Confounder selection via iterative graph expansion

TL;DR

This paper introduces an interactive, graph-expanding method for confounder selection in observational studies that does not require pre-specified causal graphs, relying instead on user-elicited primary adjustment sets.

Contribution

The proposed method allows confounder selection without pre-specified graphs, using iterative graph expansion and user input to identify covariates for confounding control.

Findings

The procedure is sound and complete if user correctly specifies primary adjustment sets.

It does not require prior causal graph knowledge or observed variable sets.

The method effectively identifies confounders through iterative graph expansion.

Abstract

Confounder selection, namely choosing a set of covariates to control for confounding between a treatment and an outcome, is arguably the most important step in the design of an observational study. Previous methods, such as Pearl's back-door criterion, typically require pre-specifying a causal graph, which can often be difficult in practice. We propose an interactive procedure for confounder selection that does not require pre-specifying the graph or the set of observed variables. This procedure iteratively expands the causal graph by finding what we call "primary adjustment sets" for a pair of possibly confounded variables. This can be viewed as inverting a sequence of marginalizations of the underlying causal graph. Structural information in the form of primary adjustment sets is elicited from the user, bit by bit, until either a set of covariates is found to control for confounding or it can be determined that no such set exists. Other information, such as the causal relations between confounders, is not required by the procedure. We show that if the user correctly specifies the primary adjustment sets in every step, our procedure is both sound and complete.