Pointwise Predictive Density Calibrated-Power Prior for Dynamic Borrowing of Historical Data 

Music City Center 

Incorporating historical data into the analysis of treatment effects for rare diseases has gained increasing attention. However, determining the appropriate level of congruence between historical and current data remains a significant challenge. In this work, we introduce a novel Bayesian p-value-based congruence measure to quantify heterogeneity between historical and current control data. We investigate its asymptotic properties under both congruent and incongruent scenarios and develop the pointwise predictive density calibrated-power prior (PPD-CPP) to dynamically leverage historical information. The PPD-CPP framework provides a flexible approach, allowing the power parameter to be modeled as either a fixed scalar or a random variable and enabling the assignment of unique power parameters to individual observations. Through extensive numerical studies with normal endpoints, we demonstrate that our method effectively borrows information from congruent sources while appropriately discarding incongruent data.

Bayesian p-value

Calibrated power prior

Congruence measure

Dynamic historical borrowing 

Section on Risk Analysis