Functional data collected as continuously observed trajectories arise naturally in many biomedical settings, and a key inferential goal is understanding how such functional covariates relate to time-to-event outcomes while allowing that relationship to vary across subgroups defined by scalar characteristics. Existing frequentist approaches to functional accelerated failure-time (AFT) models struggle to flexibly capture the joint, nonlinear influence of scalar covariates and time on the functional effect, and none adequately address the measurement error that frequently contaminates functionally observed exposures. We propose a Bayesian functional AFT model in which the functional coefficient is a varying effect function of both time and a set of scalar covariates, modeled through a Gaussian process single-index structure that provides a flexible, nonlinear framework for subgroup modification. Measurement error in the functional covariate is handled by pairing a proxy observation with an instrumental variable that accommodates non-linear associations with the latent functional exposure. A prominent source of such functional data is wearable devices, which can continuously monitor physical activity (PA) behavioral patterns over time, yet whose outputs are well known to be prone to measurement error and to exhibit heterogeneous associations with health outcomes across demographic subgroups. Through simulations, we show that our approach recovers the true varying functional effects and reduces bias relative tonaïve models that ignore measurement error. We apply our methods to the Reasons for Geographical and Racial Differences in Stroke (REGARDS) study to investigate how step-count physical activity relates to time-to-death from ischemic stroke across racial and regional groups.

翻译：连续观测轨迹所构成的功能性数据在生物医学场景中普遍存在。关键推断目标是理解此类功能性协变量如何影响时间事件结局，同时允许这种关联关系在由标量特征定义的亚组间产生变化。现有针对功能性加速失效时间模型的频率学派方法难以灵活捕捉标量协变量与时间对功能性效应的联合非线性影响，且均未充分处理常污染功能性观测暴露的测量误差问题。我们提出一种贝叶斯功能性AFT模型，其中功能性系数同时是时间与一组标量协变量的变效应函数，通过高斯过程单指标结构建模，为亚组修正提供灵活的非线性框架。功能性协变量中的测量误差通过配对代理观测与工具变量处理，该工具变量可容纳与潜在功能性暴露的非线性关联。此类功能性数据的重要来源是可穿戴设备——它们能持续监测体力活动行为模式随时间的变化，但其输出结果已知易受测量误差影响，且与不同人口学亚组健康结局呈现异质性关联。通过仿真验证，我们的方法能恢复真实的变功能性效应，并相较于忽略测量误差的朴素模型降低了偏差。我们将方法应用于"卒中地理与种族差异成因"研究，探讨步数体力活动如何与缺血性卒中死亡时间在不同种族与区域群体间产生关联。