On Proximal Causal Learning with Many Hidden Confounders

TL;DR

This paper extends the proximal g-formula to broader causal models with many hidden confounders, enabling causal inference using proxy variables even when unobserved confounders are complex and numerous.

Contribution

It generalizes the proximal g-formula to include models with arbitrarily many unobserved confounder levels, broadening its applicability in causal inference.

Findings

The generalized formula holds for a wide class of models.

Simulations support the theoretical results.

The approach is practical for complex confounding scenarios.

Abstract

We generalize the proximal g-formula of Miao, Geng, and Tchetgen Tchetgen (2018) for causal inference under unobserved confounding using proxy variables. Specifically, we show that the formula holds true for all causal models in a certain equivalence class, and this class contains models in which the total number of levels for the set of unobserved confounders can be arbitrarily larger than the number of levels of each proxy variable. Although straightforward to obtain, the result can be significant for applications. Simulations corroborate our formal arguments.