Prior Effective Sample Size When Borrowing on the Treatment Effect Scale

TL;DR

This paper extends the concept of prior effective sample size (ESS) to Bayesian models that borrow information on the treatment effect scale, providing a framework for better prior elicitation in external data borrowing.

Contribution

It introduces a novel extension of the ELIR ESS definition to treatment effect scale, covering various endpoints and treatment measures, with implementation in R.

Findings

Derived prior ESS formulas for different endpoints

Analyzed posterior distribution and predictive consistency of ESS

Provided R implementation available on GitHub

Abstract

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.