  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.
