Bias-Targeted Nonparametric Balancing for Stable Causal Mediation Analysis

Influence function (IF)-based estimators are widely used in mediation analysis due to their modeling flexibility, but standard implementations require direct estimation of the distribution functions of the mediator and treatment variables. Since these functions appear in the denominator of IF-based estimators, they can induce significant instability, particularly with continuous mediators. In this work, we propose an alternative implementation of IF-based estimators for both single- and multiple-mediator settings, based on reparametrizations of the likelihood. The key idea is to estimate the involved nuisance functions according to their role in the bias structure of the IF-based estimators. In our approach, key nuisance functions that are potential sources of instability are estimated using a novel nonparametric weighted balancing method-which can be viewed as a nonparametric extension of covariate balancing generalized to mediation analysis-fully stabilizing the estimators. We establish consistency and multiple robustness under suitable regularity conditions, and asymptotic normality. Simulation studies demonstrate substantial reductions in bias and variance relative to existing methods for continuous mediators. We further illustrate the approach using NHANES 2013-2014 data to estimate the effect of obesity on coronary heart disease mediated by Glycohemoglobin.