Cross-Sectional Separability versus Longitudinal Response in Short-Record Parkinsonian Gait Analysis Using FEG-Pro: Nordic Walking and Adapted Physical Activity

Abstract

\textbf{Objective:} Machine-learning separation of rehabilitation cohorts does not inherently establish a differential intervention response. This study used Forecast-Error Growth Profiling (FEG-Pro) to distinguish cross-sectional cohort separability from subject-level longitudinal change following Nordic Walking (NW) and Adapted Physical Activity (APA) in Parkinson's disease. \textbf{Methods:} Publicly available short gait records from 24 participants (NW=14, APA=10) were analyzed. Lower-limb signals at baseline and 12 weeks were transformed into FEG-Pro and Forecast-Error Distribution Entropy descriptors. We compared individual change scores ($Δ=T1-T0$) between groups using baseline-adjusted sensitivity analyses and false-discovery-rate (FDR) correction. Additionally, a fully nested machine-learning pipeline evaluated whether multidimensional change vectors could identify the intervention. \textbf{Results:} The self-selected cohorts already differed clinically at baseline. Among 1,098 extracted features, none exhibited robust between-group differences in longitudinal change after FDR correction or baseline adjustment. Furthermore, nested classification based on multidimensional change vectors failed to perform above chance (mean MCC = $-0.178 \pm 0.228$). In contrast, exploratory cross-sectional models separated the cohorts with peak MCC values of 0.604 at baseline and 0.554 post-intervention. \textbf{Conclusion:} This cohort did not provide robust evidence of modality-specific longitudinal responses to NW or APA. These findings demonstrate that cross-sectional separability of self-selected cohorts must not be interpreted as an intervention effect; true rehabilitation biomarkers require subject-level longitudinal validation, baseline adjustment, and leakage-safe evaluation.