Title : From gait features to latent instability: A Bayesian threshold framework for fall occurrence in Parkinson’s disease
Abstract:
Falls represent a major source of morbidity in Parkinson’s disease (PD), yet their mechanistic modeling remains largely feature-centric. Most wearable-based studies directly associate individual gait metrics with fall history, implicitly assuming feature-level causality. We propose an alternative formulation in which fall occurrence is conceptualized as the probabilistic manifestation of an underlying latent gait instability process inferred from trunk biomechanics with explicit uncertainty propagation.
We analyzed 269 individuals with idiopathic PD performing a standardized 30-meter walking task using a single lumbar (L5) inertial sensor. Trunk-derived biomechanical features were grouped into three a priori domains: lower trunk kinematics, rhythmicity–recurrence, and neuromotor complexity. Within each domain, principal component analysis extracted a domain-specific latent axis. These axes were integrated into a Bayesian hierarchical measurement model to infer a continuous subject-specific latent gait instability variable with posterior uncertainty estimates.
Fall occurrence (≥1 fall in the previous year) was modeled using a Bayesian probit threshold formulation: fall probability was defined as the cumulative normal distribution evaluated at the difference between latent instability and an estimated population-level threshold. This formulation allowed propagation of measurement uncertainty from the latent model into fall-risk estimation.
Latent instability showed a positive probabilistic association with falls (posterior probability β > 0 = 0.964). Crucially, fall risk did not increase linearly across the instability continuum. Instead, an instability threshold (τ ≈ 0.32 on the standardized scale) defined a structured transition region where small changes in latent instability corresponded to disproportionately large changes in fall probability. Outside this region, marginal sensitivity attenuated, with probability saturation at high instability and stability plateaus at low values.
Baseline-dependent counterfactual contrasts further demonstrated that hypothetical reductions in instability produced maximal risk reduction in proximity to the inferred threshold. Approximately 74% of individuals exhibited an absolute posterior mean reduction ≥5% in fall probability under a modest instability shift (Δs = 0.3), with the largest benefit concentrated around the transition zone.
These findings suggest that fall susceptibility in PD reflects a structured latent instability process rather than isolated biomechanical abnormalities. Modeling falls through a Bayesian latent–threshold framework enables uncertainty-aware digital biomarker inference and provides a mechanistically interpretable representation of individual risk positioning along an instability continuum.
