Confounder selection strategies targeting stable treatment effect estimators

Abstract: Inferring the causal effect of a treatment on an outcome in an observational study requires adjusting for observed baseline confounders to avoid bias. However, adjusting for all observed baseline covariates, when only a subset are confounders of the effect of interest, is known to yield potentially inefficient and unstable estimators of the treatment effect. Furthermore, it raises the risk of finite-sample bias and bias due to model misspecification. For these stated reasons, confounder (or covariate) selection is commonly used to determine a subset of the available covariates that is sufficient for confounding adjustment. In this article, we propose a confounder selection strategy that focuses on stable estimation of the treatment effect. In particular, when the propensity score model already includes covariates that are sufficient to adjust for confounding, then the addition of covariates that are associated with either treatment or outcome alone, but not both, should not systematically change the effect estimator. The proposal, therefore, entails first prioritizing covariates for inclusion in the propensity score model, then using a change-in-estimate approach to select the smallest adjustment set that yields a stable effect estimate. The ability of the proposal to correctly select confounders, and to ensure valid inference of the treatment effect following data-driven covariate selection, is assessed empirically and compared with existing methods using simulation studies. We demonstrate the procedure using three different publicly available datasets commonly used for causal inference.