Annals of Applied Statistics

Propensity score weighting for causal inference with multiple treatments

Fan Li and Fan Li

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Abstract

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.

Article information

Source
Ann. Appl. Stat., Volume 13, Number 4 (2019), 2389-2415.

Dates
Received: September 2018
Revised: June 2019
First available in Project Euclid: 28 November 2019

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1574910049

Digital Object Identifier
doi:10.1214/19-AOAS1282

Mathematical Reviews number (MathSciNet)
MR4037435

Zentralblatt MATH identifier
07160944

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

Citation

Li, Fan; Li, Fan. Propensity score weighting for causal inference with multiple treatments. Ann. Appl. Stat. 13 (2019), no. 4, 2389--2415. doi:10.1214/19-AOAS1282. https://projecteuclid.org/euclid.aoas/1574910049


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Supplemental materials

  • Supplement to “Propensity score weighting for causal inference with multiple treatments”. Supplement A: On Transitivity. We provide a detailed discussion on transitivity of the target estimands for pairwise comparisons. Supplement B: Proof of Propositions. We present detailed proofs of Propositions 1 to 3 in Section 2.3. Supplement C: Proof of Theorem 1. We provide the derivation and related discussions of the variance estimator for the generalized overlap weighting. Supplement D: Additional Simulation Results. We present additional figures and numerical results for the simulation study in Section 5.
    Digital Object Identifier: doi:10.1214/19-AOAS1282SUPP
    Supplemental files are immediately available to subscribers. Non-subscribers gain access to supplemental files with the purchase of the article.

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