How Effective Are Machine Learning and Doubly Robust Estimators in Incorporating High-Dimensional Proxies to Reduce Residual Confounding?

Background: Residual confounding presents a persistent challenge in observational studies, particularly in high-dimensional settings. High-dimensional proxy adjustment methods, such as the high-dimensional propensity score (hdPS), are widely used to address confounding bias by incorporating proxies for unmeasured confounders. Extensions of hdPS have integrated machine learning, such as LASSO and super learner (SL), and doubly robust estimators, such as targeted maximum likelihood estimation (TMLE). However, the comparative performance of these methods, especially under different learner configurations and high-dimensional proxies, remains unclear.

Method: We conducted plasmode simulations to evaluate the performance of standard methods, SL, TMLE, and double cross-fit TMLE (DC-TMLE) under varying exposure and outcome prevalence scenarios. Learner libraries included: 1 learner (logistic regression), 3 learners (logistic regression, MARS, and LASSO), and 4 learners (adding XGBoost, a non-Donsker learner). Metrics included bias, coverage, and variability.

Results: Methods without proxies exhibited the highest bias and poorest coverage, highlighting the critical role of proxies in confounding adjustment. Standard methods incorporating high-dimensional proxies showed robust performance, achieving low bias and near-nominal coverage. TMLE and DC-TMLE reduced bias but exhibited worse coverage compared to standard methods, particularly with larger learner libraries. Notably, DC-TMLE, expected to address under-coverage issues, failed to perform adequately in high-dimensional settings with non-Donsker learners, further emphasizing the instability introduced by complex libraries.

Conclusion: Our findings underscore the utility of high-dimensional proxies in standard methods and the importance of tailoring learner configurations in SL and TMLE to ensure reliable confounding adjustment in high-dimensional contexts.