Roy Anuradha
Department of Management Science and Statistics, The University of Texas at San Antonio, 6900 N Loop 1604 West, San Antonio, Texas 78249, USA.
Biom J. 2006 Apr;48(2):286-301. doi: 10.1002/bimj.200510192.
We estimate the correlation coefficient between two variables with repeated observations on each variable, using linear mixed effects (LME) model. The solution to this problem has been studied by many authors. Bland and Altman (1995) considered the problem in many ad hoc methods. Lam, Webb and O'Donnell (1999) solved the problem by considering different correlation structures on the repeated measures. They assumed that the repeated measures are linked over time but their method needs specialized software. However, they never addressed the question of how to choose the correlation structure on the repeated measures for a particular data set. Hamlett et al. (2003) generalized this model and used Proc Mixed of SAS to solve the problem. Unfortunately, their method also cannot implement the correlation structure on the repeated measures that is present in the data. We also assume that the repeated measures are linked over time and generalize all the previous models, and can account for the correlation structure on the repeated measures that is present in the data. We study how the correlation coefficient between the variables gets affected by incorrect assumption of the correlation structure on the repeated measures itself by using Proc Mixed of SAS, and describe how to select the correlation structure on the repeated measures. We also extend the model by including random intercept and random slope over time for each subject. Our model will also be useful when some of the repeated measures are missing at random.
我们使用线性混合效应（LME）模型来估计两个具有重复观测值的变量之间的相关系数。许多作者都研究过这个问题的解决方案。布兰德和奥尔特曼（1995年）在许多临时方法中考虑了这个问题。林、韦伯和奥唐奈（1999年）通过考虑重复测量上的不同相关结构解决了这个问题。他们假设重复测量在时间上是相关联的，但他们的方法需要专门的软件。然而，他们从未解决过如何为特定数据集选择重复测量上的相关结构这一问题。哈姆雷特等人（2003年）对该模型进行了推广，并使用SAS的Proc Mixed来解决这个问题。不幸的是，他们的方法也无法实现数据中存在的重复测量上的相关结构。我们也假设重复测量在时间上是相关联的，并对所有先前的模型进行了推广，且能够考虑数据中存在的重复测量上的相关结构。我们使用SAS的Proc Mixed研究了重复测量本身的相关结构假设错误时变量之间的相关系数是如何受到影响的，并描述了如何选择重复测量上的相关结构。我们还通过为每个受试者纳入随时间变化的随机截距和随机斜率来扩展该模型。当一些重复测量值随机缺失时，我们的模型也将很有用处。
