TY - JOUR

T1 - A distributional approach for causal inference using propensity scores

AU - Tan, Zhiqiang

N1 - Funding Information:
Zhiqiang Tan is Assistant Professor, Department of Biostatistics, Bloomberg School of Public Health, Johns Hopkins University, Baltimore, MD 21205 (E-mail: ztan@jhsph.edu). This research is supported by a Faculty Innovation Fund from the school. The author thanks Tom Louis, James Robins, and Dan Scharfstein for valuable discussions, Constantine Frangakis and Chuck Rhode for helpful comments, and the editor and an associate editor for handling the review.

PY - 2006/12

Y1 - 2006/12

N2 - Drawing inferences about the effects of treatments and actions is a common challenge in economics, epidemiology, and other fields. We adopt Rubin's potential outcomes framework for causal inference and propose two methods serving complementary purposes. One can be used to estimate average causal effects, assuming no confounding given measured covariates. The other can be used to assess how the estimates might change under various departures from no confounding. Both methods are developed from a nonparametric likelihood perspective. The propensity score plays a central role and is estimated through a parametric model. Under the assumption of no confounding, the joint distribution of covariates and each potential outcome is estimated as a weighted empirical distribution. Expectations from the joint distribution are estimated as weighted averages or, equivalently to first order, regression estimates. The likelihood estimator is at least as efficient and the regression estimator is at least as efficient and robust as existing estimators. Regardless of the no-confounding assumption, the marginal distribution of covariates times the conditional distribution of observed outcome given each treatment assignment and covariates is estimated. For a fixed bound on unmeasured confounding, the marginal distribution of covariates times the conditional distribution of counterfactual outcome given each treatment assignment and covariates is explored to the extreme and then compared with the composite distribution corresponding to observed outcome given the same treatment assignment and covariates. We illustrate the methods by analyzing the data from an observational study on right heart catheterization.

AB - Drawing inferences about the effects of treatments and actions is a common challenge in economics, epidemiology, and other fields. We adopt Rubin's potential outcomes framework for causal inference and propose two methods serving complementary purposes. One can be used to estimate average causal effects, assuming no confounding given measured covariates. The other can be used to assess how the estimates might change under various departures from no confounding. Both methods are developed from a nonparametric likelihood perspective. The propensity score plays a central role and is estimated through a parametric model. Under the assumption of no confounding, the joint distribution of covariates and each potential outcome is estimated as a weighted empirical distribution. Expectations from the joint distribution are estimated as weighted averages or, equivalently to first order, regression estimates. The likelihood estimator is at least as efficient and the regression estimator is at least as efficient and robust as existing estimators. Regardless of the no-confounding assumption, the marginal distribution of covariates times the conditional distribution of observed outcome given each treatment assignment and covariates is estimated. For a fixed bound on unmeasured confounding, the marginal distribution of covariates times the conditional distribution of counterfactual outcome given each treatment assignment and covariates is explored to the extreme and then compared with the composite distribution corresponding to observed outcome given the same treatment assignment and covariates. We illustrate the methods by analyzing the data from an observational study on right heart catheterization.

KW - Causal inference

KW - Control variate

KW - Nonparametric likelihood

KW - Observational study

KW - Propensity score

KW - Sensitivity analysis

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U2 - 10.1198/016214506000000023

DO - 10.1198/016214506000000023

M3 - Article

AN - SCOPUS:33846066470

VL - 101

SP - 1619

EP - 1637

JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

SN - 0162-1459

IS - 476

ER -