The Targeted Virtual Control Approach for Single-Arm Clinical Trials with External Controls

In single-arm clinical trials with external controls, usually the estimand of interest is defined as the average treatment effect on the treated (ATT), and external controls are leveraged to provide an estimator of the estimand. Recently, virtual control approaches have been proposed to predict the outcomes for experimental study subjects as if they were receiving the control treatment, resulting in so-called "virtual controls" for comparison with their observed outcomes under the experimental intervention. We consider the virtual control approaches within the causal inference framework, discussing the properties of the vanilla virtual control approach and the targeted virtual control approach. We illustrate via simulation that the targeted virtual control approach is doubly robust, whereas the vanilla virtual control approach is not. We demonstrate the targeted virtual control approach is the same as the targeted maximum likelihood estimator (TMLE) when targeted at the ATT estimand. Therefore, through the notion of virtual controls, we offer a tangible way to understand and interpret TMLE when targeted at the ATT estimand.