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arXiv · 2601.09126

Scalar-on-distribution regression via generalized odds with applications to accelerometry-assessed disability in multiple sclerosis

Pratim Guha Niyogi·Muraleetharan Sanjayan·Kathryn C. Fitzgerald·Ellen M. Mowry·Vadim Zipunnikov
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Abstract

Distributional representations of data collected using digital health technologies have been shown to outperform scalar summaries for clinical prediction, with carefully quantified tail-behavior often driving the gains. Motivated by these findings, we propose a unified generalized odds (GO) framework that represents subject-specific distributions through ratios of probabilities over arbitrary regions of the sample space, subsuming hazard, survival, and residual life representations as special cases. We develop a scale-on-odds regression model using spline-based functional representations with penalization for efficient estimation. Applied to wrist-worn accelerometry data from the HEAL-MS study, generalized odds models yield improved prediction of Expanded Disability Status Scale (EDSS) scores compared to classical scalar and survival-based approaches, demonstrating the value of odds-based distributional covariates for modeling DHT data.

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Pratim Guha Niyogi, Muraleetharan Sanjayan, Kathryn C. Fitzgerald, Ellen M. Mowry, Vadim Zipunnikov. 2026-01-14. Scalar-on-distribution regression via generalized odds with applications to accelerometry-assessed disability in multiple sclerosis. https://arxiv.org/abs/2601.09126

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