Prior Effective Sample Size When Borrowing on the Treatment Effect Scale

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. Meanwhile, Bayesian borrowing is frequently conducted on the treatment effect scale to extrapolate evidence in pediatric or global trials. 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 expected local information ratio (ELIR) ESS definition. We lay out the general framework, and derive the ESS for various types of endpoints and treatment effect measures. The desirable predictive consistency property of ELIR ESS is examined and found to only be preserved for the difference between two normal endpoints. The methods are implemented in R programs available on GitHub: https://github.com/squallteo/TrtEffESS.