（ESS）为此提供了直观且高效的度量手段。当前多数ESS定义主要针对借用对照信息场景提出。尽管许多贝叶斯模型可自然扩展至治疗效果尺度的外部信息借用，但在该情境下计算先验ESS的研究却鲜有关注。本研究通过拓展广受欢迎的ELIR ESS定义，填补了这一方法论空白。我们建立了通用框架，推导了各类终点类型与治疗效果度量指标下的先验ESS公式，并分析了后验分布及ESS的预测一致性性质。相关方法已在GitHub（https://github.com/squallteo/TrtEffESS）的R程序中实现。