Randomized controlled trials (RCTs) are the gold standard for causal inference, yet practical constraints often limit the size of the concurrent control arm. Borrowing control data from previous trials offers a potential efficiency gain, but naive borrowing can induce bias when historical and current populations differ. Existing test-then-pool (TTP) procedures address this concern by testing for equality of control outcomes between historical and concurrent trials before borrowing; however, standard implementations may suffer from reduced power or inadequate control of the Type-I error rate. We develop a new TTP framework that fuses control arms while rigorously controlling the Type-I error rate of the final treatment effect test. Our method employs kernel two-sample testing via maximum mean discrepancy (MMD) to capture distributional differences, and equivalence testing to avoid introducing uncontrolled bias, providing a more flexible and informative criterion for pooling. To ensure valid inference, we introduce partial bootstrap and partial permutation procedures for approximating null distributions in the presence of heterogeneous controls. We further establish the overall validity and consistency. We provide empirical studies demonstrating that the proposed approach achieves higher power than standard TTP methods while maintaining nominal error control, highlighting its value as a principled tool for leveraging historical controls in modern clinical trials.

翻译：随机对照试验是因果推断的金标准，但实际约束常限制并行对照组的规模。借用历史试验的对照数据可提升效率，但当历史与当前试验人群存在差异时，简单借用可能引入偏倚。现有的检验后合并方法通过检验历史与当前试验对照结果的等价性来解决此问题；然而标准实施方案可能存在检验效能降低或I类错误率控制不足的问题。我们开发了一种新的检验后合并框架，在严格控制最终治疗效果检验I类错误率的前提下融合对照组数据。该方法通过最大均值差异的核双样本检验捕捉分布差异，并采用等价性检验避免引入不可控偏倚，为数据合并提供了更灵活且信息量更充分的判断准则。为确保推断有效性，我们针对异质性对照组场景提出了部分自助法与部分置换法来近似零分布。我们进一步证明了方法的整体有效性与相合性。实证研究表明，所提方法在维持名义错误率控制的同时，较标准检验后合并方法获得了更高的检验效能，凸显了其作为现代临床试验中历史对照组利用原则性工具的价值。