  In recent years, real-world external controls (ECs) have grown in popularity
as a tool to empower randomized placebo-controlled trials (RPCTs), particularly
in rare diseases or cases where balanced randomization is unethical or
impractical. However, as ECs are not always comparable to the RPCTs, direct
borrowing ECs without scrutiny may heavily bias the treatment effect estimator.
Our paper proposes a data-adaptive integrative framework capable of preventing
unknown biases of ECs. The adaptive nature is achieved by dynamically sorting
out a set of comparable ECs via bias penalization. Our proposed method can
simultaneously achieve (a) the semiparametric efficiency bound when the ECs are
comparable and (b) selective borrowing that mitigates the impact of the
existence of incomparable ECs. Furthermore, we establish statistical
guarantees, including consistency, asymptotic distribution, and inference,
providing type-I error control and good power. Extensive simulations and two
real-data applications show that the proposed method leads to improved
performance over the RPCT-only estimator across various bias-generating
scenarios.
