B2000
Title: Robust covariate-assisted bounds in instrumental variable designs
Authors: Alexander Levis - Carnegie Mellon University (United States) [presenting]
Matteo Bonvini - Carnegie Mellon University (United States)
Zhenghao Zeng - Carnegie Mellon University (United States)
Luke Keele - University of Pennsylvania (United States)
Edward Kennedy - Carnegie Mellon University (United States)
Abstract: When exposure of interest is confounded by unmeasured factors, an instrumental variable (IV) can be used to identify and estimate certain causal contrasts. Identification of the marginal average treatment effect (ATE) from IVs typically relies on strong untestable structural assumptions. When one is unwilling to assert such structural assumptions, IVs can nonetheless be used to construct bounds on the ATE. Famously, linear programming techniques were employed to prove tight bounds on the ATE for a binary outcome, in a randomized trial with noncompliance and no covariate information. We demonstrate how these bounds remain useful in observational settings with baseline confounders of the IV, as well as randomized trials with measured baseline covariates. The resulting lower and upper bounds on the ATE are non-smooth functionals, and thus standard nonparametric efficiency theory is not immediately applicable. To remedy this, we introduce a novel margin condition, and propose an influence function-based estimator of the ATE bounds for a binary outcome that can attain parametric convergence rates when nuisance functions are modeled flexibly. We demonstrate the properties of this estimator in simulation studies and real data. Finally, we discuss various relevant design issues, and propose extensions to continuous outcomes.
