Hughes Rachael A, Kenward Michael G, Sterne Jonathan A C, Tilling Kate
School of Social and Community Medicine, University of Bristol, Bristol, UK.
Department of Medical Statistics, London School of Hygiene and Tropical Medicine, London, UK.
J Stat Comput Simul. 2017 May 24;87(8):1541-1558. doi: 10.1080/00949655.2016.1277425. Epub 2017 Jan 12.
The linear mixed model with an added integrated Ornstein-Uhlenbeck (IOU) process (linear mixed IOU model) allows for serial correlation and estimation of the degree of derivative tracking. It is rarely used, partly due to the lack of available software. We implemented the linear mixed IOU model in Stata and using simulations we assessed the feasibility of fitting the model by restricted maximum likelihood when applied to balanced and unbalanced data. We compared different (1) optimization algorithms, (2) parameterizations of the IOU process, (3) data structures and (4) random-effects structures. Fitting the model was practical and feasible when applied to large and moderately sized balanced datasets (20,000 and 500 observations), and large unbalanced datasets with (non-informative) dropout and intermittent missingness. Analysis of a real dataset showed that the linear mixed IOU model was a better fit to the data than the standard linear mixed model (i.e. independent within-subject errors with constant variance).
带有附加积分奥恩斯坦-乌伦贝克（IOU）过程的线性混合模型（线性混合IOU模型）允许进行序列相关性分析以及对导数跟踪程度的估计。该模型很少被使用，部分原因是缺乏可用的软件。我们在Stata中实现了线性混合IOU模型，并通过模拟评估了在应用于平衡和不平衡数据时使用受限最大似然法拟合该模型的可行性。我们比较了不同的（1）优化算法、（2）IOU过程的参数化、（3）数据结构和（4）随机效应结构。当应用于大型和中型平衡数据集（20,000和500个观测值）以及具有（非信息性）缺失和间歇性缺失的大型不平衡数据集时，拟合该模型是切实可行的。对一个真实数据集的分析表明，线性混合IOU模型比标准线性混合模型（即具有恒定方差的独立受试者内误差）更适合该数据。
