Primary Submission Category: Causal Inference and Common Support Violations
Efficient Nonparametric Causal Effect Estimation after Propensity Score Trimming with a Continuous Treatment
Authors: Zach Branson, Sivaraman Balakrishnan, Edward Kennedy, Larry Wasserman,
Presenting Author: Zach Branson*
This work proposes estimators using efficient influence functions (EIFs) for average treatment effects (ATEs) after propensity score trimming in observational studies with a continuous treatment. Trimming involves estimating ATEs among subjects with propensity scores above a threshold, which addresses positivity violations that complicate estimation. Most work on trimming focuses on binary treatments, and several challenges arise with continuous treatments. First, EIFs for trimmed ATEs do not exist, due to a lack of pathwise differentiability induced by trimming and a continuous treatment. Second, if we want the trimming threshold to be estimated, uncertainty in the threshold must be accounted for. To address these challenges, we target a kernel-smoothed trimmed ATE, such that an EIF exists for an estimand close to the trimmed ATE. We allow the trimming threshold to be estimated via the quantile of the propensity score, such that confidence intervals reflect uncertainty involved in threshold estimation. Our resulting EIF-based estimators exhibit doubly-robust style guarantees, where their error can be expressed as the product of errors for the outcome and propensity score models. Thus, our estimators can exhibit parametric convergence rates even when models are estimated at slower rates via flexible machine learning. These findings are validated via simulation and an application, thereby showing how to efficiently-but-flexibly estimate a dose-response function after trimming.