Primary Submission Category: Machine Learning and Causal Inference
Average Causal Effect Estimation and Efficiency Gains via Verma Constraints in the Causal Napkin Graph
Authors: Anna Guo, Razieh Nabi, David Benkeser,
Presenting Author: Anna Guo*
In causal inference, certain patterns of unmeasured confounding between treatment and outcome can invalidate conventional methods like the g-formula, or equivalently, back-door and front-door functionals. This work explores the “Napkin graph,” a causal structure that combines key features of M-bias, instrumental variables, and back-door/front-door criteria. By leveraging pre-treatment “trapdoor” variables, which influence the outcome exclusively through the treatment, nonparametric identification of the average causal effect is achieved via a ratio of two g-formulas, addressing limitations of traditional methods.
In this work, we propose novel estimators for the Napkin functional, including doubly robust one-step and targeted minimum loss-based estimators that achieve asymptotic linearity under flexible convergence rates for nuisance parameter estimation. A central innovation of our work is the principled utilization of Verma constraints—generalized independence restrictions between observable variables in graphical models with unmeasured variables. Specifically, we leverage a Verma constraint between the trapdoor variable and the outcome to achieve significant efficiency gains, advancing semiparametric causal effect estimation in such models.
The methods are validated through simulations and real data analysis using an HR dataset to estimate the causal effect of employee skill on performance. We also introduce the texttt{napkintmle} R package for easy implementation.
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