1 Department of Population and Quantitative Health Sciences, Case Western Reserve University, Cleveland, OH, USA.
2 Department of Mathematics and Statistics, University of Wyoming, Laramie, WY, USA.
Stat Methods Med Res. 2019 May;28(5):1489-1507. doi: 10.1177/0962280218764193. Epub 2018 Apr 4.
Many longitudinal studies observe time to occurrence of a clinical event such as death, while also collecting serial measurements of one or more biomarkers that are predictive of the event, or are surrogate outcomes of interest. Joint modeling can be used to examine the relationship between the biomarker and the event, and also as a way of adjusting analyses of the biomarker for non-ignorable dropout. In settings such as registry studies, an additional complexity is caused when follow-up of subjects is delayed, referred to as left-truncation of follow-up in the survival analysis setting. If not adjusted for, this can cause bias in estimation of parameters of the survival distribution for the clinical event and in parameters of the longitudinal outcome such as the profile or rate of change over time because subjects may die or have the clinical event before follow-up starts. This paper illustrates how a broad class of shared parameter models can be used to jointly model a time to event outcome along with a longitudinal marker using available nonlinear mixed modeling software, when follow-up times are left truncated. Methods are applied to jointly model survival and decline in lung function in cystic fibrosis patients.
许多纵向研究观察临床事件（如死亡）的发生时间，同时还收集一个或多个预测事件或感兴趣的替代结局的生物标志物的系列测量值。联合建模可用于检查生物标志物与事件之间的关系，以及作为调整生物标志物分析以处理不可忽略的缺失数据的一种方法。在注册研究等环境中，当对受试者的随访延迟时，会出现一个额外的复杂性，在生存分析环境中称为随访的左截断。如果不进行调整，这可能会导致对临床事件生存分布的参数和对纵向结局（如随时间变化的曲线或变化率）的参数的估计产生偏差，因为受试者可能在随访开始之前死亡或发生临床事件。本文说明了如何在可用的非线性混合建模软件中，当随访时间存在左截断时，使用广泛的共享参数模型类来联合建模时间事件结果和纵向标记物。该方法应用于联合建模囊性纤维化患者的生存和肺功能下降。
