Bayesian Joint Longitudinal-Survival Modeling of Functional Recovery Trajectories and Time to Independent Community Ambulation Following Robotic Exoskeleton-Assisted Stroke Rehabilitation: A Multi-Centre Cohort Study in Canada

ABSTRACT Background Robotic exoskeleton-assisted gait training (RAGT) has emerged as a promising modality for post-stroke rehabilitation. However, the longitudinal trajectory of functional recovery and its association with clinically meaningful milestones such as independent community ambulation remain poorly characterised. Standard analytical approaches that treat longitudinal and survival outcomes separately may yield biased estimates due to informative dropout and the endogenous nature of time-varying functional measures. Objective To jointly model the longitudinal trajectory of lower-extremity motor function and time to independent community ambulation following RAGT for stroke survivors, while accounting for the mutual dependence between the two processes using a Bayesian joint modelling framework. Methods A multi-centre retrospective cohort study was conducted across four Canadian rehabilitation hospitals (2019 to 2024). A total of 327 adults with first-ever ischaemic or haemorrhagic stroke who received RAGT using the EksoNR or Indego exoskeleton platforms were included. The primary longitudinal outcome was the Fugl-Meyer Assessment Lower Extremity (FMA-LE) score measured at baseline, weeks 4, 8, 12, 24, and 52. The survival outcome was time to achieving independent community ambulation (Functional Ambulation Category score of 4 or higher sustained for at least two consecutive assessments). A Bayesian shared-parameter joint model was specified, linking a nonlinear mixed-effects longitudinal submodel to a Weibull proportional hazards survival submodel through the current value and slope of the subject-specific FMA-LE trajectory. Estimation was performed using Hamiltonian Monte Carlo sampling with four chains of 5,000 iterations each (2,500 warmup). Results The median age was 62.4 years (IQR 54.1 to 71.8), 58.1% were male, and 63.0% had ischaemic stroke aetiology. The longitudinal submodel revealed a nonlinear recovery pattern best described by a three-knot restricted cubic spline, with rapid improvement during the first 12 weeks (mean gain 8.7 FMA-LE points, 95% CrI 7.2 to 10.3) followed by a plateau phase. The association parameter linking the current FMA-LE value to the hazard of achieving community ambulation was 0.084 (95% CrI 0.061 to 0.109), indicating that each one-point increase in the subject-specific FMA-LE trajectory was associated with an 8.8% increase in the instantaneous hazard (HR = 1.088, 95% CrI 1.063 to 1.115). The trajectory slope parameter was also significant (0.043, 95% CrI 0.012 to 0.078), suggesting that patients with steeper recovery gradients had additional survival advantages beyond their current functional level. At 52 weeks, 54.7% of participants achieved independent community ambulation. Haemorrhagic stroke (HR = 0.68, 95% CrI 0.49 to 0.93), older age (HR per decade = 0.81, 95% CrI 0.70 to 0.94), and higher baseline NIHSS score (HR per point = 0.94, 95% CrI 0.91 to 0.97) were associated with lower hazards of achieving the ambulation milestone. Conclusions The Bayesian joint model revealed that both the current functional level and the rate of functional change are independently predictive of achieving community ambulation following RAGT. These findings support individualised rehabilitation planning where treatment intensity may be dynamically adjusted based on the evolving recovery trajectory, and provide further evidence for the clinical value of robotic exoskeleton interventions in stroke rehabilitation.