An Alternative Doubly Robust Estimation in Causal Inference Model

Doubly robust (DR) methods that employ both the propensity score and outcome models are widely used to estimate the causal effect of a treatment and generally outperform those methods only using the propensity score or the outcome model. However, without appropriately chosen the working models, DR estimators may substantially lose efficiency. In this paper, based on the augmented inverse probability weighting procedure, we derive a new estimating equation for the causal effect by the strategy of combining estimating equations. The resulting estimator by solving the new estimating equation retains doubly robust and can improve the efficiency under the misspecification of conditional mean working model. We further show the large sample properties of the proposed estimator under some regularity conditions. Through simulation experiments and a real data analysis, we illustrate that the proposed method is competitive with its competitors, which is in line with those implied by the asymptotic theory.