We extend the Cox proportional hazards model to cases when the exposure is a densely sampled functional process, measured at baseline. The fundamental idea is to combine penalized signal regression with methods developed for mixed effects proportional hazards models. The model is fit by maximizing the penalized partial likelihood, with smoothing parameters estimated by a likelihood-based criterion such as AIC or EPIC. The model may be extended to allow for multiple functional predictors, time varying coefficients, and missing or unequally-spaced data. Methods were inspired by and applied to a study of the association between time to death after hospital discharge and daily measures of disease severity collected in the intensive care unit, among survivors of acute respiratory distress syndrome.

中文翻译：

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具有生存数据功能协变量的Cox回归模型。

我们将Cox比例风险模型扩展到暴露是在基线测量的密集采样的功能过程的情况。基本思想是将惩罚信号回归与为混合效应比例风险模型开发的方法相结合。该模型通过最大化受惩罚的部分似然率进行拟合，并使用基于似然性的标准（例如AIC或EPIC）估算的平滑参数。可以扩展模型以允许多个功能预测变量，时变系数以及丢失或不等距的数据。这些方法的灵感来自于急性呼吸窘迫综合征幸存者在出院后死亡时间与重症监护病房每日收集的疾病严重程度之间的关系，并将其用于研究。