Chen Baojiang, Zhou Xiao-Hua
Department of Biostatistics, College of Public Health, University of Nebraska Medical Center, Omaha, Nebraska 68198, USA.
Biometrics. 2011 Sep;67(3):830-42. doi: 10.1111/j.1541-0420.2010.01541.x. Epub 2011 Jan 31.
Longitudinal studies often feature incomplete response and covariate data. Likelihood-based methods such as the expectation-maximization algorithm give consistent estimators for model parameters when data are missing at random (MAR) provided that the response model and the missing covariate model are correctly specified; however, 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; however, we do not need to specify the distribution of the covariates that have missing values. In this article, we develop a doubly robust estimation method for longitudinal data with missing response and missing covariate when data are MAR. 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.
纵向研究常常存在不完全的应答和协变量数据。当数据为随机缺失（MAR）时，基于似然的方法（如期望最大化算法）在应答模型和缺失协变量模型被正确设定的情况下能给出模型参数的一致估计量；然而，我们无需指定缺失数据机制。另一种方法是加权估计方程，当缺失数据和应答模型被正确设定时它能给出一致估计量；但是，我们无需指定存在缺失值的协变量的分布。在本文中，我们针对数据为MAR时存在缺失应答和缺失协变量的纵向数据开发了一种双重稳健估计方法。该方法的吸引力在于，如果缺失数据模型或缺失协变量模型被正确设定，它就能提供一致估计量。模拟研究表明该方法在各种情形下都表现良好。
