Modern clinical and epidemiological studies widely employ wearables to record parallel streams of real-time data on human physiology and behavior. With recent advances in distributional data analysis, these high-frequency data are now often treated as distributional observations resulting in novel regression settings. Motivated by these modelling setups, we develop a distributional outcome regression via quantile functions (DORQF) that expands existing literature with three key contributions: i) handling both scalar and distributional predictors, ii) ensuring jointly monotone regression structure without enforcing monotonicity on individual functional regression coefficients, iii) providing statistical inference via asymptotic projection-based joint confidence bands and a statistical test of global significance to quantify uncertainty of the estimated functional regression coefficients. The method is motivated by and applied to Actiheart component of Baltimore Longitudinal Study of Aging that collected one week of minute-level heart rate (HR) and physical activity (PA) data on 781 older adults to gain deeper understanding of age-related changes in daily life heart rate reserve, defined as a distribution of daily HR, while accounting for daily distribution of physical activity, age, gender, and body composition. Intriguingly, the results provide novel insights in epidemiology of daily life heart rate reserve.

翻译：现代临床和流行病学研究广泛采用可穿戴设备实时记录人类生理与行为的并行数据流。随着分布数据分析的最新进展，这些高频数据常被视为分布型观测值，从而催生了新型回归模型。受此类建模框架启发，我们提出基于分位数函数的分布结果回归方法（DORQF），该方法在现有文献基础上实现三项关键突破：i）同时处理标量与分布型预测变量，ii）在不强制个体函数回归系数单调性的前提下保证整体回归结构的联合单调性，iii）通过基于渐近投影的联合置信带与全局显著性统计检验提供统计推断，以量化估计函数回归系数的不确定性。本方法受巴尔的摩衰老纵向研究中Actiheart组件数据的驱动并应用于该数据集——该研究收集781名老年人一周的逐分钟心率与身体活动数据，旨在深入理解日常生活中心率储备（定义为每日心率分布）的年龄相关变化，同时考虑日常身体活动分布、年龄、性别及体成分等变量。令人关注的是，研究结果为日常生活心率储备的流行病学提供了新见解。