Causal Inference with the "Napkin Graph"

TL;DR

This paper introduces the 'Napkin graph', a unified causal framework capturing various confounding structures, and develops novel estimators leveraging machine learning and constraints for improved causal effect estimation.

Contribution

It presents a new causal graph framework and estimators that handle complex confounding, including M-bias and instrumental variables, with efficiency gains from Verma constraints.

Findings

Developed doubly robust estimators for the ratio of g-formulas.

Validated methods through simulations and real data application.

Provided an R package 'napkincausal' for implementation.

Abstract

Unmeasured confounding can render identification strategies based on adjustment functionals invalid. We study the "Napkin graph", a causal structure that encapsulates patterns of M-bias, instrumental variables, and the classical back-door and front-door models within a single graphical framework, yet requires a nonstandard identification strategy: the average treatment effect is expressed as a ratio of two g-formulas. We develop novel estimators for this functional, including doubly robust one-step and targeted minimum loss-based estimators that remain asymptotically linear when nuisance functions are estimated at slower-than-parametric rates using machine learning. We also show how a generalized independence restriction encoded by the Napkin graph, known as a Verma constraint, can be exploited to improve efficiency, illustrating more generally how such constraints in hidden variable DAGs can inform semiparametric inference. The proposed methods are validated through simulations and applied to the Finnish Life Course study to estimate the effect of educational attainment on income. An accompanying R package, napkincausal, implements all proposed procedures.