應用二階層函數主成分分析於身體活動數據之分析研究

Abstract

身體活動的強度、模式以及其對人體健康的影響已經被廣泛的研究，部分現有研究基於受試者自述的身體活動，也有些研究會利用加速度計的資料(accelerometry data)來客觀的描述身體活動的模式。這些研究大多聚焦在身體活動強度與人體健康的關聯，忽略了身體活動時間上的資訊。函數型資料分析(functional data analysis)以及函數主成分分析(functional principal component analysis)常被用來分析身體活動上的時間資訊，然而單階層的函數主成分分析在降維以及特稱選取時未考慮受試者之間和受試者內部的變異。本研究應用二階層函數主成分分析於來自英國生物資料庫(UK Biobank)以及美國健康營養調查(NHANES)2011-2014年調查所收集的加速度計資料。我們透過模擬研究比較二階層函數主成分分析與其他主成分分析的異同。此外，我們也透過二階層函數所提取的特徵來研究在不同健康狀況下身體活動是否會有不同。二階層函數主成分分析將加速度計資料中的變異分成個體之間的差異以及個體內的差異，並且依據不同變異來源分別把原有資料降維成一些重要的變數。模擬和應用的結果顯示二階層函數主成分分析在各種情況下都可以有穩定的表現，並且在關注身體活動時間上的變異上有更好的表現。本論文顯示二階層函數主成分分析能夠更好的分析加速度計資料，為身體活動強度以及模式和人體之間關係的研究提供新的探索方式。

Physical activity, rest-activity rhythms, and their impact on health outcomes have been extensively studied. Existing research has utilized functional data analysis and functional principal component analysis (FPCA) to extract meaningful information from accelerometry data. However, traditional single-level FPCA fails to consider the variations between and within subjects during eigenanalysis. To address this limitation, a two-level FPCA approach is implemented on accelerometry data from the UK Biobank and NHANES 2011-2014 datasets. Simulation studies are conducted to compare different FPCA methods. Furthermore, the scores obtained from the two-level FPCA are used to examine the associations between physical activity, rest-activity patterns, and diverse health outcomes. This thesis presents the proportions of different sources of variation in accelerometry data, identifying key features that characterize variations across individuals and days. The simulation and application results show that two-level FPCA performs stably in various scenarios, and is extremely powerful when focusing on the temporal variations of physical activity and rest-activity rhythms. This thesis demonstrates that two-level FPCA can provide a better understanding of the physical activity, rest-activity rhythms, and their relationship with human health, paving the way for further investigation in the field.