Dynamic Borrowing With a Bias-Tolerance Cap in Augmented Randomized Controlled Trials.

Although randomized controlled trials (RCTs) are the gold standard for evaluating the efficacy and safety of treatments, they are challenged by cost, duration, enrollment, or ethical concerns. A possible solution is to incorporate external control data as a hybrid control group, for which various statistical methods are available. However, only a few of them account for confounding bias due to unknown/unmeasured covariates between the internal and external control data. Moreover, the amount of this potential bias cannot be measured using most existing methods without extensive simulations. Here, we propose a novel method for estimating the confounding effects of unmeasured covariates based on model-based regression standardization, inverse probability weighting, and augmented inverse probability weighting for continuous or binary outcomes. We also propose an estimator that dynamically borrows external data and uses a weighted mean, adjusting weights according to the estimated confounding effect of unmeasured covariates. In the proposed method, the expected amount of bias can be controlled within a prespecified "bias-tolerance cap," which may facilitate a better discussion among stakeholders about whether an effect estimate has unacceptable bias by utilizing external control data in a planning phase. Simulations showed that the proposed method regulates bias within the tolerance cap, regardless of the magnitude of confounding by unmeasured covariates, while greatly improving power and efficiency when confounding is absent. Finally, we illustrate an applicational example of our proposed method to an actual RCT and the external control datasets for patients with advanced pancreatic cancer.