  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.
