This paper introduces two sets of measures as exploratory tools to study physical activity patterns: active-to-sedentary/sedentary-to-active rate function (ASRF/SARF), and active/sedentary rate function (ARF/SRF). These two sets of measures are complementary to each other and can be effectively used together to understand physical activity patterns. The specific features are illustrated by an analysis of wearable device data from National Health and Nutrition Examination Survey (NHANES). A two-level semiparametric regression model for ARF and the associated activity magnitude is developed under a unified framework using the marked point process formulation. The inactive and active states measured by accelerometers are treated as a 0-1 point process, and the activity magnitude measured at each active state is defined as a marked variable. The commonly encountered missing data problem due to device non-wear is referred to as 'window censoring,' which is handled by a proper estimation approach that adopts techniques from recurrent event data. Large sample properties of the estimator and comparison between two regression models as measurement frequency increases are studied. Simulation and NHANES data analysis results are presented. The statistical inference and analysis results suggest that ASRF/SARF and ARF/SRF provide useful analytical tools to practitioners for future research on wearable device data. This article is protected by copyright. All rights reserved.

中文翻译：

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使用标记点过程分析可穿戴设备数据

本文介绍了两组测量作为探索性工具来研究身体活动模式：活动到久坐/久坐到活动率函数 (ASRF/SARF) 和活动/久坐率函数 (ARF/SRF)。这两组测量是互补的，可以有效地结合使用来了解身体活动模式。通过对全国健康和营养检查调查 (NHANES) 的可穿戴设备数据的分析来说明具体功能。使用标记点过程公式在统一框架下开发了 ARF 和相关活动幅度的两级半参数回归模型。加速度计测量的非活动和活动状态被视为一个0-1点过程，并且在每个活动状态下测量的活动幅度定义为一个标记变量。由于设备非磨损而经常遇到的丢失数据问题被称为“窗口审查”，这是通过采用来自重复事件数据的技术的适当估计方法来处理的。随着测量频率的增加，估计量的大样本特性和两个回归模型之间的比较被研究。给出了仿真和 NHANES 数据分析结果。统计推断和分析结果表明，ASRF/SARF 和 ARF/SRF 为从业者未来研究可穿戴设备数据提供了有用的分析工具。本文受版权保护。版权所有。随着测量频率的增加，估计量的大样本特性和两个回归模型之间的比较被研究。给出了仿真和 NHANES 数据分析结果。统计推断和分析结果表明，ASRF/SARF 和 ARF/SRF 为从业者未来研究可穿戴设备数据提供了有用的分析工具。本文受版权保护。版权所有。随着测量频率的增加，估计量的大样本特性和两个回归模型之间的比较被研究。给出了仿真和 NHANES 数据分析结果。统计推断和分析结果表明，ASRF/SARF 和 ARF/SRF 为从业者未来研究可穿戴设备数据提供了有用的分析工具。本文受版权保护。版权所有。