A new criterion for confounder selection

By Tyler J. VanderWeele, Ilya Shpitser. 2011

437 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Causal Inference through a Witness Protection Program (2014, background): “By postulating knowledge of the causal graph relating components of U , one can infer whether a measured subset of the causes of X and Y is enough (Pearl, 2000; VanderWeele and Shpitser, 2011; Pearl, 2009).”
Variable selection – A review and recommendations for the practicing statistician (2018, methodology): “Therefore, robust confounder selection procedures based on DAGs were proposed such as the disjunctive cause criterion (VanderWeele & Shpitser, 2011).”
Graphical criteria for efficient total effect estimation via adjustment in causal linear models (2019, methodology): “variables to a given valid adjustment set decreases the eciency, while adding precision variables increases it. Model selection procedures taking these notions into account have also been developed (VanderWeele and Shpitser, 2011; Shortreed and Ertefaie, 2017). While the above notions provide useful”
Data-driven covariate selection for nonparametric estimation of causal effects (2013, methodology): “In this section we evaluate the performance of our approach as described in Sections 3 and 4, and empirically compare it with the simple approaches mentioned in Section 2, as well as to the method of VanderWeele and Shpitser (2011) (providing the necessary information about causes of x and y taken f”
Do-calculus when the True Graph Is Unknown (2015, methodology): “More data-driven methods to ﬁnd adjustment sets have also been developed (De Luna et al., 2011; Entner et al., 2013; VanderWeele and Shpitser, 2011).”