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Primary Submission Category: Propensity Scores

A Graphical Adjustment Criterion for Differential Covariate Selection for Doubly Robust Estimators

Authors: Peter Steiner, Weicong Lyu,

Presenting Author: Peter Steiner*

Doubly robust (DR) estimators are widely used in causal inference because they are consistent whenever either the outcome or the treatment selection is correctly modeled (Robins et al., 1994). They rely on an implicit but in practice rarely noticed condition: the set of adjustment covariates in the outcome and selection (propensity score) model must be identical (but predictors may differ). Double robustness is not guaranteed if the two models use different covariates, even if one or both models are correctly specified on their own. Using causal graphs (Pearl, 2009) this paper explains why DR estimators are in general inconsistent when different covariate sets are used and presents a graphical DR adjustment criterion that enables researchers to check whether different covariates sets for the outcome and selection model are able to remove the entire confounding bias in DR estimation procedure. In addition to the graphical adjustment criterion, we also discuss the DR covariate selection criterion in terms of potential outcomes. Using an example and simulated data, we demonstrate the application of the DR adjustment criterion and present results for two commonly used doubly robust estimators—augmented inverse probability weighting (Scharfenstein et al., 1999) and inverse probability weighted regression estimation (Schafer & Kang, 2008; Wooldridge, 2007). We conclude with suggestions for practice.