Title: Propensity score weighting for covariate balance
Balance of covariate distributions is crucial for an unconfounded descriptive or causal comparison between different groups. However, lack of overlap in the covariates is common in observational studies. We discuss weighting strategies for balancing covariates. A general class of weights --- the balancing weights --- that balance the expectation of the covariates in the treatment and the control groups is proposed. The methods rely on the propensity score and include several existing weights, such as the Horvitz-Thompson weight, as special cases. In particular, we advocate a new type of weight --- the overlap weight --- that leads to a comparison for the subpopulation with the most overlap in the covariates between two groups. We show that the overlap weight minimizes the asymptotic variances of the weighted average treatment effect among the class of balancing weights. Simulated and real examples are presented to illustrate the method and compare with the existing approaches. Comparison to matching and subclassification methods is also discussed.