Eliciting the discount parameter in a power prior method on the basis of the type I error consideration

In Bayesian clinical trial design, the power prior methodology offers a flexible framework for incorporating historical data into the analysis. One critical aspect of this approach is determining the effective sample size, which quantifies the amount of information borrowed from the historical dataset. In this article, we derive a formula for computing the effective sample size of a power prior by eliciting the discount parameter on the basis of the type I error consideration. Our formula takes into account various factors, including the sample size of the historical dataset and the maximally allowable type I error rate. We demonstrate the utility of our formula through illustrative examples and provide practical guidelines for its application in clinical trial planning, using a pediatric schizophrenia trial as an example. By accurately estimating the effective sample size, researchers can enhance the efficiency and validity of Bayesian analyses in the context of historical data borrowing.