Beyond Single-Score Matching: A Two-Dimensional Propensity Score Method for Mixed Covariate Types

Propensity score matching (PSM) reduces confounding bias in observational studies, yet traditional single-score approaches assume linear covariate-treatment relationships. This assumption often fails when applied to complex electronic health record data that contain mixed categorical and continuous variables and nonlinear interactions. We introduce two-dimensional PSM (2D-PSM), which estimates separate propensity scores for categorical and numerical confounders and then performs matching in two-dimensional space under an elliptical caliper constraint. We compared 2D-PSM with traditional single-score PSM using five machine learning classifiers across 5 real-world (RW) clinical datasets (n = 460 - 61,926) and 21 synthetic datasets (n = 10,000) with systematically varied confounder complexity and categorical-to-continuous ratios. Matching employed 1:1 greedy nearest-neighbor algorithm with adaptive calipers (0.1× to 0.5× propensity score interquartile range). Balance was assessed using univariate and multivariate metrics. In multivariate assessment and the smallest caliper (0.1), 2D-PSM performed comparably to conventional PSM on RW datasets and consistently outperformed it in synthetic data experiments. With larger calipers, 2D-PSM outperformed single-score methods in 85% of datasets. Our 2D-PSM approach provides superior multivariate balance for datasets with heterogeneous covariate types and complex interactions, particularly with moderate calipers.