A New Criterion for Confounder Selection
Article first published online: 31 MAY 2011
© 2011, The International Biometric Society
Volume 67, Issue 4, pages 1406–1413, December 2011
How to Cite
VanderWeele, T. J. and Shpitser, I. (2011), A New Criterion for Confounder Selection. Biometrics, 67: 1406–1413. doi: 10.1111/j.1541-0420.2011.01619.x
- Issue published online: 14 DEC 2011
- Article first published online: 31 MAY 2011
- Received August 2010. Revised March 2011. Accepted March 2011.
- Causal inference;
- Covariate selection;
- Directed acyclic graphs
Summary We propose a new criterion for confounder selection when the underlying causal structure is unknown and only limited knowledge is available. We assume all covariates being considered are pretreatment variables and that for each covariate it is known (i) whether the covariate is a cause of treatment, and (ii) whether the covariate is a cause of the outcome. The causal relationships the covariates have with one another is assumed unknown. We propose that control be made for any covariate that is either a cause of treatment or of the outcome or both. We show that irrespective of the actual underlying causal structure, if any subset of the observed covariates suffices to control for confounding then the set of covariates chosen by our criterion will also suffice. We show that other, commonly used, criteria for confounding control do not have this property. We use formal theory concerning causal diagrams to prove our result but the application of the result does not rely on familiarity with causal diagrams. An investigator simply need ask, “Is the covariate a cause of the treatment?” and “Is the covariate a cause of the outcome?” If the answer to either question is “yes” then the covariate is included for confounder control. We discuss some additional covariate selection results that preserve unconfoundedness and that may be of interest when used with our criterion.