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

TL;DR

This paper introduces a generalized odds framework for scalar-on-distribution regression, leveraging distributional data from digital health to improve clinical disability predictions in multiple sclerosis.

Contribution

It proposes a unified odds-based regression model that captures complex distributional information, outperforming traditional scalar and survival models in clinical prediction tasks.

Findings

Enhanced prediction accuracy of EDSS scores using the generalized odds model.

Distributional covariates provide better modeling of accelerometry data.

The framework unifies hazard, survival, and residual life representations.

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.