Bayesian clustering prior with overlapping indices for effective use of multisource external data

The use of external data in clinical trials offers numerous advantages, such as reducing enrollment, increasing study power, and shortening trial duration. In Bayesian inference, information in external data can be transferred into an informative prior for future borrowing (i.e. prior synthesis). However, multisource external data often exhibits heterogeneity, which can cause information distortion during the prior synthesizing. Clustering helps identifying the heterogeneity, enhancing the congruence between synthesized prior and external data. Obtaining optimal clustering is challenging due to the trade-off between congruence with external data and robustness to future data. We introduce two overlapping indices: the overlapping clustering index and the overlapping evidence index . Using these indices alongside a K-means algorithm, the optimal clustering result can be identified by balancing this trade-off and applied to construct a prior synthesis framework to effectively borrow information from multisource external data. By incorporating the (robust) meta-analytic predictive (MAP) prior within this framework, we develop (robust) Bayesian clustering MAP priors. Simulation studies and real-data analysis demonstrate their advantages over commonly used priors in the presence of heterogeneity. Since the Bayesian clustering priors are constructed without needing the data from prospective study, they can be applied to both study design and data analysis in clinical trials.