Robust quasi-oracle semiparametric estimation of average causal effects

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.