Confounder selection strategies targeting stable treatment effect estimators

Propensity score methods are widely adopted in observational studies to adjust for observed baseline confounding when either testing the null hypothesis that treatment (or exposure) has no effect on an outcome or estimating the causal effect. However, adjusting for all observed baseline covariates, when only a subset are confounders of the treatment-outcome relation, is known to yield potentially inefficient and unstable estimators of the treatment effect. Similarly, randomization-based procedures that condition on all observed covariates can be underpowered. 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.