A comparison of doubly robust estimators of the mean with missing data

We consider data with a continuous outcome that is missing at random and a fully observed set of covariates. We compare by simulation a variety of doubly-robust (DR) estimators for estimating the mean of the outcome. An estimator is DR if it is consistent when either the regression model for the mean function or the propensity to respond is correctly specified. Performance of different methods is compared in terms of root mean squared error of the estimates and width and coverage of confidence intervals or posterior credibility intervals in repeated samples. Overall, the DR methods tended to yield better inference than the incorrect model when either the propensity or mean model is correctly specified, but were less successful for small sample sizes, where the asymptotic DR property is less consequential. Two methods tended to outperform the other DR methods: penalized spline of propensity prediction [Little RJA, An H. Robust likelihood-based analysis of multivariate data with missing values. Statist Sinica. 2004;14:949-968] and the robust method proposed in [Cao W, Tsiatis AA, Davidian M. Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data. Biometrika. 2009;96:723-734].