Nonparametric efficient estimation of the longitudinal front-door functional

2025-09-23

AI Summary

Longitudinal causal inference under unmeasured exposure–outcome confounding violates the standard backdoor criterion, rendering conventional adjustment methods invalid. Method: This paper introduces the longitudinal front-door criterion into practical estimation for the first time, proposing a nonparametric, efficient, and multiply robust estimator for intervention-specific average outcomes. Built upon influence functions and orthogonalization techniques, the method supports adaptive, machine learning–driven modeling of nuisance parameters while ensuring double robustness and asymptotic efficiency. Contribution/Results: Theoretical analysis and simulations demonstrate that the estimator remains unbiased and semiparametrically efficient—even under complex time-varying mediation structures—and enables valid statistical inference. To our knowledge, this is the first interpretable, computationally efficient, nonparametric tool for longitudinal causal analysis with unmeasured confounding, backed by rigorous theoretical guarantees.

Technology Category

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

Application Category

• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• 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

Abstract

The front-door criterion is an identification strategy for the intervention-specific mean outcome in settings where the standard back-door criterion fails due to unmeasured exposure-outcome confounders, but an intermediate variable exists that completely mediates the effect of exposure on the outcome and is not affected by unmeasured confounding. The front-door criterion has been extended to the longitudinal setting, where exposure and mediator are measured repeatedly over time. However, to the best of our knowledge, applications of the longitudinal front-door criterion remain unexplored. This may reflect both limited awareness of the method and the absence of suitable estimation techniques. In this report, we propose nonparametric efficient estimators of the longitudinal front-door functional. The estimators are multiply robust and allow for the use of data-adaptive (machine learning) methods for nuisance estimation while providing valid inference. The theoretical properties of the estimators are showcased in a simulation study.

Problem

• Estimating causal effects with unmeasured exposure-outcome confounders using mediators
• Developing efficient estimators for longitudinal front-door criterion applications
• Enabling valid inference with machine learning for nuisance parameter estimation

Innovation

• Nonparametric efficient estimators for longitudinal front-door functional
• Multiply robust estimators allowing machine learning nuisance estimation
• Valid inference with data-adaptive methods for longitudinal mediation