Longitudinal studies often feature incomplete response and covariate data. Likelihood-based methods such as the EM algorithm give consistent estimators for model parameters when data are missing at random provided that the response model and the missing covariate model are correctly specified; but we do not need to specify the missing data mechanism. An alternative method is the weighted estimating equation which gives consistent estimators if the missing data and response models are correctly specified; but we do not need to specify the distribution of the covariates that have missing values. In this paper we develop a doubly robust estimation method for longitudinal data with missing response and missing covariate when data are missing at random. This method is appealing in that it can provide consistent estimators if either the missing data model or the missing covariate model is correctly specified. Simulation studies demonstrate that this method performs well in a variety of situations.
Chen, Baojiang and Zhou, Xiao-Hua, "Doubly Robust Estimates for Binary Longitudinal Data Analysis with Missing Response and Missing Covariates" (January 2011). UW Biostatistics Working Paper Series. Working Paper 373.