Propensity Score Weighting for Causal Inference with Multi-valued Treatments
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This article proposes a unified framework, the balancing weights, for estimating causal effects with multi-valued treatments using propensity score weighting. These weights incorporate the generalized propensity score to balance the weighted covariate distribution of each treatment group, all weighted toward a common pre-specified target population. The class of balancing weights include several existing approaches such as inverse probability weights and trimming weights as special cases. Within this framework, we propose a class of target estimands based on linear contrasts and their corresponding nonparametric weighting estimators. We further propose the generalized overlap weights, constructed as the product of the inverse probability weights and the harmonic mean of the generalized propensity scores, to focus on the target population with the most overlap in covariates. These weights are bounded and thus bypass the problem of extreme propensities. We show that the generalized overlap weights minimize the total asymptotic variance of the nonparametric estimators for the pairwise contrasts within the class of balancing weights. We also develop two new balance check criteria and a sandwich variance estimator for estimating the causal effects with generalized overlap weights. We illustrate these methods by simulations and apply them to study the racial disparities in medical expenditure.
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