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Summary Object-oriented data analysis is a fascinating and evolving field in modern statistical science, with the potential to make significant contributions to biomedical applications. This statistical framework facilitates the development of new methods to analyze complex data objects that capture more information than traditional clinical biomarkers. This paper applies the object-oriented framework to analyze physical activity levels, measured by accelerometers, as response objects in a regression model. Unlike traditional summary metrics, we utilize a recently proposed representation of physical activity data as a distributional object, providing a more nuanced and complete profile of individual energy expenditure across all ranges of monitoring intensity. A novel hybrid Fréchet regression model is proposed and applied to US population accelerometer data from National Health and Nutrition Examination Survey (NHANES) 2011 to 2014. The semi-parametric nature of the model allows for the inclusion of nonlinear effects for critical variables, such as age, which are biologically known to have subtle impacts on physical activity. Simultaneously, the inclusion of linear effects preserves interpretability for other variables, particularly categorical covariates such as ethnicity and sex. The results obtained are valuable from a public health perspective and could lead to new strategies for optimizing physical activity interventions in specific American subpopulations. 

Biosensor data have the potential to improve disease control and detection. However, the analysis of these data under free-living conditions is not feasible with current statistical techniques. To address this challenge, we introduce a new functional representation of biosensor data, termed the glucodensity, together with a data analysis framework based on distances between them. The new data analysis procedure is illustrated through an application in diabetes with continuous-time glucose monitoring (CGM) data. In this domain, we show marked improvement with respect to state-of-the-art analysis methods. In particular, our findings demonstrate that (i) the glucodensity possesses an extraordinary clinical sensitivity to capture the typical biomarkers used in the standard clinical practice in diabetes; (ii) previous biomarkers cannot accurately predict glucodensity, so that the latter is a richer source of information and; (iii) the glucodensity is a natural generalization of the time in range metric, this being the gold standard in the handling of CGM data. Furthermore, the new method overcomes many of the drawbacks of time in range metrics and provides more in-depth insight into assessing glucose metabolism.