Primary Submission Category: Mediation Analysis, Mechanisms
Two-Stage Nuisance Function Estimation for Causal Mediation Analysis
Authors: Chang Liu, AmirEmad Ghassami,
Presenting Author: Chang Liu*
When estimating the direct and indirect causal effects using the influence function-based estimator of the mediation functional, it is crucial to understand what aspects of the treatment, the mediator, and the outcome mean mechanisms should be focused on. Specifically, considering them as nuisance functions and attempting to fit these nuisance functions as accurate as possible is not necessarily the best approach to take. In this work, we propose a two-stage estimation strategy for the nuisance functions that estimates the nuisance functions based on the role they play in the structure of the bias of the influence function-based estimator of the mediation functional. We use the weighted balancing approach of Imai and Ratkovic (2014) to design the estimator of the treatment mechanism in Stage 1 and one of the nuisance functions in Stage 2. The weights in these balancing estimators are designed directly based on the bias of the final estimator of the parameter of interest. We provide parametric and nonparametric versions of the balancing estimators. The other two nuisance functions are obtained using standard parametric or nonparametric regressions. We provide robustness analysis of the proposed method, as well as sufficient conditions for consistency and asymptotic normality of the estimator of the parameter of interest. We evaluate our methods through simulations and compare with existing methods.