Assessment of Wiener Process Degradation Models With Application to Amyotrophic Lateral Sclerosis Decline

Degradation models are commonly used in engineering to analyze the deterioration of systems over time. These models offer an alternative to standard longitudinal methods as they explicitly account for within-subject temporal variability through a latent stochastic process, allowing random fluctuations within a patient to be captured. This work investigates Wiener process-based degradation models with linear drift (i.e., slope) while considering a diffusion term to represent within-subject temporal variability, a random-effects term to capture between-subject variability of the slope, and a time-invariant term to account for measurement error. First-difference estimators that stabilize covariance matrix inversion and remove the influence of time-invariant confounders are presented and validated in clinically relevant settings. Monte Carlo simulations assessing relative error and coverage probability demonstrate that these models yield consistent and stable estimates. Profile likelihood methods, which reduce the dimensionality of the parameter space, also performed reliably, but should be used with caution when follow-up times are highly clustered. As a proof of concept, we applied these models to amyotrophic lateral sclerosis (ALS) data from the Pooled Resource Open-Access ALS Clinical Trials Database (PRO-ACT). We observed steeper slopes of the revised ALS Functional Rating Scale (ALSFRS-R) in individuals who died compared to those who survived, indicating that degradation model estimates are consistent with expected patterns of ALS decline. Our results demonstrate that these stochastic models provide accurate and efficient estimates of longitudinal deterioration. Future work aims to incorporate Wiener process degradation models into a joint modeling framework.