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Physical activity plays a significant role in the well-being of individualswith Chronic obstructive Pulmonary Disease (COPD). Specifically, it has beendirectly associated with changes in hospitalization rates for these patients.However, previous investigations have primarily been conducted in across-sectional or longitudinal manner and have not considered a continuousperspective. Using the telEPOC program we use telemonitoring data to analyzethe 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 telEPOCprogram exhibits variable domains, presenting a challenge since the majority offunctional data methods, are based on the fact that data are observed in thesame domain. To address this challenge, we introduce a novel fully functionalmethodology tailored to variable domain functional data, eliminating the needfor data alignment, which can be computationally taxing. Although modelsdesigned for variable domain data are relatively scarce and may have inherentlimitations in their estimation methods, our approach circumvents these issues.We substantiate the effectiveness of our methodology through a simulationstudy, comparing our results with those obtained using establishedmethodologies. Finally, we apply our methodology to analyze the impact ofphysical activity in COPD patients using the telEPOC program's data. Softwarefor 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}.

Modelling physical activity profiles in COPD patients: a fully functional approach to variable domain functional regression models