PhD: Individually tailored digital-motor outcomes in real life

Medicine Made to Measure (MMM)

• Doctoral network
• Funded by the Marie Curie Actions Scheme
• 10 PhD candidates
• 22 participating organisations

• Aim: to develop
• Antisense oligonucleotide treatments (ASOs)
• Tailored to single patients with nano-rare disease mutations

Rare diseases

• A rare disease is any disease with a prevalence of <0.05%.

• There are >6000 rare diseases.

• Taken together, their prevalence is ~4%.

• >70% have genetic causes.

• Nano-rare mutations: Worldwide <30 patients.

(approximate numbers, for Europe)

“rare individually, common collectively”

Supervisors

Dr. Sabato Mellone
University of Bologna

Prof. Dr. Matthis Synofzik
University of Tübingen

Prof. Dr. Mats Karlsson
University of Uppsala

Co-supervisors

Carlo Tacconi
mHealth Technologies s.r.l., Bologna

Prof. Dr. Lorenzo Chiari
University of Bologna

Secondments

• Uppsala, Sweden
• Aug 2025 - Sep 2025

• Tübingen, Germany
• Sep 2024 - Nov 2024
• Three more months in the coming years

Individualized ASOs for nano-rare mutations:
Trial design challenges

• ASO treatment is taylor-made for the mutation
• Tiny number of patients worldwide
• ASO treatment has slow, disease-modifying effect

• Traditional clinical trial designs infeasible
• Traditional N-of-1 trial designs infeasible

Spinocerebellar Ataxia (SCA)

• Inherited neurodegenerative disease
• Affects the cerebellum and spinal cord
• Rare disease: ≤5 people per 100,000

PhD Objective

• Robust assessment of motor performance in genetic ataxias
• Based on body-worn sensor recordings in real-life settings
• Sensitive to moderate-term change in a single patient

Deliverables

Inertial measurement units

• Can be attached to various body parts
• Measure movement
• Accelerometer
• Gyroscope
• (Magnetometer, Barometer, …)

IMU hardware suppliers:

	mHealth Technologies
	APDM
	Any smartphone can be used as IMU

Sensor configurations

Lower back and feet

Lower back only

Gait analysis pipelines

Software	Mobility Lab	gaitmap	mobgap
Organization
Configuration	Feet & trunk	Feet only	Trunk only
Open source	✗	✓	✓
Validated*	✓	✗	✓
Stride DMOs	58	12	4

*Note:
Clinical validation is outcome- and population-specific.
Only Mobility Lab has been validated in ataxias.

Gait measures

Gait cycle analysis

Double support

Spatial and temporal analysis

Elevation at mid-swing

Foot contact angles

Circumduction

Lateral step variability

Gait cycle analysis

Spatial and temporal analysis

Elevation at mid-swing

Foot contact angles

Circumduction

Lateral step variability

Walking bouts

• Continuous sequences of steps
• Delimited by periods of non-walking

Walking segments

Split long walking bouts evenly into segments ≥25 strides.

• Better temporal resolution and homogeneity

Additional features

Stride-to-stride comparisons

Discrete transform coefficients

Complexity measures

Feature aggregation

• Result: Many candidate outcomes, each with one value per subject and session/condition

Feature transformation

Transform features on the per-stride, per-segment, or per-session/condition level.

Environmental context effects

• Real-life context factors are known to affect gait features
• Indoors vs. outdoors
• Type or absence of shoes
• Slope, stairs
• Ground texture
• Weather
• …

• Exogenous variables, introducing variance
• Estimateable to some degree from signal-derived proxies

Context stratification

Context compensation

Dataset

• Gait recordings from Tübingen University Hospital
• 27 genetic spinocerebellar (pre-)ataxia patients
• 36 healthy controls
• Lab-based & real-life
• Yearly follow-ups over several years

• Patients further categorized into:
• 6 pre-symptomatic (SARA 2 ± 1)
• 21 symptomatic (SARA 10 ± 3)

• In total:
• ~200 visits
• ~20000 walking segments
• ~570,000 gait cycles

Other potential datasets

• PROSPAX
• Lab-based movement recordings only
• ≥74 ARSACS (spastic ataxi) patients
• ≥113 SPG7 (spastic paraplegia) patients
• ≥50 healthy controls

• Planned prospective study
• ≥10 ataxia (SCA or AT) patients

Outcomes

• Clinician- / patient-rated scores (per visit)
• SARA
• ABC
• Others, but incomplete (SPRS, INAS, PGI, ADL)

• Digital motor outcomes
• Large space of combinations, small fraction suitable

Further covariates

• Demographics (age, gender)
• Diagnosis / gene affected
• Anthropometrics at first visit (weight, height, handedness, …)
• Estimated age of disease onset (only 19 of 27 patients)

SARA score

ABC score

• Traditionally 16 items
• In the Tübingen dataset: extended to 41 items

Qualitative characteristics

• Generally constant over time in the absence of disease
• Effect of age, if present, is small
• Roughly linear rise at disease onset
• Theoretical saturation not/barely represented in the dataset
• Clinical scales bounds not reached
• DMOs said to saturate around SARA 12-15

Data: Per-segment level

Cross-sectional testing

(lab based)

(real life)

Pooled sample size estimates

TODO: Focused disease range, new pooling

ESSs are unstable under varying:

• Year pair selection criteria
• Time between baseline and follow-up year

• Pool 1-, 2-, and 3-year effect sizes
• With inverse variance weighting
• Pre-normalize to 1-year by linear interpolation
• Assumes outcomes change linearly on average

