Every missingness not at random model has a missingness at random counterpart with equal fit
Every missingness not at random model has a missingness at random counterpart with equal fit
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DOI：
10.1111/j.1467-9868.2007.00640.x
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发表时间：
2008-01-01
影响因子：
5.8
通讯作者：
Kenward, Michael G.
中科院分区：
文献类型：
--
作者：
Molenberghs, Geert;Beunckens, Caroline;Kenward, Michael G.
在过去的十年中，已经提出了各种模型来分析不完整的多变量和纵向数据，其中许多允许缺失不是随机的，在这个意义上说，未观察到的测量影响的过程中管理缺失，除了来自观察到的测量和/或协变量的影响。这些模型所隐含的基本问题，我们称之为对无法验证的建模假设的敏感性，反过来又引发了现在称为敏感性分析的各种研究。敏感性的本质源于这样一个事实，即非随机缺失（MNAR）模型不能从数据中完全验证，从而使MNAR和随机缺失（MAR）之间的经验区别，其中只有协变量和观察结果影响缺失，困难甚至不可能，除非我们愿意以毫无疑问的方式接受假设的MNAR模型。我们表明，MAR和MNAR之间的经验区别是不可能的，在这个意义上说，每个MNAR模型拟合一组观测数据可以完全重现MAR对应。当然，这样的一对模型会对未观察到的结果产生不同的预测，给出观察到的结果。理论上的考虑是补充说明，是根据斯洛文尼亚的民意调查，这已经在敏感性分析的背景下进行了分析。
Over the last decade a variety of models to analyse incomplete multivariate and longitudinal data have been proposed, many of which allowing for the missingness to be not at random, in the sense that the unobserved measurements influence the process governing missingness, in addition to influences coming from observed measurements and/or covariates. The fundamental problems that are implied by such models, to which we refer as sensitivity to unverifiable modelling assumptions, has, in turn, sparked off various strands of research in what is now termed sensitivity analysis. The nature of sensitivity originates from the fact that a missingness not at random (MNAR) model is not fully verifiable from the data, rendering the empirical distinction between MNAR and missingness at random (MAR), where only covariates and observed outcomes influence missingness, difficult or even impossible, unless we are willing to accept the posited MNAR model in an unquestioning way. We show that the empirical distinction between MAR and MNAR is not possible, in the sense that each MNAR model fit to a set of observed data can be reproduced exactly by an MAR counterpart. Of course, such a pair of models will produce different predictions of the unobserved outcomes, given the observed outcomes. Theoretical considerations are supplemented with an illustration that is based on the Slovenian public opinion survey, which has been analysed before in the context of sensitivity analysis.