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Randomized experiments (REs) are the cornerstone for treatment effectevaluation. However, due to practical considerations, REs may encounterdifficulty recruiting sufficient patients. External controls (ECs) cansupplement REs to boost estimation efficiency. Yet, there may beincomparability between ECs and concurrent controls (CCs), resulting inmisleading treatment effect evaluation. We introduce a novel bias function tomeasure the difference in the outcome mean functions between ECs and CCs. Weshow that the ANCOVA model augmented by the bias function for ECs renders aconsistent estimator of the average treatment effect, regardless of whether ornot the ANCOVA model is correct. To accommodate possibly different structuresof the ANCOVA model and the bias function, we propose a double penaltyintegration estimator (DPIE) with different penalization terms for the twofunctions. With an appropriate choice of penalty parameters, our DPIE ensuresconsistency, oracle property, and asymptotic normality even in the presence ofmodel misspecification. DPIE is more efficient than the estimator derived fromREs alone, validated through theoretical and experimental results.

Enhancing Treatment Effect Estimation: A Model Robust Approach  Integrating Randomized Experiments and External Controls using the Double  Penalty Integration Estimator