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In recent years, real-world external controls (ECs) have grown in popularityas a tool to empower randomized placebo-controlled trials (RPCTs), particularlyin rare diseases or cases where balanced randomization is unethical orimpractical. However, as ECs are not always comparable to the RPCTs, directborrowing ECs without scrutiny may heavily bias the treatment effect estimator.Our paper proposes a data-adaptive integrative framework capable of preventingunknown biases of ECs. The adaptive nature is achieved by dynamically sortingout a set of comparable ECs via bias penalization. Our proposed method cansimultaneously achieve (a) the semiparametric efficiency bound when the ECs arecomparable and (b) selective borrowing that mitigates the impact of theexistence of incomparable ECs. Furthermore, we establish statisticalguarantees, including consistency, asymptotic distribution, and inference,providing type-I error control and good power. Extensive simulations and tworeal-data applications show that the proposed method leads to improvedperformance over the RPCT-only estimator across various bias-generatingscenarios.

Integrating Randomized Placebo-Controlled Trial Data with External Controls: A Semiparametric Approach with Selective Borrowing