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

Anna Guo; David Benkeser; Razieh Nabi

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arXiv · 2312.10234

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

Anna Guo·David Benkeser·Razieh Nabi

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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.

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Anna Guo, David Benkeser, Razieh Nabi. 2023-12-15. Flexible Nonparametric Inference for Causal Effects under the Front-Door Model. https://arxiv.org/abs/2312.10234

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