Abstract

We propose the additive functional Cox model to flexibly quantify the association between functional covariates and time to event data. The model extends the linear functional proportional hazards model by allowing the association between the functional covariate and log hazard to vary nonlinearly in both the functional domain and the value of the functional covariate. Additionally, we introduce critical transformations of the functional covariate which address the weak model identifiability in areas of information sparsity and discuss their impact on interpretation and inference. We also introduce a novel estimation procedure that accounts for identifiability constraints directly during model fitting. Methods are applied to the National Health and Nutrition Examination Survey 2003–2006 accelerometry data and quantify new and interpretable circadian patterns of physical activity that are associated with all-cause mortality. We also introduce a simple and novel simulation framework for generating survival data with functional predictors which resemble the observed data. The accompanying inferential R software is fast, open source, and publicly available. Our data application and simulations are fully reproducible through the accompanying vignette. Supplementary materials for this article are available online.

 抽象的

我们提出了加性函数 Cox 模型来灵活量化函数协变量与事件数据时间之间的关联。该模型通过允许函数协变量和对数风险之间的关联在函数域和函数协变量的值中非线性变化来扩展线性函数比例风险模型。此外，我们还介绍了函数协变量的关键变换，这些变换解决了信息稀疏领域中模型可识别性较弱的问题，并讨论了它们对解释和推理的影响。我们还引入了一种新颖的估计程序，可以在模型拟合期间直接考虑可识别性约束。方法适用于 2003-2006 年国家健康和营养检查调查的加速测量数据，并量化与全因死亡率相关的新的、可解释的身体活动昼夜节律模式。我们还介绍了一个简单而新颖的模拟框架，用于生成具有类似于观察数据的功能预测变量的生存数据。随附的推理 R 软件速度快、开源且公开可用。我们的数据应用和模拟可以通过随附的插图完全重现。本文的补充材料可在线获取。