Albert Einstein College of Medicine, 1300 Morris Park Ave, Bronx, NY 10461, USA.
Stat Med. 2010 Mar 15;29(6):671-9. doi: 10.1002/sim.3821.
Missing data are common in longitudinal studies due to drop-out, loss to follow-up, and death. Likelihood-based mixed effects models for longitudinal data give valid estimates when the data are missing at random (MAR). These assumptions, however, are not testable without further information. In some studies, there is additional information available in the form of an auxiliary variable known to be correlated with the missing outcome of interest. Availability of such auxiliary information provides us with an opportunity to test the MAR assumption. If the MAR assumption is violated, such information can be utilized to reduce or eliminate bias when the missing data process depends on the unobserved outcome through the auxiliary information. We compare two methods of utilizing the auxiliary information: joint modeling of the outcome of interest and the auxiliary variable, and multiple imputation (MI). Simulation studies are performed to examine the two methods. The likelihood-based joint modeling approach is consistent and most efficient when correctly specified. However, mis-specification of the joint distribution can lead to biased results. MI is slightly less efficient than a correct joint modeling approach and can also be biased when the imputation model is mis-specified, though it is more robust to mis-specification of the imputation distribution when all the variables affecting the missing data mechanism and the missing outcome are included in the imputation model. An example is presented from a dementia screening study.
由于脱落、失访和死亡，缺失数据在纵向研究中很常见。当数据是随机缺失（MAR）时，基于似然的混合效应模型可以对纵向数据进行有效估计。然而，在没有进一步信息的情况下，这些假设是无法检验的。在某些研究中，以辅助变量的形式提供了额外的信息，这些辅助变量与缺失的感兴趣结局相关。这种辅助信息的可用性为我们提供了一个检验 MAR 假设的机会。如果 MAR 假设被违反，那么当缺失数据过程通过辅助信息依赖于未观察到的结局时，这种信息可以被用来减少或消除偏差。我们比较了利用辅助信息的两种方法：感兴趣结局和辅助变量的联合建模，以及多重插补（MI）。进行了模拟研究来检验这两种方法。基于似然的联合建模方法在正确指定时是一致和最有效的。然而，联合分布的错误指定可能会导致有偏的结果。MI 比正确的联合建模方法效率略低，并且当插补模型错误指定时也可能有偏，尽管当所有影响缺失数据机制和缺失结局的变量都包含在插补模型中时，它对插补分布的错误指定更稳健。从一个痴呆症筛查研究中给出了一个示例。
