Approximate Bayesian Analysis for Borrowing External Controls for Randomized Controlled Trials With Dynamic Borrowing and Covariate Balancing Adjustment.

Borrowing controls from external sources has become popular for augmenting the control arm in small randomized controlled trials (RCTs). Due to the difference between the external and RCT populations, bias can be introduced that may lead to invalid statistical inference based on combined data. To mitigate this risk, dynamic borrowing which adaptively determines the amount of borrowing, can be used together with pre-adjustment for prognostic factors in the external data. To take into account the variability due to the estimation of the amount of borrowing and the pre-adjustment, we propose a Bayesian bootstrap (BB)-based integrated Bayesian approach together with covariate balancing (CB) for pre-adjustment. We show that the proposed BB based approach is a valid approximate Bayesian approach with CB using different distances, particularly Euclidean or entropy distance. This justification is not trivial because CB has a different nature from the probability-based approach. We also propose a BB-algorithm for generating an approximate posterior sample, which is easy to implement and computationally efficient. Statistical inference for estimand of interest using combined external and internal data can be based on the bootstrapped posterior sample or on an approximate normal distribution with parameters estimated by BB. To examine the properties of the proposed approach, we conduct an extensive simulation study. The approach is illustrated by borrowing controls for an acute myeloid leukemia trial from another study.