Two-Stage Nuisance Function Estimation for Causal Mediation Analysis

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 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.