Predicting Distributions of Physical Activity Profiles in the NHANES Database Using a Partially Linear Fr\'echet Single Index Model

TL;DR

This paper introduces a novel hybrid Fréchet regression model for analyzing distributional physical activity data from accelerometers in NHANES, capturing complex patterns and nonlinear effects for improved public health insights.

Contribution

It develops a new semi-parametric Fréchet regression framework for distributional objects, enabling nuanced analysis of physical activity profiles with interpretability.

Findings

Model effectively captures nonlinear effects of age on activity distributions.

Provides detailed physical activity profiles for different subpopulations.

Offers insights for targeted public health interventions.

Abstract

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 Fr\'echet regression model is proposed and applied to US population accelerometer data from National Health and Nutrition Examination Survey (NHANES) 2011-2014. 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.