Optimal Adjustment Sets for Nonparametric Estimation of Weighted Controlled Direct Effect

The weighted controlled direct effect (WCDE) generalizes the standard controlled direct effect (CDE) by averaging over the mediator distribution, providing a robust estimate when treatment effects vary across mediator levels. This work establishes three fundamental advances for WCDE in observational studies: First, we establish necessary and sufficient conditions for the identifiability of the WCDE, clarifying when it diverges from the CDE. Next, we consider nonparametric estimation of the WCDE and derive its influence function. Lastly, we characterize the optimal covariate adjustment set that minimizes the asymptotic variance among regular and asymptotically linear estimators, demonstrating how mediator-confounder interactions introduce distinct requirements compared to average treatment effect (ATE) estimation. Using synthetic and real-world data, we validate our theory numerically, showing that the proposed optimal valid adjustment set yields the lowest variance at practical sample sizes. Our results offer a principled framework for efficient estimation of direct effects in complex causal systems, with practical applications in fairness and mediation analysis.

(This talk is part of the weekly Machine Learning Lunch Meetings (MLLM), held every Tuesday from 12:15 to 1:15 p.m.  Professors from Computer Sciences, Statistics, ECE, the iSchool, and other departments will discuss their latest research in machine learning, covering both theory and applications. This is a great opportunity to network with faculty and fellow researchers, learn about cutting-edge research at our university, and foster new collaborations. For the talk schedule, please visit https://sites.google.com/view/wiscmllm/home. To receive future weekly talk announcements, please subscribe to our UW Google Group at https://groups.google.com/u/1/a/g-groups.wisc.edu/g/mllm.)