The control outcome calibration approach for causal inference with unobserved confounding

Unobserved confounding can seldom be ruled out with certainty in nonexperimental studies. Negative controls are sometimes used in epidemiologic practice to detect the presence of unobserved confounding. An outcome is said to be a valid negative control variable to the extent that it is influenced by unobserved confounders of the exposure effects on the outcome in view, although not directly influenced by the exposure. Thus, a negative control outcome found to be empirically associated with the exposure after adjustment for observed confounders indicates that unobserved confounding may be present. In this paper, we go beyond the use of control outcomes to detect possible unobserved confounding and propose to use control outcomes in a simple but formal counterfactual-based approach to correct causal effect estimates for bias due to unobserved confounding. The proposed control outcome calibration approach is developed in the context of a continuous or binary outcome, and the control outcome and the exposure can be discrete or continuous. A sensitivity analysis technique is also developed, which can be used to assess the degree to which a violation of the main identifying assumption of the control outcome calibration approach might impact inference about the effect of the exposure on the outcome in view.