Department of Biostatistics, Amgen Inc., Thousand Oaks, CA, USA.
Stat Med. 2011 Aug 30;30(19):2435-50. doi: 10.1002/sim.4294. Epub 2011 Jul 12.
We address statistical issues regarding modeling a collection of longitudinal response trajectories characterized by the presence of subject-specific phase-dependent effects and variation. To accommodate these two time-varying individual characteristics, we employ a geometric stochastic differential equation for modeling based on a Brownian motion process and develop a two-step paradigm for statistical analysis. This paradigm reverses the order of statistical inference in random effects model. We first extract individual information about phase-dependent treatment effects and volatility parameters for all subjects. Then, we derive the association relationship between the parameters characterizing the individual longitudinal trajectories and the corresponding covariates by means of multiple regression analysis. The stochastic differential equation model and the two-step paradigm together provide significant advantages both in modeling flexibility and in computational efficiency. The modeling flexibility is due to the easy adaptation of temporal change points for subject-specific phase transition in treatment effects, whereas the computational efficiency benefits in part from the independent increment property of Brownian motion that avoids high-dimensional integration. We demonstrate our modeling approach and statistical analysis on a real data set of longitudinal measurements of disease activity scores from a rheumatoid arthritis study.
我们解决了与建模一组具有个体特定相位相关效应和变异性的纵向响应轨迹相关的统计问题。为了适应这两个随时间变化的个体特征，我们基于布朗运动过程采用了几何随机微分方程进行建模，并开发了一种两步统计分析范式。该范式反转了随机效应模型中统计推断的顺序。我们首先为所有受试者提取关于与相位相关的治疗效果和波动率参数的个体信息。然后，我们通过多元回归分析推导出描述个体纵向轨迹的参数与相应协变量之间的关联关系。随机微分方程模型和两步范式在建模灵活性和计算效率方面都具有显著优势。建模灵活性归因于易于适应治疗效果中个体特定相位转换的时间变化点，而计算效率的提高部分得益于布朗运动的独立增量特性，避免了高维积分。我们在来自类风湿关节炎研究的疾病活动评分的纵向测量的真实数据集上演示了我们的建模方法和统计分析。
