Reducing Bias in Observational Studies Using Subclassification on the Propensity Score

TLDR

The propensity score is the conditional probability of treatment assignment given observed covariates, and subclassification on it has been theoretically shown to balance all observed covariates. This study examines the effectiveness of subclassification on the propensity score in removing bias and its balancing properties when data are incomplete. Using observational data on coronary artery disease treatments, the authors illustrate subclassification on an estimated propensity score, then apply the resulting subclasses within sub‑populations and employ model‑based adjustments to estimate treatment effects. Five subclasses defined by the estimated propensity score balance 74 covariates, enabling direct adjustment estimates of treatment effects.

Abstract

Abstract The propensity score is the conditional probability of assignment to a particular treatment given a vector of observed covariates. Previous theoretical arguments have shown that subclassification on the propensity score will balance all observed covariates. Subclassification on an estimated propensity score is illustrated, using observational data on treatments for coronary artery disease. Five subclasses defined by the estimated propensity score are constructed that balance 74 covariates, and thereby provide estimates of treatment effects using direct adjustment. These subclasses are applied within sub-populations, and model-based adjustments are then used to provide estimates of treatment effects within these sub-populations. Two appendixes address theoretical issues related to the application: the effectiveness of subclassification on the propensity score in removing bias, and balancing properties of propensity scores with incomplete data.