Wang Chenguang, Daniels Michael J
Division of Biostatistics, Center for Devices and Radiological Health, FDA, Silver Spring, Maryland 20993, USA.
Biometrics. 2011 Sep;67(3):810-8. doi: 10.1111/j.1541-0420.2011.01565.x. Epub 2011 Mar 1.
Pattern mixture modeling is a popular approach for handling incomplete longitudinal data. Such models are not identifiable by construction. Identifying restrictions is one approach to mixture model identification (Little, 1995, Journal of the American Statistical Association 90, 1112-1121; Little and Wang, 1996, Biometrics 52, 98-111; Thijs et al., 2002, Biostatistics 3, 245-265; Kenward, Molenberghs, and Thijs, 2003, Biometrika 90, 53-71; Daniels and Hogan, 2008, in Missing Data in Longitudinal Studies: Strategies for Bayesian Modeling and Sensitivity Analysis) and is a natural starting point for missing not at random sensitivity analysis (Thijs et al., 2002, Biostatistics 3, 245-265; Daniels and Hogan, 2008, in Missing Data in Longitudinal Studies: Strategies for Bayesian Modeling and Sensitivity Analysis). However, when the pattern specific models are multivariate normal, identifying restrictions corresponding to missing at random (MAR) may not exist. Furthermore, identification strategies can be problematic in models with covariates (e.g., baseline covariates with time-invariant coefficients). In this article, we explore conditions necessary for identifying restrictions that result in MAR to exist under a multivariate normality assumption and strategies for identifying sensitivity parameters for sensitivity analysis or for a fully Bayesian analysis with informative priors. In addition, we propose alternative modeling and sensitivity analysis strategies under a less restrictive assumption for the distribution of the observed response data. We adopt the deviance information criterion for model comparison and perform a simulation study to evaluate the performances of the different modeling approaches. We also apply the methods to a longitudinal clinical trial. Problems caused by baseline covariates with time-invariant coefficients are investigated and an alternative identifying restriction based on residuals is proposed as a solution.
模式混合建模是处理不完全纵向数据的一种常用方法。此类模型从构建上看是不可识别的。识别约束是混合模型识别的一种方法（利特尔，1995年，《美国统计协会杂志》90卷，1112 - 1121页；利特尔和王，1996年，《生物统计学》52卷，98 - 111页；蒂伊斯等人，2002年，《生物统计学》3卷，245 - 265页；肯沃德、莫伦伯格斯和蒂伊斯，2003年，《生物计量学》90卷，53 - 71页；丹尼尔斯和霍根，2008年，《纵向研究中的缺失数据：贝叶斯建模与敏感性分析策略》），并且是随机缺失敏感性分析的自然起点（蒂伊斯等人，2002年，《生物统计学》3卷，245 - 265页；丹尼尔斯和霍根，2008年，《纵向研究中的缺失数据：贝叶斯建模与敏感性分析策略》）。然而，当模式特定模型为多元正态时，可能不存在与随机缺失（MAR）相对应的识别约束。此外，在具有协变量的模型中（例如，具有时不变系数的基线协变量），识别策略可能会出现问题。在本文中，我们探讨了在多元正态性假设下导致MAR存在的识别约束所需的条件，以及用于敏感性分析或具有信息先验的完全贝叶斯分析的敏感性参数识别策略。此外，我们在对观测响应数据分布的限制较少的假设下，提出了替代建模和敏感性分析策略。我们采用偏差信息准则进行模型比较，并进行模拟研究以评估不同建模方法的性能。我们还将这些方法应用于一项纵向临床试验。研究了具有时不变系数的基线协变量所导致的问题，并提出了一种基于残差的替代识别约束作为解决方案。
