Nonlinear model with random inflection points for modeling neurodegenerative disease progression

Due to a lack of a gold standard objective marker, the current practice for diagnosing a neurological disorder is mostly based on clinical symptoms, which may occur in the late stage of the disease. Clinical diagnosis is also subject to high variance due to between- and within-subject variability of patient symptomatology and between-clinician variability. Effectively modeling disease course and making early prediction using biomarkers and subtle clinical signs are critical and challenging both for improving diagnostic accuracy and designing preventive clinical trials for neurological disorders. Leveraging the domain knowledge that certain biological characteristics (ie, causal genetic mutation) is part of the disease mechanism, and certain markers (eg, neuroimaging measures, motor and cognitive ability measures) reflect pathological process, we propose a nonlinear model with random inflection points depending on subject-specific characteristics to jointly estimate the changing trajectories of the markers in the same disease domain. The model scales different markers into comparable progression curves with a temporal order based on the mean inflection point and establishes the relationship between the progression of markers with the underlying disease mechanism. The model also assesses how subject-specific characteristics affect the dynamic trajectory of different markers, which offers information on designing preventive therapeutics and personalized disease management strategy. We perform extensive simulation studies and apply our method to markers in neuroimaging, cognitive, and motor domains of Huntington's disease using the data collected from a large multisite natural history study of Huntington's disease, where we assess the temporal ordering of disease impairment between domains. We show that atrophy from certain brain area occurs first, followed by motor and cognitive domain, and show that an average patient has already experienced substantial regional brain atrophy when reaching clinical diagnosis age.