Physical activity plays a significant role in the well-being of individuals with Chronic obstructive Pulmonary Disease (COPD). Specifically, it has been directly associated with changes in hospitalization rates for these patients. However, previous investigations have primarily been conducted in a cross-sectional or longitudinal manner and have not considered a continuous perspective. Using the telEPOC program we use telemonitoring data to analyze the impact of physical activity adopting a functional data approach. However, Traditional functional data methods, including functional regression models, typically assume a consistent data domain. However, the data in the telEPOC program exhibits variable domains, presenting a challenge since the majority of functional data methods, are based on the fact that data are observed in the same domain. To address this challenge, we introduce a novel fully functional methodology tailored to variable domain functional data, eliminating the need for data alignment, which can be computationally taxing. Although models designed for variable domain data are relatively scarce and may have inherent limitations in their estimation methods, our approach circumvents these issues. We substantiate the effectiveness of our methodology through a simulation study, comparing our results with those obtained using established methodologies. Finally, we apply our methodology to analyze the impact of physical activity in COPD patients using the telEPOC program's data. Software for our method is available in the form of R code on request at \url{https://github.com/Pavel-Hernadez-Amaro/V.D.F.R.M-new-estimation-approach.git}.

翻译：体力活动在慢性阻塞性肺疾病（COPD）患者的健康管理中具有重要作用，尤其与患者住院率的变化存在直接关联。然而，既往研究主要采用横断面或纵向设计，未能从连续视角进行系统分析。本研究依托telEPOC项目，利用远程监测数据，采用函数型数据分析方法探究体力活动的影响。传统函数型数据方法（包括函数回归模型）通常假设数据域具有一致性，但telEPOC项目中的数据呈现变域特征——大多数函数型数据方法基于数据在相同观测域采集的假设，而该变域特性构成方法论挑战。为应对这一挑战，我们提出了一种面向变域函数数据的新型全函数方法，该方法无需进行计算代价高昂的数据对齐处理。尽管当前针对变域数据的模型相对稀缺且其估计方法存在固有局限，但本方法成功规避了这些缺陷。通过模拟研究验证方法有效性，并将结果与基于既有方法论的分析进行对比。最终，我们运用该方法分析telEPOC项目数据中COPD患者体力活动的影响效应。本方法对应的R语言代码可通过向指定邮箱申请获取，开源地址为：\url{https://github.com/Pavel-Hernadez-Amaro/V.D.F.R.M-new-estimation-approach.git}。