Semiparametric Theory for Causal Inference with Negative Controls

• Activity Number: 6 - Recent Advance of Nonparametric and Semiparametric Techniques with Complex Data Structure
• Type: Invited
• Date/Time: Sunday, July 29, 2018 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Xu Shi* and Wang Miao and Eric Tchetgen Tchetgen
• Companies: Harvard University and Peking University and The Wharton School at the University of Pennsylvania
• Keywords: causal inference; negative control; semiparametric theory; unmeasured confounding

Abstract

Negative controls have a long history in laboratory sciences and epidemiology to rule out non-causal explanations and to detect unmeasured confounding. A negative control outcome is a variable known not to be causally affected by the treatment, while a negative control exposure is a variable known not to causally affect the outcome of interest. Recently, sufficient conditions have been established for nonparametric identification of the average causal effect subject to unmeasured confounding leveraging a pair of negative control exposure-outcome variables. In this talk, we provide a general semiparametric framework for estimation and inference about the average treatment effect with double negative control adjustment for unmeasured confounding. In particular, we derive the semiparametric efficiency bound under a nonparametric model for the observed data distribution, and we propose multiply robust locally efficient estimators when nonparametric estimation may not be feasible. We assess the performance of our methods under model misspecification in extensive simulation studies. Finally, we illustrate our methods with an application to evaluate the effect of higher education on wage.