Taylor J M, Law N
Department of Biostatistics, University of California, Los Angeles 90095-1772, USA.
Stat Med. 1998 Oct 30;17(20):2381-94. doi: 10.1002/(sici)1097-0258(19981030)17:20<2381::aid-sim926>3.0.co;2-s.
We investigate the importance of the assumed covariance structure for longitudinal modelling of CD4 counts. We examine how individual predictions of future CD4 counts are affected by the covariance structure. We consider four covariance structures: one based on an integrated Ornstein-Uhlenbeck stochastic process; one based on Brownian motion, and two derived from standard linear and quadratic random-effects models. Using data from the Multicenter AIDS Cohort Study and from a simulation study, we show that there is a noticeable deterioration in the coverage rate of confidence intervals if we assume the wrong covariance. There is also a loss in efficiency. The quadratic random-effects model is found to be the best in terms of correctly calibrated prediction intervals, but is substantially less efficient than the others. Incorrectly specifying the covariance structure as linear random effects gives too narrow prediction intervals with poor coverage rates. Fitting using the model based on the integrated Ornstein-Uhlenbeck stochastic process is the preferred one of the four considered because of its efficiency and robustness properties. We also use the difference between the future predicted and observed CD4 counts to assess an appropriate transformation of CD4 counts; a fourth root, cube root and square root all appear reasonable choices.
我们研究了假定的协方差结构在CD4细胞计数纵向建模中的重要性。我们考察了协方差结构如何影响对未来CD4细胞计数的个体预测。我们考虑了四种协方差结构：一种基于积分奥恩斯坦-乌伦贝克随机过程；一种基于布朗运动，还有两种源自标准线性和二次随机效应模型。利用多中心艾滋病队列研究的数据以及一项模拟研究的数据，我们表明，如果我们假设了错误的协方差，置信区间的覆盖率会有明显下降。效率也会有所损失。就预测区间校准正确而言，二次随机效应模型被发现是最佳的，但比其他模型的效率要低得多。将协方差结构错误地指定为线性随机效应会导致预测区间过窄且覆盖率不佳。基于积分奥恩斯坦-乌伦贝克随机过程的模型拟合是所考虑的四种模型中首选的，因为它具有效率和稳健性。我们还利用未来预测CD4细胞计数与观察到的CD4细胞计数之间的差异来评估CD4细胞计数的合适变换；四次方根、立方根和平方根似乎都是合理的选择。
