Zhou Jie, Zhang Jiajia, Mclain Alexander C, Lu Wenbin, Sui Xuemei, Hardin James W
Department of Epidemiology and Biostatistics, University of South Carolina, Columbia, South Carolina.
Department of Statistics, North Carolina State University, Raliegh, North Carolina.
Biometrics. 2019 Sep;75(3):853-863. doi: 10.1111/biom.13057. Epub 2019 Jun 17.
Varying-coefficient models have become a common tool to determine whether and how the association between an exposure and an outcome changes over a continuous measure. These models are complicated when the exposure itself is time-varying and subjected to measurement error. For example, it is well known that longitudinal physical fitness has an impact on cardiovascular disease (CVD) mortality. It is not known, however, how the effect of longitudinal physical fitness on CVD mortality varies with age. In this paper, we propose a varying-coefficient generalized odds rate model that allows flexible estimation of age-modified effects of longitudinal physical fitness on CVD mortality. In our model, the longitudinal physical fitness is measured with error and modeled using a mixed-effects model, and its associated age-varying coefficient function is represented by cubic B-splines. An expectation-maximization algorithm is developed to estimate the parameters in the joint models of longitudinal physical fitness and CVD mortality. A modified pseudoadaptive Gaussian-Hermite quadrature method is adopted to compute the integrals with respect to random effects involved in the E-step. The performance of the proposed method is evaluated through extensive simulation studies and is further illustrated with an application to cohort data from the Aerobic Center Longitudinal Study.
变系数模型已成为一种常用工具，用于确定暴露因素与结局之间的关联是否以及如何随连续测量值而变化。当暴露因素本身随时间变化且存在测量误差时，这些模型会变得复杂。例如，众所周知，纵向体能对心血管疾病（CVD）死亡率有影响。然而，纵向体能对CVD死亡率的影响如何随年龄变化尚不清楚。在本文中，我们提出了一种变系数广义优势率模型，该模型能够灵活估计纵向体能对CVD死亡率的年龄修正效应。在我们的模型中，纵向体能通过含误差测量，并使用混合效应模型进行建模，其相关的年龄变化系数函数由三次B样条表示。我们开发了一种期望最大化算法来估计纵向体能和CVD死亡率联合模型中的参数。在E步中，采用改进的伪自适应高斯 - 埃尔米特求积法来计算涉及随机效应的积分。通过广泛的模拟研究评估了所提出方法的性能，并通过应用有氧中心纵向研究的队列数据进一步进行了说明。
