🤖 AI Summary
Small-sample randomized controlled trials (RCTs) often suffer from low statistical efficiency, leading to imprecise treatment effect estimation. To address bias arising from insufficient comparability when borrowing external control data, this paper proposes an influence-function-based adaptive borrowing method: it quantifies the exchangeability between external controls and the RCT via a formal exchangeability hypothesis test, and determines data-driven optimal weights by balancing bias and variance. Theoretically, the approach integrates semiparametric efficient estimation with asymptotic analysis to ensure consistency and efficiency of the estimator. Simulation studies and real-data analyses demonstrate that the method substantially improves estimation precision while maintaining unbiasedness, outperforming existing strategies for integrating external controls.
📝 Abstract
Randomized controlled trials (RCTs) often exhibit limited inferential efficiency in estimating treatment effects due to small sample sizes. In recent years, the combination of external controls has gained increasing attention as a means of improving the efficiency of RCTs. However, external controls are not always comparable to RCTs, and direct borrowing without careful evaluation can introduce substantial bias and reduce the efficiency of treatment effect estimation. In this paper, we propose a novel influence-based adaptive sample borrowing approach that effectively quantifies the "comparability'' of each sample in the external controls using influence function theory. Given a selected set of borrowed external controls, we further derive a semiparametric efficient estimator under an exchangeability assumption. Recognizing that the exchangeability assumption may not hold for all possible borrowing sets, we conduct a detailed analysis of the asymptotic bias and variance of the proposed estimator under violations of exchangeability. Building on this bias-variance trade-off, we further develop a data-driven approach to select the optimal subset of external controls for borrowing. Extensive simulations and real-world applications demonstrate that the proposed approach significantly enhances treatment effect estimation efficiency in RCTs, outperforming existing approaches.