Discussion on "LEAP: the latent exchangeability prior for borrowing information from historical data" by Ethan M. Alt, Xiuya Chang, Xun Jiang, Qing Liu, May Mo, H. Amy Xia, and Joseph G. Ibrahim.

In the following discussion, we describe the various assumptions of exchangeability that have been made in the context of Bayesian borrowing and related models. In this context, we are able to highlight the difficulty of dynamic Bayesian borrowing under the assumption of individuals in the historical data being exchangeable with the current data and thus the strengths and novel features of the latent exchangeability prior. As borrowing methods are popular within clinical trials to augment the control arm, some potential challenges are identified with the application of the approach in this setting.