Principled and modern Bayesian analysis with the normalised power prior

Incorporating historical data into new clinical trials can enhance inference and accelerate regulatory approval processes. The power prior is a widely used Bayesian approach to historical borrowing. However, this method presents key challenges: (i) the selection of an appropriate prior for discounting parameter, ensuring optimal information incorporation, and (ii) computational difficulties arising from the intractability of the normalizing constant in the posterior distribution. To address these issues, we propose a modern Bayesian framework that leverages prior predictive simulations, posterior predictive checks and prior effective sample size (PESS).