We propose two novel approaches for estimating time-varying effects of functional predictors within a linear functional Cox model framework. This model allows for time-varying associations of a functional predictor observed at baseline, estimated using penalized regression splines for smoothness across the functional domain and event time. The first approach, suitable for small-to-medium datasets, uses the Cox-Poisson likelihood connection for valid estimation and inference. The second, a landmark approach, significantly reduces computational burden for large datasets and high-dimensional functional predictors. Both methods address proportional hazards violations for functional predictors and model associations as a bivariate smooth coefficient. Motivated by analyzing diurnal motor activity patterns and all-cause mortality in NHANES (N=4445, functional predictor dimension=1440), we demonstrate the first method's computational limitations and the landmark approach's efficiency. These methods are implemented in stable, high-quality software using the mgcv package for penalized spline regression with automated smoothing parameter selection. Simulations show both methods achieve high accuracy in estimating functional coefficients, with the landmark approach being computationally faster but slightly less accurate. The Cox-Poisson method provides nominal coverage probabilities, while landmark inference was not assessed due to inherent bias. Sensitivity to landmark modeling choices was evaluated. Application to NHANES reveals an attenuation of diurnal effects on mortality over an 8-year follow-up.

翻译：我们在线性函数Cox模型框架内提出了两种估计函数预测因子时变效应的新方法。该模型允许对基线观测的函数预测因子进行时变关联估计，通过惩罚回归样条实现函数域和事件时间上的平滑性。第一种方法适用于中小型数据集，利用Cox-Poisson似然关联进行有效估计与推断。第二种地标法显著降低了大型数据集和高维函数预测因子的计算负担。两种方法均解决了函数预测因子的比例风险假设违例问题，并将关联建模为双变量平滑系数。基于对NHANES数据中昼夜运动活动模式与全因死亡率关系的分析（N=4445，函数预测因子维度=1440），我们展示了第一种方法的计算局限性及地标法的高效性。这些方法通过mgcv包实现了稳定、高质量的软件实现，采用惩罚样条回归并自动选择平滑参数。模拟实验表明两种方法在估计函数系数时均具有高精度，其中地标法计算速度更快但精度略低。Cox-Poisson方法提供了名义覆盖概率，而地标推断因固有偏差未予评估。研究还评估了地标建模选择的敏感性。NHANES数据应用显示，在8年随访期间昼夜效应对死亡率的影响呈现衰减趋势。