On the definition of a confounder

Area of Science:

• Causal Inference
• Epidemiology
• Statistical Modeling

Background:

• The field of causal inference formally defines confounding using counterfactual independence.
• However, a clear, formal definition for a

Purpose of the Study:

• To formally define a

Main Methods:

• Evaluating candidate definitions of confounders based on informal statements in the literature.
• Assessing whether controlling for all identified confounders adequately controls for confounding.
• Determining if confounders, in certain contexts, help eliminate or reduce confounding bias.

Main Results:

• Several proposed definitions failed to satisfy the key properties of controlling for confounding and reducing bias.
• One candidate definition emerged as satisfying both critical properties.

Conclusions:

• A formal definition for a confounder is proposed: a pre-exposure covariate C, which, with a set of covariates X, makes the exposure-outcome effect unconfounded conditional on (X, C), but not for any proper subset.
• Variables that reduce but do not eliminate bias are termed "surrogate confounders."