The advent of wearable and sensor technologies now leads to functional predictors which are intrinsically infinite dimensional. While the existing approaches for functional data and survival outcomes lean on the well-established Cox model, the proportional hazard (PH) assumption might not always be suitable in real-world applications. Motivated by physiological signals encountered in digital medicine, we develop a more general and flexible functional time-transformation model for estimating the conditional survival function with both functional and scalar covariates. A partially functional regression model is used to directly model the survival time on the covariates through an unknown monotone transformation and a known error distribution. We use Bernstein polynomials to model the monotone transformation function and the smooth functional coefficients. A sieve method of maximum likelihood is employed for estimation. Numerical simulations illustrate a satisfactory performance of the proposed method in estimation and inference. We demonstrate the application of the proposed model through two case studies involving wearable data i) Understanding the association between diurnal physical activity pattern and all-cause mortality based on accelerometer data from the National Health and Nutrition Examination Survey (NHANES) 2011-2014 and ii) Modelling Time-to-Hypoglycemia events in a cohort of diabetic patients based on distributional representation of continuous glucose monitoring (CGM) data. The results provide important epidemiological insights into the direct association between survival times and the physiological signals and also exhibit superior predictive performance compared to traditional summary based biomarkers in the CGM study.

翻译：可穿戴设备与传感器技术的兴起催生了本质上无限维的功能型预测因子。尽管现有的功能数据与生存结局分析方法主要依赖于成熟的Cox模型，但比例风险（PH）假设在实际应用中可能并不总是适用。受数字医疗中生理信号的启发，我们开发了一种更通用、更灵活的功能时间转换模型，用于估计包含功能型与标量协变量的条件生存函数。该模型通过部分功能回归框架，借助未知单调转换函数与已知误差分布，直接建立生存时间与协变量之间的建模关系。我们采用伯恩斯坦多项式对单调转换函数及光滑功能系数进行建模，并运用极大似然筛法进行参数估计。数值模拟表明所提方法在估计与推断方面具有令人满意的性能。我们通过两项涉及可穿戴数据的案例研究展示该模型的应用：i) 基于2011-2014年美国国家健康与营养调查（NHANES）加速度计数据，探究昼夜体力活动模式与全因死亡率之间的关联；ii) 基于连续血糖监测（CGM）数据的分布表征，建立糖尿病患者低血糖事件发生时间的预测模型。研究结果不仅为生存时间与生理信号之间的直接关联提供了重要的流行病学见解，在CGM研究中相较于传统基于统计摘要的生物标志物方法也展现出更优的预测性能。