Robust quasi-oracle semiparametric estimation of average causal effects

Abstract

Causal effects estimation is one of the central problems in real clinical data analysis. Outcome regression and inverse probability weighting are two basic strategies to estimate causal effects in observational studies. The former suffers the problem of implicitly making extrapolation and the latter encounters the problem of volatility in the presence of extreme weights (some propensity score values are close to 0 or 1), which sometimes occurs in clinical data. In this work, we propose two asymptotically equivalent semiparametric estimators of average causal effects based on propensity score. The proposed approaches apply machine learning techniques to estimate propensity score and can circumvent the problem of model extrapolation. It is easy to implement and robust to extreme weights. The proposed estimators are shown to be consistent and asymptotically normal, and the asymptotic variances can also be estimated. In addition, the proposed estimators enjoy the property of quasi-oracle: the resulting estimators of average causal effects based on estimated propensity score are asymptotically indistinguishable from the estimators with true propensity score. Simulation studies and empirical applications further demonstrate the advantages of the proposed methods compared with competing ones.

Keywords:

• Average causal effects
• propensity score
• semiparametric estimation
• machine learning
• quasi-oracle

Acknowledgments

The authors thank AE and anonymous reviewers for their helpful comments and valuable suggestions on this article.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by the National Natural Science Foundation of China [grant numbers 12026606, 81773546, 11971064 and 12171374], and the BNU-HKBU United International College Start-up Research Fund [grant number R72021106].

Notes on contributors

Peng Wu

Dr. Peng Wu is a postdoctoral student at Beijing International Center for Mathematical Research, Peking University. His research interests include causal inference, recommender systems, and policy learning.

Xingwei Tong

Dr. Xingwei Tong is now the professor of statistics at Beijing Normal University. His research interests include survival analysis, causal inference, and robust statistics. He has published more than 50 peer-reviewed articles.

Yi Wang

Dr. Yi Wang is a postdoctoral student at Beijing International Center for Mathematical Research, Peking University. His research interests cover casual inference, functional data analysis, and hypothesis testing.

Jiajuan Liang

Dr. Jiajuan Liang is now an associate professor in statistics at BNU-HKBU United International College. He worked as a tenured Associate Professor (until August 2020) in the College of Business, University of New Haven, Connecticut, U.S.A. Dr. Liang has been doing research in multivariate statistical inference, methodologies in dimension reduction in high-dimensional data analysis, and structural equation modeling. He has published more than 40 peer-reviewed articles. Dr. Liang's publications have been cited by Google Scholar more than 550 times.

Xiao-Hua Zhou

Dr. Xiao-Hua Zhou is the PKU Endowed Chair Professor, the Chair of Department of Biostatistics, the Director of Laboratory for Biostatistics and Bioinformatics, Beijing International Center for Mathematical Research in Peking University. His research interests include missing data, causal inference, semi-parametric models, big data analysis, brain science, health economics, health services research. He has published more than 200 peer-reviewed articles.