Detecting hidden confounding in observational data using multiple environments

TL;DR

This paper introduces a method to detect hidden confounders in observational data by leveraging multiple datasets from different environments, based on testable conditional independencies under causal assumptions.

Contribution

It develops a theoretical framework and a practical procedure for identifying unobserved confounding using multiple environments, addressing limitations of single-dataset analysis.

Findings

The procedure accurately detects hidden confounding in simulations.

It performs well with large confounding biases.

The method's empirical behavior is validated on semi-synthetic data.

Abstract

A common assumption in causal inference from observational data is that there is no hidden confounding. Yet it is, in general, impossible to verify this assumption from a single dataset. Under the assumption of independent causal mechanisms underlying the data-generating process, we demonstrate a way to detect unobserved confounders when having multiple observational datasets coming from different environments. We present a theory for testable conditional independencies that are only absent when there is hidden confounding and examine cases where we violate its assumptions: degenerate & dependent mechanisms, and faithfulness violations. Additionally, we propose a procedure to test these independencies and study its empirical finite-sample behavior using simulation studies and semi-synthetic data based on a real-world dataset. In most cases, the proposed procedure correctly predicts the presence of hidden confounding, particularly when the confounding bias is large.