Multiply robust causal inference with double-negative control adjustment for categorical unmeasured confounding

Unmeasured confounding is a threat to causal inference in observational studies. In recent years, the use of negative controls to mitigate unmeasured confounding has gained increasing recognition and popularity. Negative controls have a long‐standing tradition in laboratory sciences and epidemiology to rule out non‐causal explanations, although they have been used primarily for bias detection. Recently, Miao and colleagues have described sufficient conditions under which a pair of negative control exposure and outcome variables can be used to identify non‐parametrically the average treatment effect (ATE) from observational data subject to uncontrolled confounding. We establish non‐parametric identification of the ATE under weaker conditions in the case of categorical unmeasured confounding and negative control variables. We also provide a general semiparametric framework for obtaining inferences about the ATE while leveraging information about a possibly large number of measured covariates. In particular, we derive the semiparametric efficiency bound in the non‐parametric model, and we propose multiply robust and locally efficient estimators when non‐parametric estimation may not be feasible. We assess the finite sample performance of our methods in extensive simulation studies. Finally, we illustrate our methods with an application to the post‐licensure surveillance of vaccine safety among children.