Hazard and Beyond: Exploring Five Distributional Representations of Accelerometry Data for Disability Discrimination in Multiple Sclerosis

TL;DR

This study compares five distributional representations of accelerometry data to determine their effectiveness in discriminating MS disability levels, finding hazard functions most effective.

Contribution

It introduces and evaluates five alternative distributional representations of accelerometry data for clinical disability discrimination in MS.

Findings

Hazard functions achieved the highest discriminatory accuracy.

Quantile functions were the second most effective.

Distributional representations capturing tail behavior improve clinical analysis.

Abstract

Research on modeling the distributional aspects in sensor-based digital health (sDHT) data has grown significantly in recent years. Most existing approaches focus on using individual-specific density or quantile functions. However, there has been limited exploration to assess the practical utility of alternative distributional representations in clinical contexts collecting sDHT data. This study is motivated by accelerometry data collected on 246 individuals with multiple sclerosis (MS)representing a wide range of disability (Expanded Disability Status Scale, EDSS: 0-7). We consider five different individual-level distributional representations of minute-level activity counts: density, survival, hazard, quantile, and total time on test functions. For each of the five distributional representations, scalar-on-function regression fits linear discriminators for binary and continuously measured MS disability, and cross-validated discriminatory performance of these linear discriminators is compared across. The results show that individual-level hazard functions provide the highest discriminatory accuracy, more than double the accuracy compared to density functions. Individual-level quantile functions provided the second-highest discriminatory accuracy. These findings highlight the importance of focusing on distributional representations that capture the tail behavior of distributions when analyzing digital health data, especially in clinical contexts.