  Use of historical control data to augment a small internal control arm in a
randomized control trial (RCT) can lead to significant improvement of the
efficiency of the trial. It introduces the risk of potential bias, since the
historical control population is often rather different from the RCT. Power
prior approaches have been introduced to discount the historical data to
mitigate the impact of the population difference. However, even with a Bayesian
dynamic borrowing which can discount the historical data based on the outcome
similarity of the two populations, a considerable population difference may
still lead to a moderate bias. Hence, a robust adjustment for the population
difference using approaches such as the inverse probability weighting or
matching, can make the borrowing more efficient and robust. In this paper, we
propose a novel approach integrating propensity score for the covariate
adjustment and Bayesian dynamic borrowing using power prior. The proposed
approach uses Bayesian bootstrap in combination with the empirical Bayes method
utilizing quasi-likelihood for determining the power prior. The performance of
our approach is examined by a simulation study. We apply the approach to two
Acute Myeloid Leukemia (AML) studies for illustration.
