Lee Myeonggyun, Troxel Andrea B, Kwon Sophia, Crowley George, Schwartz Theresa, Zeig-Owens Rachel, Prezant David J, Nolan Anna, Liu Mengling
Division of Biostatistics, Department of Population Health, New York University Grossman School of Medicine, 180 Madison Avenue, New York, NY, USA.
Division of Pulmonary, Critical Care and Sleep Medicine, Department of Medicine, New York University Grossman School of Medicine, New York, NY, USA.
BMC Med Res Methodol. 2024 Dec 20;24(1):311. doi: 10.1186/s12874-024-02434-9.
In cohort studies with time-to-event outcomes, covariates of interest often have values that change over time. The classical Cox regression model can handle time-dependent covariates but assumes linear effects on the log hazard function, which can be limiting in practice. Furthermore, when multiple correlated covariates are studied, it is of great interest to model their joint effects by allowing a flexible functional form and to delineate their relative contributions to survival risk.
Motivated by the World Trade Center (WTC)-exposed Fire Department of New York cohort study, we proposed a partial-linear single-index Cox (PLSI-Cox) model to investigate the effects of repeatedly measured metabolic syndrome indicators on the risk of developing WTC lung injury associated with particulate matter exposure. The PLSI-Cox model reduces the dimensionality of covariates while providing interpretable estimates of their effects. The model's flexible link function accommodates nonlinear effects on the log hazard function. We developed an iterative estimation algorithm using spline techniques to model the nonparametric single-index component for potential nonlinear effects, followed by maximum partial likelihood estimation of the parameters.
Extensive simulations showed that the proposed PLSI-Cox model outperformed the classical time-dependent Cox regression model when the true relationship was nonlinear. When the relationship was linear, both the PLSI-Cox model and classical time-dependent Cox regression model performed similarly. In the data application, we found a possible nonlinear joint effect of metabolic syndrome indicators on survival risk. Among the different indicators, BMI had the largest positive effect on the risk of developing lung injury, followed by triglycerides.
The PLSI-Cox models allow for the evaluation of nonlinear effects of covariates and offer insights into their relative importance and direction. These methods provide a powerful set of tools for analyzing data with multiple time-dependent covariates and survival outcomes, potentially offering valuable insights for both current and future studies.
在具有事件发生时间结局的队列研究中，感兴趣的协变量的值通常会随时间变化。经典的Cox回归模型可以处理随时间变化的协变量，但假设其对对数风险函数有线性影响，这在实际应用中可能具有局限性。此外，当研究多个相关协变量时，通过允许灵活的函数形式来建模它们的联合效应并描述它们对生存风险的相对贡献是非常有意义的。
受纽约市消防部门世贸中心暴露队列研究的启发，我们提出了一种部分线性单指标Cox（PLSI-Cox）模型，以研究反复测量的代谢综合征指标对与颗粒物暴露相关的世贸中心肺损伤发生风险的影响。PLSI-Cox模型降低了协变量的维度，同时提供了对其效应的可解释估计。该模型灵活的连接函数适应了对数风险函数的非线性效应。我们开发了一种迭代估计算法，使用样条技术对潜在非线性效应的非参数单指标成分进行建模，然后对参数进行最大偏似然估计。
广泛的模拟表明，当真实关系为非线性时，所提出的PLSI-Cox模型优于经典的随时间变化的Cox回归模型。当关系为线性时，PLSI-Cox模型和经典的随时间变化的Cox回归模型表现相似。在数据应用中，我们发现代谢综合征指标对生存风险可能存在非线性联合效应。在不同指标中，体重指数对肺损伤发生风险的正向影响最大，其次是甘油三酯。
PLSI-Cox模型允许评估协变量的非线性效应，并深入了解它们的相对重要性和方向。这些方法为分析具有多个随时间变化的协变量和生存结局的数据提供了一套强大的工具，可能为当前和未来的研究提供有价值的见解。
