Doubly Safe Estimation for the Average Treatment Effect on the Treated with External Control Data under High-Dimensionality

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Randomized controlled trial (RCT) has been a gold standard for causal discovery in various biomedical studies. In this paper, we consider the situation that some external control data, possibly with a much larger sample size, are available. However, the standard doubly robust estimator for ATT incorporating external controls might be even less efficient than the naive doubly robust estimator without using the external controls. This is not ideal because it means the incorporation of external controls might be harmful for our estimation. To fix this issue, we propose a novel doubly robust estimator which is guaranteed to be always more efficient than the naïve doubly robust estimator without using the external controls. Further, if all models are correct, the proposed estimator is the same as the standard doubly robust estimator incorporating external controls, and it is semiparametrically efficient. The asymptotic theory developed in this paper, including both estimation and statistical inference, is under the general high-dimensional confounder situation. We conduct comprehensive simulation studies, as well as a real data application, to illustrate our proposed methodology.