Albert Paul S, Shih Joanna H
Biostatistics and Bioinformatics Branch, Division of Epidemiology, Statistics, and Prevention Research, Eunice Kennedy Shriver National Institute of Child Health and Human Development, Bethesda, Maryland 20892, USA.
Biometrics. 2010 Sep;66(3):983-7; discussion 987-91. doi: 10.1111/j.1541-0420.2009.01324_1.x.
Ye, Lin, and Taylor (2008, Biometrics 64, 1238-1246) proposed a joint model for longitudinal measurements and time-to-event data in which the longitudinal measurements are modeled with a semiparametric mixed model to allow for the complex patterns in longitudinal biomarker data. They proposed a two-stage regression calibration approach that is simpler to implement than a joint modeling approach. In the first stage of their approach, the mixed model is fit without regard to the time-to-event data. In the second stage, the posterior expectation of an individual's random effects from the mixed-model are included as covariates in a Cox model. Although Ye et al. (2008) acknowledged that their regression calibration approach may cause a bias due to the problem of informative dropout and measurement error, they argued that the bias is small relative to alternative methods. In this article, we show that this bias may be substantial. We show how to alleviate much of this bias with an alternative regression calibration approach that can be applied for both discrete and continuous time-to-event data. Through simulations, the proposed approach is shown to have substantially less bias than the regression calibration approach proposed by Ye et al. (2008). In agreement with the methodology proposed by Ye et al. (2008), an advantage of our proposed approach over joint modeling is that it can be implemented with standard statistical software and does not require complex estimation techniques.
叶、林和泰勒（2008年，《生物统计学》64卷，第1238 - 1246页）提出了一种针对纵向测量数据和事件发生时间数据的联合模型，其中纵向测量数据采用半参数混合模型进行建模，以考虑纵向生物标志物数据中的复杂模式。他们提出了一种两阶段回归校准方法，该方法比联合建模方法更易于实施。在他们方法的第一阶段，拟合混合模型时不考虑事件发生时间数据。在第二阶段，将混合模型中个体随机效应的后验期望作为协变量纳入Cox模型。尽管叶等人（2008年）承认他们的回归校准方法可能由于存在信息删失和测量误差问题，可能会导致偏差，但他们认为相对于其他方法，这种偏差较小。在本文中，我们表明这种偏差可能很大。我们展示了如何通过一种可应用于离散和连续事件发生时间数据的替代回归校准方法来大幅减轻这种偏差。通过模拟，结果表明所提出的方法比叶等人（2008年）提出的回归校准方法偏差要小得多。与叶等人（2008年）提出的方法一致，我们所提出方法相对于联合建模的一个优点是它可以用标准统计软件实现，并且不需要复杂的估计技术。
