Bartlett Jonathan W, Carpenter James R, Tilling Kate, Vansteelandt Stijn
Centre for Statistical Methodology, London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, UK
Centre for Statistical Methodology, London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, UK and MRC Clinical Trial Trials Unit, Kingsway, London WC2B 6NH, UK.
Biostatistics. 2014 Oct;15(4):719-30. doi: 10.1093/biostatistics/kxu023. Epub 2014 Jun 6.
Missing values in covariates of regression models are a pervasive problem in empirical research. Popular approaches for analyzing partially observed datasets include complete case analysis (CCA), multiple imputation (MI), and inverse probability weighting (IPW). In the case of missing covariate values, these methods (as typically implemented) are valid under different missingness assumptions. In particular, CCA is valid under missing not at random (MNAR) mechanisms in which missingness in a covariate depends on the value of that covariate, but is conditionally independent of outcome. In this paper, we argue that in some settings such an assumption is more plausible than the missing at random assumption underpinning most implementations of MI and IPW. When the former assumption holds, although CCA gives consistent estimates, it does not make use of all observed information. We therefore propose an augmented CCA approach which makes the same conditional independence assumption for missingness as CCA, but which improves efficiency through specification of an additional model for the probability of missingness, given the fully observed variables. The new method is evaluated using simulations and illustrated through application to data on reported alcohol consumption and blood pressure from the US National Health and Nutrition Examination Survey, in which data are likely MNAR independent of outcome.
回归模型协变量中的缺失值是实证研究中普遍存在的问题。分析部分观测数据集的常用方法包括完全病例分析（CCA）、多重填补（MI）和逆概率加权（IPW）。在协变量值缺失的情况下，这些方法（通常的实现方式）在不同的缺失性假设下是有效的。特别是，CCA在非随机缺失（MNAR）机制下是有效的，在这种机制中，协变量的缺失取决于该协变量的值，但与结果有条件地独立。在本文中，我们认为在某些情况下，这样的假设比支撑MI和IPW大多数实现方式的随机缺失假设更合理。当前者假设成立时，虽然CCA给出了一致的估计，但它没有利用所有观测到的信息。因此，我们提出了一种增强的CCA方法，该方法对缺失性做出与CCA相同的条件独立性假设，但通过为给定完全观测变量的缺失概率指定一个额外的模型来提高效率。使用模拟对新方法进行了评估，并通过应用于美国国家健康和营养检查调查中报告的酒精消费和血压数据进行了说明，在该数据中，数据可能是与结果无关的MNAR。
