Open Access
December 2019 Propensity score weighting for causal inference with multiple treatments
Fan Li, Fan Li
Ann. Appl. Stat. 13(4): 2389-2415 (December 2019). DOI: 10.1214/19-AOAS1282


Causal or unconfounded descriptive comparisons between multiple groups are common in observational studies. Motivated from a racial disparity study in health services research, we propose a unified propensity score weighting framework, the balancing weights, for estimating causal effects with multiple treatments. These weights incorporate the generalized propensity scores to balance the weighted covariate distribution of each treatment group, all weighted toward a common prespecified target population. The class of balancing weights include several existing approaches such as the inverse probability weights and trimming weights as special cases. Within this framework, we propose a set of target estimands based on linear contrasts. We further develop the generalized overlap weights, constructed as the product of the inverse probability weights and the harmonic mean of the generalized propensity scores. The generalized overlap weighting scheme corresponds to the target population with the most overlap in covariates across the multiple treatments. 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 moment weighting estimators for the pairwise contrasts within the class of balancing weights. We consider two balance check criteria and propose a new sandwich variance estimator for estimating the causal effects with generalized overlap weights. We apply these methods to study the racial disparities in medical expenditure between several racial groups using the 2009 Medical Expenditure Panel Survey (MEPS) data. Simulations were carried out to compare with existing methods.


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Fan Li. Fan Li. "Propensity score weighting for causal inference with multiple treatments." Ann. Appl. Stat. 13 (4) 2389 - 2415, December 2019.


Received: 1 September 2018; Revised: 1 June 2019; Published: December 2019
First available in Project Euclid: 28 November 2019

zbMATH: 07160944
MathSciNet: MR4037435
Digital Object Identifier: 10.1214/19-AOAS1282

Keywords: Balancing weights , generalized overlap weights , generalized propensity score , health services research , pairwise comparison , racial disparity

Rights: Copyright © 2019 Institute of Mathematical Statistics

Vol.13 • No. 4 • December 2019
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