Zhang Peng, Song Peter X-K, Qu Annie, Greene Tom
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada.
Biometrics. 2008 Mar;64(1):29-38. doi: 10.1111/j.1541-0420.2007.00824.x. Epub 2007 May 14.
This article presents a new class of nonnormal linear mixed models that provide an efficient estimation of subject-specific disease progression in the analysis of longitudinal data from the Modification of Diet in Renal Disease (MDRD) trial. This new analysis addresses the previously reported finding that the distribution of the random effect characterizing disease progression is negatively skewed. We assume a log-gamma distribution for the random effects and provide the maximum likelihood inference for the proposed nonnormal linear mixed model. We derive the predictive distribution of patient-specific disease progression rates, which demonstrates rather different individual progression profiles from those obtained from the normal linear mixed model analysis. To validate the adequacy of the log-gamma assumption versus the usual normality assumption for the random effects, we propose a lack-of-fit test that clearly indicates a better fit for the log-gamma modeling in the analysis of the MDRD data. The full maximum likelihood inference is also advantageous in dealing with the missing at random (MAR) type of dropouts encountered in the MDRD data.
本文提出了一类新的非正态线性混合模型，该模型在分析来自肾脏疾病饮食改良（MDRD）试验的纵向数据时，能有效地估计个体特定的疾病进展情况。这项新的分析解决了先前报告的一个发现，即表征疾病进展的随机效应分布呈负偏态。我们假设随机效应服从对数伽马分布，并为所提出的非正态线性混合模型提供最大似然推断。我们推导出了患者特定疾病进展率的预测分布，这表明其个体进展情况与从正态线性混合模型分析中得到的结果有很大不同。为了验证随机效应采用对数伽马假设与通常的正态假设相比是否合适，我们提出了一个失拟检验，该检验清楚地表明在MDRD数据分析中对数伽马模型拟合得更好。完全最大似然推断在处理MDRD数据中遇到的随机缺失（MAR）类型的失访情况时也具有优势。
