18  Compare results

Summary of model results

	OR	Beta-coef	coef-SE	CI (2.5 %)	CI (97.5 %)	p-value
Crude (no adjustment)	2.08	0.73	0.05	0.63	0.84	< 2e-16
PS (no proxies)	1.98	0.68	0.07	0.61	0.76	< 2e-16
hdPS	1.52	0.42	0.04	0.35	0.49	< 2e-16
Pure LASSO	1.34	0.29	0.05	0.19	0.39	5.9e-08
Hybrid (hdPS, then LASSO)	1.37	0.32	0.05	0.21	0.42	3.0e-09
Super learner (GLM, LASSO, MARS)	1.53	0.42	0.10	0.31	0.53	2.6e-14
TMLE (GLM, LASSO, MARS in SL)	1.43	0.36	0.08	0.21	0.51	4.7e-06
TMLE (only GLM in SL)	1.46	0.38	0.08	0.23	0.53	7.7e-07
Kitchen Sink	1.50	0.41	0.04	0.32	0.48	< 2e-16
Random Forest	1.54	0.43	0.04	0.35	0.51	< 2e-16
XGBoost	1.51	0.41	0.04	0.33	0.49	< 2e-16
Forward Selection	1.56	0.44	0.04	0.36	0.52	< 2e-16
Backward Elimination	1.53	0.43	0.04	0.34	0.50	< 2e-16

• PS is the result from the propensity score approach that did not include any proxies.
• Results from this approach is somewhat different than other approaches.
• More detailed results from simulations are available elsewhere (Karim 2023).

Across all methods evaluated—including hdPS, regularized regression (LASSO, Hybrid), ensemble learners (Super Learner, TMLE), and high-dimensional variable selection strategies (e.g., Kitchen Sink, Random Forest, XGBoost)—adjusted odds ratios ranged from 1.34 to 1.56, with most clustering between 1.50 and 1.56. In contrast, unadjusted and PS-only models produced substantially higher ORs (>1.9).

Karim, ME. 2023. “Rethinking Residual Confounding Bias Reduction: Why Vanilla hdPS Alone Is No Longer Enough.”