Balancing Covariates via Propensity Score Weighting

TL;DR

This paper introduces a unified class of weighting methods, including a novel overlap weighting scheme, to improve covariate balance in observational studies for more accurate causal inference.

Contribution

It unifies existing weighting methods under a general framework and proposes the overlap weights that optimize variance and balance properties.

Findings

Overlap weights minimize asymptotic variance of treatment effect estimates.

Overlap weights are bounded and achieve exact covariate balance.

Applications demonstrate improved covariate balance compared to other methods.

Abstract

Covariate balance is crucial for unconfounded descriptive or causal comparisons. However, lack of balance is common in observational studies. This article considers weighting strategies for balancing covariates. We define a general class of weights---the balancing weights---that balance the weighted distributions of the covariates between treatment groups. These weights incorporate the propensity score to weight each group to an analyst-selected target population. This class unifies existing weighting methods, including commonly used weights such as inverse-probability weights as special cases. General large-sample results on nonparametric estimation based on these weights are derived. We further propose a new weighting scheme, the overlap weights, in which each unit's weight is proportional to the probability of that unit being assigned to the opposite group. The overlap weights are bounded, and minimize the asymptotic variance of the weighted average treatment effect among the class of balancing weights. The overlap weights also possess a desirable small-sample exact balance property, based on which we propose a new method that achieves exact balance for means of any selected set of covariates. Two applications illustrate these methods and compare them with other approaches.