Randomized controlled trials (RCTs) often suffer from limited inferential efficiency in estimating treatment effects due to their small sample sizes. In recent years, incorporating external controls (ECs) has gained increasing attention as an effective way to augment small RCTs and thereby enhance estimation efficiency. However, ECs are not always comparable to RCTs, and direct borrowing without careful evaluation can introduce substantial bias and, paradoxically, undermine the accuracy of treatment effect estimation. In this paper, we propose a novel adaptive influence-based sample borrowing framework to improve average treatment effect (ATE) estimation in RCTs. The framework quantifies the ``comparability'' of each sample in ECs using influence functions and identifies the optimal subset of ECs that minimizes the mean squared error of the ATE estimator. The proposed framework is assumption-lean regarding the distribution of ECs and is robust to outliers, making it broadly applicable across diverse settings. Moreover, we develop an outcome calibration method to improve the data utilization efficiency of ECs, further strengthening the adaptive influence-based sample-borrowing framework. We demonstrate the effectiveness of the proposed method using both simulated and real-world datasets.

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