Randomized experiments (REs) are the cornerstone for treatment effect evaluation. However, due to practical considerations, REs may encounter difficulty recruiting sufficient patients. External controls (ECs) can supplement REs to boost estimation efficiency. Yet, there may be incomparability between ECs and concurrent controls (CCs), resulting in misleading treatment effect evaluation. We introduce a novel bias function to measure the difference in the outcome mean functions between ECs and CCs. We show that the ANCOVA model augmented by the bias function for ECs renders a consistent estimator of the average treatment effect, regardless of whether or not the ANCOVA model is correct. To accommodate possibly different structures of the ANCOVA model and the bias function, we propose a double penalty integration estimator (DPIE) with different penalization terms for the two functions. With an appropriate choice of penalty parameters, our DPIE ensures consistency, oracle property, and asymptotic normality even in the presence of model misspecification. DPIE is more efficient than the estimator derived from REs alone, validated through theoretical and experimental results.

翻译：随机实验（REs）是治疗效果评估的基石。然而，出于实际考量，REs在招募足够患者时可能面临困难。外部对照（ECs）可补充REs以提高估计效率。但ECs与同期对照（CCs）之间可能存在不可比性，从而导致误导性的治疗效果评估。我们引入一种新型偏差函数来衡量ECs与CCs结果均值函数间的差异。研究表明，通过偏差函数增强的ANCOVA模型（用于ECs）可得到平均治疗效果的一致估计量，无论ANCOVA模型是否正确。为适应ANCOVA模型与偏差函数可能存在的不同结构，我们提出一种双重惩罚集成估计器（DPIE），对这两个函数采用不同的惩罚项。在适当选择惩罚参数的情况下，即使在模型误设存在时，我们的DPIE仍能确保一致性、神谕性质及渐近正态性。经理论与实验验证，DPIE比仅基于REs得到的估计量更为高效。