Capturing the Curve: Functional Data Analysis for Validated Digital Outcome Measures

Mia S. Tackney; Marcos Matabuena; Marco Palma; Michael Wester; Claire Maassen; Thomas Krammer; Julian Mustroph; Peter H. Charlton; James Carpenter; Sofia S. Villar

arXiv · 2605.28344

Capturing the Curve: Functional Data Analysis for Validated Digital Outcome Measures

Mia S. Tackney·Marcos Matabuena·Marco Palma·Michael Wester·Claire Maassen·Thomas Krammer·Julian Mustroph·Peter H. Charlton·James Carpenter·Sofia S. Villar

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Abstract

Digital health technologies enable high-frequency collection of data in near-continuous time and capture rich information about the health of individuals. The raw data collected by these devices often have a hierarchical functional structure: repeated physiological functions are observed over time and on multiple time scales (seconds, days, weeks). While many summaries can be derived from digital data, typically, only a small subset of pre-defined scalars is validated as outcome measures in clinical trials. We explore data-driven summaries based on between-subject scores from Multilevel Functional Principal Component Analysis (MFPCA), which are low-dimensional representations of functional data with robust statistical properties. Specifically, we compute MFPCA projection scores with respect to a reference population, summarising how individuals differ from the dominant directions of variation at each hierarchical level. Through a simulation study based on smartwatch electrocardiogram (ECG) signals, we compare MFPCA scores with pre-specified summaries in terms of validation criteria, including test-retest reliability and known-groups discrimination. We demonstrate that MFPCA scores generally have high reliability and can discriminate between groups across simulated scenarios of change. This offers an advantage when digital tools enable the measurement of novel physiological signals and the characteristics of the change are not yet defined. Finally, using knee flexion-extension data from individuals living with Parkinson's disease, we demonstrate that one of the MFPCA scores more strongly correlates with established gold-standard metrics and can detect clinical change, compared to a pre-specified scalar. We conclude that MFPCA-derived scores retain more information than typical outcome measures and open the door to using learning representation strategies in clinical trial settings.

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Mia S. Tackney, Marcos Matabuena, Marco Palma, Michael Wester, Claire Maassen, Thomas Krammer, Julian Mustroph, Peter H. Charlton, James Carpenter, Sofia S. Villar. 2026-05-27. Capturing the Curve: Functional Data Analysis for Validated Digital Outcome Measures. https://arxiv.org/abs/2605.28344

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