1 Department of Population and Quantitative Health Sciences, Case Western Reserve University, Cleveland, OH, USA.
2 School of Mathematics and Statistics, Carleton University, Ottawa, ON, Canada.
Stat Methods Med Res. 2019 Feb;28(2):486-502. doi: 10.1177/0962280217729573. Epub 2017 Sep 28.
We develop and study an innovative method for jointly modeling longitudinal response and time-to-event data with a covariate subject to a limit of detection. The joint model assumes a latent process based on random effects to describe the association between longitudinal and time-to-event data. We study the role of the association parameter on the regression parameters estimators. We model the longitudinal and survival outcomes using linear mixed-effects and Weibull frailty models, respectively. Because of the limit of detection, missing covariate (explanatory variable, x) values may lead to the non-ignorable missing, resulting in biased parameter estimates with poor coverage probabilities of the confidence interval. We define and estimate the probability of missing due to the limit of detection. Then we develop a novel joint density and hence the likelihood function that incorporates the effect of left-censored covariate. Monte Carlo simulations show that the estimators of the proposed method are approximately unbiased and provide expected coverage probabilities for both longitudinal and survival submodels parameters. We also present an application of the proposed method using a large clinical dataset of pneumonia patients obtained from the Genetic and Inflammatory Markers of Sepsis study.
我们开发并研究了一种创新方法，用于联合建模具有检测极限的协变量的纵向响应和生存数据。联合模型假设基于随机效应的潜在过程来描述纵向和生存数据之间的关联。我们研究了关联参数对回归参数估计的作用。我们分别使用线性混合效应和 Weibull 脆弱性模型对纵向和生存结果进行建模。由于检测极限，缺失的协变量（解释变量，x）值可能导致不可忽略的缺失，从而导致参数估计有偏差，置信区间的覆盖率较差。我们定义并估计由于检测极限导致的缺失的概率。然后，我们开发了一种新的联合密度，从而得到了包含左截断协变量影响的似然函数。蒙特卡罗模拟表明，所提出方法的估计量是近似无偏的，并为纵向和生存子模型参数提供了预期的覆盖率概率。我们还使用从遗传和炎症标志物脓毒症研究中获得的肺炎患者的大型临床数据集介绍了所提出方法的应用。
