Modeling Physical Activity Change as Smooth Transformations: Temporal and Amplitude Patterns Associated with Physical Function in Older Women

Rong W. Zablocki; Steve Nguyen; Yacun Wang; Lindsay Dillon; Michael J. LaMonte; Phyllis A. Richey; Ramon Casanova; Marcia L. Stefanick; Sheri J. Hartman; Chongzhi Di; Charles Kooperberg; Loki Natarajan; Andrea Z. LaCroix; Jingjing Zou

arXiv · 2604.22123

Modeling Physical Activity Change as Smooth Transformations: Temporal and Amplitude Patterns Associated with Physical Function in Older Women

Rong W. Zablocki·Steve Nguyen·Yacun Wang·Lindsay Dillon·Michael J. LaMonte·Phyllis A. Richey·Ramon Casanova·Marcia L. Stefanick·Sheri J. Hartman·Chongzhi Di·Charles Kooperberg·Loki Natarajan·Andrea Z. LaCroix·Jingjing Zou

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Abstract

Purpose: To investigate whether longitudinal changes in timing and magnitude of PA are associated with physical function (PF) in older women. Methods: Women from OPACH study with accelerometry at baseline and WHISH study W1 and W2 were included. Minute-level PA counts were averaged and smoothed as diurnal PA curves. Consecutive-visit change was modeled within periods (baseline--W1 and W1--W2) as a Riemannian deformation from earlier to later curves, with two-dimensional initial momenta characterizing timing and magnitude shifts. Multivariate functional principal component analysis (MFPCA) summarized coupled timing-magnitude patterns, and principal component (PC) scores and deformation energy were derived for each participant-period. Linear mixed-effects models related these features to RAND-36 PF, adjusting for baseline PF and covariates. Results: Mean PA deformation in both periods showed downward shifts in PA magnitude and temporal redistribution after 10:00. Top 15 PCs explained at least 90% of variability in both periods. PC1 captured diurnal PA increase/decrease, explaining 22.4% of variability for baseline--W1 and 20.8% for W1--W2. Among participants with complete PF scores and baseline covariates (N=1,157), higher PC1 scores, reflecting relative increase/maintenance of PA across day, were positively associated with PF (P<0.0001). Deformation energy, a metric for overall diurnal pattern change between visits, showed a significant interaction with period for PF (P=0.003), with a larger positive association during W1--W2 than during baseline--W1. Conclusions: In older women, longitudinal changes in diurnal PA accumulation were associated with PF. Riemannian deformation analysis identified clinically interpretable markers of PA pattern change that may capture functional-aging information not represented by conventional PA summaries.

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Rong W. Zablocki, Steve Nguyen, Yacun Wang, Lindsay Dillon, Michael J. LaMonte, Phyllis A. Richey, Ramon Casanova, Marcia L. Stefanick, Sheri J. Hartman, Chongzhi Di, Charles Kooperberg, Loki Natarajan, Andrea Z. LaCroix, Jingjing Zou. 2026-04-23. Modeling Physical Activity Change as Smooth Transformations: Temporal and Amplitude Patterns Associated with Physical Function in Older Women. https://arxiv.org/abs/2604.22123

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