Doubly Robust Control Outcome Calibration Approach Estimation of Conditional Effects with Uncontrolled Confounding

Drawing causal conclusions about nonrandomized exposures rests on assuming no uncontrolled confounding, but it is rarely justifiable to rule out all putative violations of this routinely made yet empirically untestable assumption. Alternatively, this assumption can be avoided by leveraging negative control outcomes using the control outcome calibration approach (COCA). The existing COCA estimator of the average causal effect relies on correctly specifying the mean negative control outcome model, with a closed-form solution for the main exposure effect. In this article, we propose a doubly robust COCA estimator of the average causal effect that relaxes this modeling requirement and permits effect modification through covariate-exposure interaction terms. The doubly robust COCA estimator uses correctly specified exposure and focal outcome models to protect against biases from an incorrectly specified negative control outcome model. The ability to obtain unbiased point estimates and inferences is empirically evaluated using a simulation study. We demonstrate doubly robust COCA using a publicly available dataset to evaluate the effect of volunteering on mental health. This method is practical and easy to implement and permits unbiased estimation of causal effects even amid uncontrolled confounding.