Generalized Heterogeneous Functional Model with Applications to Large-scale Mobile Health Data

TL;DR

This paper introduces a generalized heterogeneous functional model for analyzing large-scale mobile health data, capturing subgroup-specific effects of physical activity on health outcomes, with improved prediction and interpretability.

Contribution

It proposes a novel generalized heterogeneous functional regression method with a pre-clustering approach, enhancing subgroup detection and computational efficiency in large datasets.

Findings

Identified four subgroups for mental disorders

Found three subgroups for Parkinson's disease

Outperformed existing methods in prediction accuracy

Abstract

Physical activity is crucial for human health. With the increasing availability of large-scale mobile health data, strong associations have been found between physical activity and various diseases. However, accurately capturing this complex relationship is challenging, possibly because it varies across different subgroups of subjects, especially in large-scale datasets. To fill this gap, we propose a generalized heterogeneous functional method which simultaneously estimates functional effects and identifies subgroups within the generalized functional regression framework. The proposed method captures subgroup-specific functional relationships between physical activity and diseases, providing a more nuanced understanding of these associations. Additionally, we introduce a pre-clustering method that enhances computational efficiency for large-scale data through a finer partition of subjects compared to true subgroups. In the real data application, we examine the impact of physical activity on the risk of mental disorders and Parkinson's disease using the UK Biobank dataset, which includes over 79,000 participants. Our proposed method outperforms existing methods in future-day prediction accuracy, identifying four subgroups for mental disorder outcomes and three subgroups for Parkinson's disease diagnosis, with detailed scientific interpretations for each subgroup. We also demonstrate theoretical consistency of our methods. Supplementary materials are available online. Codes implementing the proposed method are available at: https://github.com/xiaojing777/GHFM.