Flexible Nonparametric Inference for Causal Effects under the Front-Door Model

• URL: http://arxiv.org/abs/2312.10234v2
• Date: Thu, 17 Jul 2025 14:45:40 GMT
• Title: Flexible Nonparametric Inference for Causal Effects under the Front-Door Model
• Authors: Anna Guo, David Benkeser, Razieh Nabi,
• Abstract summary: We develop novel one-step and targeted minimum loss-based estimators for both the average treatment effect and the average treatment effect on the treated under front-door assumptions.<n>Our estimators are built on multiple parameterizations of the observed data distribution, including approaches that avoid mediator density entirely.<n>We show how these constraints can be leveraged to improve the efficiency of causal effect estimators.
• Score: 2.6900047294457683
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Evaluating causal treatment effects in observational studies requires addressing confounding. While the back-door criterion enables identification through adjustment for observed covariates, it fails in the presence of unmeasured confounding. The front-door criterion offers an alternative by leveraging variables that fully mediate the treatment effect and are unaffected by unmeasured confounders of the treatment-outcome pair. We develop novel one-step and targeted minimum loss-based estimators for both the average treatment effect and the average treatment effect on the treated under front-door assumptions. Our estimators are built on multiple parameterizations of the observed data distribution, including approaches that avoid modeling the mediator density entirely, and are compatible with flexible, machine learning-based nuisance estimation. We establish conditions for root-$n$ consistency and asymptotic linearity by deriving second-order remainder bounds. We also develop flexible tests for assessing identification assumptions, including a doubly robust testing procedure, within a semiparametric extension of the front-door model that encodes generalized (Verma) independence constraints. We further show how these constraints can be leveraged to improve the efficiency of causal effect estimators. Simulation studies confirm favorable finite-sample performance, and real-data applications in education and emergency medicine illustrate the practical utility of our methods. An accompanying R package, fdcausal, implements all proposed procedures.

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