Panel model

\[ y_{ij} = \beta_1\mathrm{BOn}_{ij} + \beta_2\mathrm{BSat}_{ij} + \beta_3\mathrm{BOn}_{ij}\left(\mathrm{EDO}_\mathrm{o}\right)_{i} + \beta_4\mathrm{BOn}_{ij}\mathrm{Gender}_{i} + \beta_4\mathrm{BOn}_{ij}\mathrm{BMI}_{i} \]

• Fixed-effects panel model (= linear model with de-meaning)
• Done as a course exercise
• Non-parametric bootstrap & Monte Carlo methods employed

Fit results

Simulating outcome data

Simulating outcome data

Assumption violations

Model overview

• Subject-centered growth model
• The “minimal” longitudinal mixed-effects model

\[ y_{ij} = \beta_0 + \beta_1 \tilde{x}_{ij} + b_{0i} + b_{1i} \tilde{x}_{ij} + \epsilon_{ij} \]

\[ \begin{pmatrix} b_{0i} \\ b_{1i} \end{pmatrix} \sim \mathcal{N}\!\left( \begin{pmatrix} 0 \\ 0 \end{pmatrix}, \begin{pmatrix} \sigma_{b0}^2 & 0 \\ 0 & \sigma_{b1}^2 \end{pmatrix} \right), \qquad \varepsilon_{ij} \sim \mathcal{N}(0, \sigma^2) \]

Outcome ranking: Metrics

TODO: Update metrics

Outcome ranking: Filtering

TODO: Update filtering

Why composite measures?

• Many candidate outcomes, capturing variance from:
• Various aspects of disease severity
• Various nuisance factors

• Combining them into a composite score could:
• Leverage orthogonal information from different features
• Average out some of the unwanted variance
• Similar to a test battery for a clinical score

Optimized composite measures

• Idea: Formulate the search for the ideal combination of outcomes as an optimization problem.
• E.g. Find linear combination that minimizes some loss.
• Loss: E.g. Composite change vs. disease time change.

\[ \min_\beta \sum_{i, j} \left( \left( t_{i j} - \bar{t}_{i \cdot} \right) \cdot I_{\mathrm{symptomatic}}(i) - \sum_{k} \left( y_{k i j} - \bar{y}_{k i \cdot} \right) \cdot \beta_k \right)^2 + \Omega(\beta) \]

• Result \(\theta = \beta y\) is a generated regressor – likely suboptimal compared to a jointly estimated latent variable model.

Factor analysis

• The “original” latent variable model
• Distills a set of observed variables into a few conceptual factors

Coni et al. 2019

• Pilot test on visit level resulted in subpar composites

Cross-sectional latent disease severity modeling

• Model disease severity itself
• Using a non-linear, single-factor, latent variable model

1. Cross-sectionally, on the segment level
2. Use established relationships between features and severity for a longitudinal model

• This has been done with success recently by Hamdan et al.
• On lab-based, visit-level features + SARA score

Model overview

• Bayesian non-linear single-factor model
• “Cross-sectional”, i.e. considers each visit as an individual
• Relates segment-level features to the latent disease severity
• By fitting a non-linear function per feature
• No incorporation of clinical scores

\[ y_{ij} = f\left(s_{v(i)}, \gamma_j\right) \, \beta_j + \alpha_j + \epsilon_{ij} \qquad \epsilon_{ij} \sim t_\nu\left(0, \sigma^2_j\right), \, s_v \sim \mathcal{N}(0, 1) \]

Choice of \(f\)

\[ \begin{align} \mathrm{exprel}(x) &= \frac{e^x - 1}{x} \\ \mathrm{tilt}(x, \gamma) &= x \, \mathrm{exprel}(\gamma x) \\ f(x, \gamma) &= \mathrm{tilt}(x, \gamma) \, \mathrm{scale}(\gamma) + \mathrm{offset}(\gamma) \end{align} \]

Where \(\mathrm{scale(\gamma)}\) and \(\mathrm{offset}(\gamma)\) are deterministic functions of \(\gamma\) chosen such that \[ x \sim \mathcal{N}(0, 1) \Rightarrow \mathrm{E}\left[f(x, \gamma)\right] = 0, \mathrm{Var}\left[f(x, \gamma)\right] = 1 \]

• \(\gamma\) becomes a shape parameter that does not affect the offset and scale of \(x\)

Choice of \(f\)

Choice of residual prior

\[ \epsilon_{ij} \sim t_\nu\left(0, \sigma^2_j\right) \]

And e.g. \[ \mu_{\mu_\sigma} = 0.8 \qquad \sigma_{\mu_\sigma} = 1.5 \qquad \mu_{\sigma_\sigma} = 0.3 \qquad \sigma_{\sigma_\sigma} = 1.6 \]

• Hierarchical prior with feature-specific scale
• \(t\)-distributed residuals for robustness against outliers

Choice of parameter priors

\[ \begin{align} \alpha_j &\sim \mathcal{N}(0, \sigma^2_\alpha) \\ \beta_j &= \mathrm{softplus}(\eta_j, \delta) \qquad \eta_j \sim \mathcal{N}(\mu_\eta, \sigma^2_\eta) \\ \gamma_j &\sim \mathcal{N}(0, \sigma^2_\gamma) \end{align} \]

Where e.g. \[ \sigma_\alpha = 0.5 \qquad \mu_\eta = -1 \qquad \sigma_\eta = 0.7 \qquad \sigma_\gamma = 0.5 \qquad \delta = 1 \]

And \[ \mathrm{softplus}(x, \delta) = \max(x, 0) + \log\left(1 + e^{-\frac{|x|}{\delta}}\right) \, \delta \]

softplus function