Sharp partial proximal inference: an assumption-lean approach for leveraging negative controls

Thomas M. Menino Convention & Exhibition Center 

Negative controls--or proxies--are variables assumed or known not to be involved in certain causal pathways, and have historically been used as bias detection agents. Recently, proximal causal inference has emerged as a promising framework for using these variables to directly identify a causal relationship of interest in the face of unmeasured confounding. Proximal methods, however, rely on untestable, often opaque identifying assumptions involving so-called "bridge function" or "completeness" conditions. In this work, we relax these assumptions in a commonly adopted single outcome proxy setting, and show that the negative control non-trivially restricts the counterfactual outcome distribution. Moreover, we derive nonparametric, robust, efficient estimators of sharp bounds for mean counterfactuals. These bounds are non-smooth, non-closed-form solutions to linear programs involving potentially high-dimensional nuisance functions; our statistical approach has implications for a wide class of such challenging functionals. Practically, our proposal can be used to leverage proxies for causal and missing data problems, achieving sharp, valid inference under transparent assumptions.

causal inference

unmeasured confounding

partial identification

negative controls

proximal causal inference 

Section on Statistics in Epidemiology