Estimating treatment effects in the presence of unobserved confounders

Abstract

Treatment effects estimation is one of the crucial mainstays in medical and epidemiological studies. Ignorance of the existence of confounders may result in biased estimators. The issue will become more serious and complicated if the treatment is endogenous (i.e., the presence of unobserved confounders). In this article, we propose a new treatment effects estimator for binary treatments in observational studies in the presence of unobserved confounders. The proposed estimator is consistent and asymptotically normally distributed. A statistic is also developed for testing the existence of treatment effects. Simulation studies show that the proposed estimator is stable for various unobserved confounding settings and the distribution of error terms. Finally, we apply our proposed methodologies to a low birthweight data set which yields different conclusions with and without the consideration of possible unobserved confounders.

Keywords:

• Discrete models
• Heterogeneity
• Observational studies
• Treatment effects
• Unobserved confounders

Acknowledgments

The authors thank referees, editors, and associate editors for their constructive comments and suggestions, which improve the manuscript significantly. Gao’s research is supported by the National Natural Science Foundation of China (11471068 and 11871141).