🤖 AI Summary
This paper addresses the challenge of confounder selection in observational studies by proposing an interactive, iterative method that requires neither a pre-specified causal graph nor a complete set of candidate variables. Grounded in latent projection theory, the method dynamically expands a causal graph through successive user-provided local adjustment sets and automatically identifies a minimal “principal adjustment set,” thereby determining whether confounding is controllable. Its key contributions are threefold: (1) it is the first approach to achieve sound and complete confounding control assessment without prior structural assumptions on the causal graph; (2) it makes no assumptions about causal relationships among potential confounders; and (3) it bridges theoretical rigor with practical feasibility. Both theoretical analysis and empirical evaluation demonstrate that, under correct user feedback, the algorithm accurately identifies admissible adjustment sets and correctly determines confounding controllability.
📝 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 observational studies. Previous methods, such as Pearl's celebrated 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 latent projections 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 are 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.
