Missing data is a very common problem in medical and social studies, especially when data are collected longitudinally. It is a challenging problem to utilize observed data effectively. Many papers on missing data problems can be found in statistical literature. It is well known that the inverse weighted estimation is neither efficient nor robust. On the other hand, the doubly robust (DR) method can improve the efficiency and robustness. As is known, the DR estimation requires a missing data model (i.e., a model for the probability that data are observed) and a working regression model (i.e., a model for the outcome variable given covariates and surrogate variables). Because the DR estimating function has mean zero for any parameters in the working regression model when the missing data model is correctly specified, in this paper, we derive a formula for the estimator of the parameters of the working regression model that yields the optimally efficient estimator of the marginal mean model (the parameters of interest) when the missing data model is correctly specified. Furthermore, the proposed method also inherits the DR property. Simulation studies demonstrate the greater efficiency of the proposed method compared with the standard DR method. A longitudinal dementia data set is used for illustration.

译文

缺少数据是医学和社会研究中非常普遍的问题,尤其是在纵向收集数据时。有效利用观测数据是一个具有挑战性的问题。在统计文献中可以找到许多有关缺失数据问题的论文。众所周知,逆加权估计既不有效也不稳健。另一方面,双鲁棒 (DR) 方法可以提高效率和鲁棒性。众所周知,DR估计需要缺失数据模型 (即,用于观察到数据的概率的模型) 和工作回归模型 (即,用于给定协变量和替代变量的结果变量的模型)。由于当正确指定缺失数据模型时,DR估计函数对于工作回归模型中的任何参数均为零,因此,我们推导了工作回归模型参数估计器的公式,该公式可在正确指定缺失数据模型时得出边际均值模型 (感兴趣的参数) 的最佳有效估计器。此外,所提出的方法还继承了DR属性。仿真研究表明,与标准DR方法相比,该方法具有更高的效率。纵向痴呆症数据集用于说明。

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