Data-driven covariate selection for confounding adjustment by focusing on the stability of the effect estimator.

Abstract

Valid inference of cause-and-effect relations in observational studies necessitates adjusting for common causes of the focal predictor (i.e., treatment) and the outcome. When such common causes, henceforth termed confounders, remain unadjusted for, they generate spurious correlations that lead to biased causal effect estimates. But routine adjustment for all available covariates, when only a subset are truly confounders, is known to yield potentially inefficient and unstable estimators. In this article, we introduce a datadriven confounder selection strategy that focuses on stable estimation of the treatment effect. The approach exploits the causal knowledge that after adjusting for confounders to eliminate all confounding biases, adding any remaining non-confounding covariates associated with only treatment or outcome, but not both, should not systematically change the effect estimator. The strategy proceeds in two steps. First, we prioritize covariates for adjustment by probing how strongly each covariate is associated with treatment and outcome. Next, we gauge the stability of the effect estimator by evaluating its trajectory adjusting for different covariate subsets. The smallest subset that yields a stable effect estimate is then selected. Thus, the strategy offers direct insight into the (in)sensitivity of the effect estimator to the chosen covariates for adjustment. The ability to correctly select confounders and yield valid causal inferences following data-driven covariate selection is evaluated empirically using extensive simulation studies. Furthermore, we compare the introduced method empirically with routine variable selection methods. Finally, we demonstrate the procedure using two publicly available real-world datasets. A step-by-step practical guide with user-friendly R functions is included.

The Incremental Propensity Score Approach for Diversity Science

“…Researchers should strive to record and adjust for all predictors of the outcomes of interest (VanderWeele, 2019). Adjusting for covariates that are strongly associated with the outcome can improve the finite sample precision of the estimators even if they are unhelpful for confounding when weakly (or un)associated with the treatment (Brookhart et al, 2006;Loh & Ren, 2023a). In contrast, covariates that are associated solely with the treatment-and not with the outcomeare redundant for confounding, yet adjusting for them results in inefficient estimators that are prone to finitesample bias simply because of sampling variability (Brookhart et al, 2006;Kelcey, 2011).…”

The Causal Cookbook: Recipes for Propensity Scores, G-Computation, and Doubly Robust Standardization

“…Wysocki et al (2022) suggested spelling out several plausible causal structures and selecting the controls as the minimal set blocking all backdoor paths. The selection of controls can also be achieved by data-driven procedures (for such an approach introduced in psychology, see Loh & Ren, 2023a)-however, such procedures in themselves are unaware of the underlying causal structure, and they thus need to be combined with existing domain knowledge to achieve exchangeability. As spelled out before, doubly robust estimators may offer advantages here because even if a confounder is missing in one nuisance model, groups remain conditionally exchangeable if it is present in the other nuisance model (Chatton et al, 2022).…”