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

2026-01-14

AI Summary

This study addresses the challenge of improving prediction performance for clinical outcomes—such as the Expanded Disability Status Scale (EDSS) in multiple sclerosis—using digital health data from wearable accelerometers. To this end, the authors propose a Generalized Odds (GO) framework that represents distributional covariates as probability ratios over arbitrary regions of the sample space. They develop a scalar-on-odds regression model based on spline functions, incorporating penalization for efficient estimation. This framework is the first to introduce odds-type distributional covariates into digital health modeling and unifies various representations from survival analysis—including hazard and survival functions—as special cases. Empirical evaluation on the HEAL-MS cohort demonstrates that the proposed method significantly outperforms conventional scalar and survival analysis approaches.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• scalar-on-distribution regression
• generalized odds
• accelerometry
• multiple sclerosis
• disability prediction

Innovation

• generalized odds
• distributional regression
• spline-based functional representation
• digital health technologies
• accelerometry