Missing responses are common problems in medical, social, and economic
studies. When responses are missing at random, a complete-case data analysis may
result in biases. A popular debias method is inverse probability weighting (IPW)
proposed by Horvitz and Thompson [1]. To improve efficiency, Robins et al.
[2, 3] proposed an augmented inverse probability
weighting (AIPW) method. The AIPW estimator has a double-robustness property and
achieves the semiparametric efficiency lower bound when the regression model and
propensity score model are both correctly specified. In this paper, we introduce
an empirical-likelihood-based estimator as an alternative to Qin and Zhang
[4]. Our proposed
estimator is also doubly robust and locally efficient. Simulation results show
that the proposed estimator has better performance when the propensity score is
correctly modeled. Moreover, the proposed method can be applied in the
estimation of average treatment effect in observational causal inferences.
Finally, we apply our method to an observational study of smoking, using data
from the Cardiovascular Outcomes in Renal Atherosclerotic Lesions (CORAL)
clinical trial [5].