Doubly robust estimation of the causal effects in the causal inference with missing outcome data

The goal of this article is to attempt to develop doubly robust (DR) estimator in the causal inference with ignorable missing outcome data. In the causal inference with missing outcome data, an estimator is doubly robust if it remains consistent and asymptotically normal (CAN) when either (but not necessarily both) a model for the treatment assignment mechanism or a model for the regression is correctly specified. We also derive an explicit expression for the asymptotic variance of the proposed DR estimator using the delta-method. Simulation studies show that the doubly robust estimator of the causal effect which was constructed by us, compared to the estimator from the inverse probability weighting method or regression method, has better statistical properties in terms of bias and mean squared error (MSE); the values calculated from the asymptotic variance of our proposed estimator and the empirical variance are relatively close. We by simulation studies also prove that our proposed estimator and its asymptotic variance are correct and have good applicability and excellent efficacy. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.