Efficient Nonparametric Inference for Mediation Analysis with Nonignorable Missing Confounders

Music City Center 

Mediation analysis is widely used for exploring treatment mechanisms, but it faces challenges due to the presence of nonignorable missing confounders, particularly in questionnaire surveys of observational studies. Efficient inference about mediation effects and efficiency loss due to nonignorable missingness have rarely been studied in literature because of the difficulties arising from the ill-posed inverse problem. To address this issue, we first show that the mediation effect of interest can be identified as a weighted average of an iterated conditional expectation with an available shadow variable. We then propose a Sieve-based Iterative Outward (SIO) approach for estimation. We establish the large sample theory, particularly the asymptotic normality, of the proposed estimator despite the challenges of the ill-posed problem. We show 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 mediation effects. The finite-sample performance of our proposed approach is evaluated through simulation studies, and we apply it to the CFPS data to demonstrate its practical applicability.

Direct and indirect effects

Ill-posed inverse problem

Missing not at random

Semiparametric efficiency bound

Sieve approximation 

Biometrics Section