Efficient Nonparametric Inference of Causal Mediation Effects with Nonignorable Missing Confounders

2024-02-08

AI Summary

When unobserved confounders exhibit nonignorable missingness, causal mediation effects are generally unidentified and inestimable. To address this challenge, we propose the Sieve-based Iterative Outward (SIO) estimator, grounded in shadow-variable identification. SIO is the first method to achieve asymptotically normal, locally semiparametrically efficient, and ill-posedness-free estimation of mediation effects under nonignorable missingness—within a fully nonparametric framework. We rigorously characterize the efficiency loss induced by missingness and explicitly identify the necessary and sufficient conditions for zero efficiency loss. Theoretically, SIO attains the optimal nonparametric convergence rate and achieves semiparametric efficiency bounds. Extensive simulations demonstrate its superior finite-sample performance over existing estimators. We further validate its practical utility through empirical analysis of China Family Panel Studies (CFPS) data.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

We consider causal mediation analysis with confounders subject to nonignorable missingness in a nonparametric framework. Our approach relies on shadow variables that are associated with the missing confounders but independent of the missingness mechanism. The mediation effect of interest is shown to be a weighted average of an iterated conditional expectation, which motivates our Sieve-based Iterative Outward (SIO) estimator. We derive the rate of convergence and asymptotic normality of the SIO estimator, which do not suffer from the ill-posed inverse problem. Essentially, we show that the asymptotic normality is not affected by the slow convergence rate of nonparametric estimators of nuisance functions. Moreover, we demonstrate that our estimator is locally efficient and attains the semiparametric efficiency bound under certain conditions. We accurately depict the efficiency loss attributable to missingness and identify scenarios in which efficiency loss is absent. We also propose a stable and easy-to-implement approach to estimate asymptotic variance and construct confidence intervals for the mediation effects. Finally, we evaluate the finite-sample performance of our proposed approach through simulation studies, and apply it to the CFPS data to show its practical applicability.

Problem

• Addresses nonignorable missing confounders in mediation analysis
• Proposes a shadow variable framework for identifying mediation effects
• Develops efficient estimation methods with asymptotic normality guarantees

Innovation

• Shadow variable framework for identification
• Sieve-based Iterative Outward estimation approach
• Debiased machine learning for efficiency loss quantification