Robust Covariate Selection for Doubly Robust Estimators in Causal Inference

Doubly robust (DR) estimators are widely used in causal inference because they are consistent whenever either the outcome or propensity score (PS) model is correctly specified with regard to a covariate set that meets the adjustment criterion. For data sets with many covariates, researchers are advised to separately select model-specific subsets for the outcome and PS model. Since these subsets are selected independently of each other, double robustness is in general not guaranteed even if one or both models would remove the entire confounding bias on their own. DR estimators are consistent only if the correctly specified model succeeds in removing both the confounding bias and any new biases induced by the misspecified model (i.e., collider or amplified bias).To allow for differential but robust covariate selection a graphical DR adjustment criterion is introduced. For a given directed acyclic graph, the criterion is able to determine all combinations of model-specific covariate subsets that jointly maintain the DR property. A simple example and simulation study demonstrate that DR estimators fail to consistently estimate the causal effect if the correctly specified model has been kept blind to any bias-inducing misspecifications of the other model.