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Cross-Sectional Separability versus Longitudinal Response in Short-Record Parkinsonian Gait Analysis Using FEG-Pro: Nordic Walking and Adapted Physical Activity
Xuanbao Xiang, Andrei Velichko, Xiaobo Rao, Jianshe Gao
TL;DR
The study addresses whether machine-learning separation of rehabilitation cohorts demonstrates differential intervention response. It applies FEG-Pro and FEDE to individual longitudinal gait changes from self-selected Nordic Walking and Adapted Physical Activity cohorts, using baseline adjustment, FDR correction, and nested validation. No robust modality-specific longitudinal response was demonstrated, so cross-sectional separability should not be interpreted as an intervention effect.
Problem
Cohort separability at baseline or after treatment does not necessarily measure differential intervention response, especially in self-selected, non-randomized rehabilitation groups.
Method
FEG-Pro and FEDE descriptors were computed from short gait records, and individual changes were compared with baseline-adjusted statistics, FDR correction, and nested machine learning on multidimensional change vectors.
Results
No individual descriptor showed a multiplicity-controlled between-group longitudinal difference, and nested change-vector classification failed to identify the intervention above chance.
Takeaways & Limitations
Rehabilitation biomarkers should be validated through individual longitudinal change, baseline-aware statistics, multiplicity correction, and leakage-safe model evaluation.
Takeaways & Limitations
The evidence is limited by a small, self-selected, non-randomized cohort, a large multiple-testing burden, and no healthy reference group.
Abstract
from arXiv · showhide
\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.
1. Introduction
This study frames Parkinsonian gait rehabilitation analysis around individual pre–post change rather than single-time-point cohort separability. It applies FEG-Pro and FEDE to short gait records from self-selected Nordic Walking and Adapted Physical Activity cohorts.
- Methodological rationale: FEG-Pro targets nonlinear instability and predictability from short gait records that conventional spatiotemporal variables may overlook.The pipeline uses forecast-error growth and signed-error distribution entropy descriptors derived from short lower-limb time series.
- Motivation: Self-selected rehabilitation cohorts can differ at baseline, so cohort classification does not by itself establish a differential intervention response.Baseline imbalance, preferences, physical capacity, and latent motor phenotype can support classification before treatment; treatment-associated comparisons should prioritize individual pre–post changes.
- Study design: The analysis uses short instrumented gait records collected before and after 12-week rehabilitation programs in 24 participants who self-selected Nordic Walking or Adapted Physical Activity.The dataset includes hip, knee, ankle, and heel signals recorded at baseline and follow-up during the medication ON state.
- Study design: The study compares subject-level change, Δ = T1 − T0, across Nordic Walking and Adapted Physical Activity rather than treating group membership at one time point as the primary target.Descriptors were retained by side or bilateral aggregation, and three trial-level values were averaged into subject-level profiles.
- Analysis plan: The primary between-group comparison includes 1,098 analyzable features, with continuous and discrete descriptors tested using group-specific statistical procedures and Benjamini–Hochberg FDR correction.Continuous changes use ANOVA, F-ratio ranking, and Cohen’s d; discrete changes use Mann–Whitney U tests and rank-biserial correlation, with q < 0.05 defining significance.
3. Results
Across 1,098 features, neither corrected between-group change tests nor baseline-adjusted analyses established a differential NW-versus-APA response. Nested change-vector classification failed above chance, whereas exploratory cross-sectional searches separated the self-selected cohorts at both time points.
- 3.1. Primary comparison of individual change: None of the 1,098 features showed multiplicity-controlled evidence of different longitudinal change after NW versus APA.Eight continuous and nine discrete features were nominally significant, but minimum adjusted values were q = 0.977 and q = 0.930, respectively.
- 3.1. Primary comparison of individual change: The largest nominal continuous contrast was right-ankle autocorrelation return scale, increasing in NW by Δ = +4.738 and decreasing in APA by Δ = −11.833.Its effect size was d = 1.060 with F = 6.559 and uncorrected p = 0.018; related candidates remain hypothesis-generating.
- 3.2. Within-group and baseline-adjusted analyses: Within-group paired analyses also produced only exploratory findings, with no feature surviving FDR correction in either intervention.The minimum adjusted values were approximately q = 0.733 for NW and q = 0.671 for APA.
- 3.2. Within-group and baseline-adjusted analyses: Baseline adjustment removed significance from all nominal between-group candidates, with the smallest p = 0.060.The attenuation is compatible with baseline imbalance or low power, while not proving that all candidate differences were confounded.
- 3.3. Machine learning on multidimensional change vectors: The nested change-vector analysis failed to identify the intervention above chance, with mean MCC = -0.178 ± 0.228 across repeated partitions.The authors caution that negative values indicate unstable or directionally inverted predictions, not a biological anti-learning phenomenon.
- 3.4. Exploratory cross-sectional context: Exploratory cross-sectional models reached peak internal MCC values of 0.604 at baseline and 0.554 after intervention, but these estimates are not directly comparable with the nested longitudinal estimate.Feature rankings shifted from hip-centered FEDE descriptors at baseline toward knee- and heel-related descriptors at T1.
