WOW: WAIC-Optimized Gating of Mixture Priors for External Data Borrowing

The integration of external data using Bayesian mixture priors has become a powerful approach in clinical trials, offering significant potential to improve trial efficiency. Despite their strengths in analytical tractability and practical flexibility, existing methods such as the robust meta-analytic-predictive (rMAP) and self-adapting mixture (SAM) often presume borrowing without rigorously assessing whether, how, or when integration is appropriate. When external and concurrent data are discordant, excessive borrowing can bias estimates and lead to misleading conclusions. To address this, we introduce WOW, a Kullback-Leibler-based gating strategy guided by the widely applicable information criterion (WAIC). WOW conducts a preliminary compatibility assessment between external and concurrent trial data and gates the level of borrowing accordingly. The approach is prior-agnostic and can be seamlessly integrated with any mixture prior method, whether using fixed or adaptive weighting schemes, after the WOW step. Simulation studies demonstrate that incorporating the WOW strategy before Bayesian mixture prior borrowing methods effectively mitigates excessive borrowing and improves estimation accuracy. By providing robust and reliable inference, WOW strengthens the performance of mixture-prior methods and supports better decision-making in clinical trials.