Which Regularized Propensity-Score and Doubly Robust Methods Are Best Calibrated When Exposures or Outcomes Are Rare? A Plasmode Study of Proxy-Based Confounding Adjustment

Purpose. Confounding adjustment in health-care database studies screens large proxy libraries where events per variable are low, straining standard propensity score (PS) methods, and many regularized variable-selection strategies exist (outcome-adaptive LASSO [OAL], group LASSO/GLiDeR, highly adaptive LASSO [HAL]). Yet few comparisons have varied exposure prevalence within such a selection menu, and none pairs it with doubly robust estimation, compute accounting, and a null-RD truth anchor.
Methods. We conducted a plasmode simulation anchored on National Health and Nutrition Examination Survey data (2013-2018; 25 investigator-specified covariates, 142 prescription-derived proxies), comparing ten pipelines combining these strategies with inverse probability of treatment weighting (IPTW) and targeted maximum likelihood estimation (TMLE). Three scenarios were evaluated under a known null (true risk difference, RD = 0): frequent, rare-exposure, and rare-outcome. We report bias, standard error (SE), relative error, 95% coverage, and runtime.
Results. HAL (G-Computation) had near-zero bias but highly concentrated estimates, giving near-unity coverage and large relative error (106-186%). OAL (IPTW), GLiDeR, and HAL (TMLE) were best calibrated, whereas the regularized-LASSO TMLE pipelines under-covered modestly (91-93%) in the rare scenarios. Under rare exposure, LASSO-IPTW had the largest bias and inflated SE and over-covered (conservatively), problems that TMLE removed. On real data, methods agreed (RD approximately 0.07-0.085). Runtimes spanned <1 s to >16 h.
Conclusions. Under a null benchmark, pairing outcome-aware selection (OAL, GLiDeR) or doubly robust estimation (TMLE) with regularized models best balanced bias, calibration, and robustness to rarity. The rare-exposure arm exposed the largest gaps; method choice should weigh the prioritized metric against compute.