4. Discussion
The analysis separates descriptive cohort separability from evidence of differential longitudinal response. Exploratory classifiers separated self-selected cohorts, but longitudinal FEG-Pro findings were not robust after correction and baseline adjustment.
- Cross-sectional separability did not establish a differential intervention effect in this dataset.The distinction remained despite cohort separation before and after intervention.
- No FEG-Pro feature showed a robust between-group longitudinal change after multiplicity correction, and baseline-adjusted candidate effects were non-significant.The smallest baseline-adjusted p value was 0.060.
- Several localized descriptors, including right-ankle autocorrelation return scale and early hip FEG slopes, remained exploratory candidates with standardized effects near or above one before correction.Their clinical direction could not be labeled beneficial or adverse without a healthy reference range.
- FEG-Pro's contribution is a structured family of short-record descriptors that can undergo longitudinal biomarker validation rather than classifier-score optimization alone.The proposed sequence includes subject-level aggregation, change scores, effect sizes, FDR control, baseline adjustment, nested modeling, and permutation testing.
- The baseline MCC of 0.604 may reflect self-selection, physical capacity, latent motor phenotype, or model-selection optimism rather than treatment response.The post-intervention feature-ranking shift likewise does not prove that training created new biomarkers.
5. Limitations
Interpretation is constrained by the small, self-selected cohort, extensive feature search, absent healthy reference group, and exploratory modeling. Additional design and reliability limitations further restrict physiological and clinical conclusions.
- The sample was small and non-randomized, with participants self-selecting NW or APA and nominal baseline clinical and gait differences.
- The large feature pool imposed a severe multiple-testing burden, leaving even large uncorrected candidate effects uncertain.
- Without a healthy reference group, feature directions could not be interpreted as normalization or deterioration.
- Averaging trial-level discrete indicators across three trials simplifies subject-level analysis but requires cautious physiological interpretation.
- Exploratory cross-sectional feature and model selection may be optimistic, while fixed FEG-Pro parameters require independent evaluation of sensitivity, reliability, and clinical validity.
6. Conclusion
FEG-Pro enabled nonlinear analysis of short lower-limb gait records but did not provide robust evidence of different longitudinal responses to NW and APA. The conclusion emphasizes baseline-aware, leakage-safe longitudinal validation over cross-sectional separability.
- The small, non-randomized cohort provided no robust evidence that NW and APA produced different longitudinal FEG-Pro or FEDE responses.
- Cross-sectional machine-learning separability before and after treatment did not establish a differential intervention effect.
- Rehabilitation-related nonlinear gait markers should be validated using individual longitudinal change, baseline-aware statistics, multiplicity correction, and fully nested model evaluation.
Ethics statement
The present work was a secondary analysis of de-identified public data from an ethically approved study.
- The original data collection received University of Pisa bioethics approval, participants gave informed consent, and the protocol followed the Declaration of Helsinki.The present study analyzed de-identified public data secondarily.
CRediT authorship contribution statement
The CRediT statement assigns investigation, data curation, formal analysis, methodology, software, supervision, conceptualization, and writing contributions across the authors.
- Xuanbao Xiang contributed investigation, data curation, formal analysis, and original-draft writing.
- Andrei Velichko contributed methodology, software, formal analysis, and review-and-editing writing.
- Xiaobo Rao contributed methodology, supervision, and review-and-editing writing.
- Jianshe Gao contributed conceptualization, supervision, and review-and-editing writing.
Funding
The research received no specific grant funding from public, commercial, or not-for-profit funding agencies.
- No specific grant supported the research from public, commercial, or not-for-profit funding agencies.
Supplementary Material
Supplementary materials document the fixed FEG-Pro configuration and implementation choices for short gait records, including horizon constraints and the absence of interpolation or resampling.
- Table S1 documents the fixed FEG-Pro parameters used in the gait analysis.
- Forecast horizons were limited by record length, and horizons lacking sufficient training or test samples were omitted.
- The gait signals were analyzed without artificial interpolation or resampling.
Feature naming and readable labels
Supplementary tables map feature prefixes and candidate-feature identifiers to readable labels, while exploratory figures describe cross-sectional feature rankings and trajectories rather than intervention effects.
- Table S2 defines feature prefixes and readable labels used in the main manuscript.
- Feature names describe fitted FEG curves or diagnostic regimes, including early two-line-fit slopes, local fit quality, slope reliability, and curve-shape indicators.
- Table S3 lists machine-readable identifiers for candidate features shown in the main manuscript.
- Figures S1–S3 present exploratory permutation, descriptor-count, and anatomical-distribution information for cross-sectional analyses.
- Figure S4 shows descriptive T0-to-T1 trajectories for cross-sectional feature MCC values, not validated intervention effects.
Supplementary Tables
Baseline-adjusted supplementary analyses retained no candidate at p < 0.05, while exploratory cross-sectional models were explicitly treated as non-independent validation estimates.
- No candidate retained p < 0.05 after adjustment for its baseline value.
- Supplementary analyses included checks of record length, effective horizon, and walking speed.
- Exploratory supplementary tables documented top cross-sectional features at baseline and after intervention, plus compact cross-sectional models.
- Peak internal estimates followed exhaustive feature-combination searches and therefore were not independent validation results.