A multidimensional ODE-based model of Alzheimer's disease progression.

Data-driven Alzheimer's disease (AD) progression models are useful for clinical prediction, disease mechanism understanding, and clinical trial design. Most dynamic models were inspired by the amyloid cascade hypothesis and described AD progression as a linear chain of pathological events. However, the heterogeneity observed in healthy and sporadic AD populations challenged the amyloid hypothesis, and there is a need for more flexible dynamical models that accompany this conceptual shift. We present a statistical model of the temporal evolution of biomarkers and cognitive tests that allows diverse biomarker paths throughout the disease. The model consists of two elements: a multivariate dynamic model of the joint evolution of biomarkers and cognitive tests; and a clinical prediction model. The dynamic model uses a system of ordinary differential equations to jointly model the rate of change of an individual's biomarkers and cognitive tests. The clinical prediction model is an ordinal logistic model of the diagnostic label. Prognosis and time-to-onset predictions are obtained by computing the clinical label probabilities throughout the forecasted biomarker trajectories. The proposed dynamical model is interpretable, free of one-dimensional progression hypotheses or disease staging paradigms, and can account for the heterogeneous dynamics observed in sporadic AD. We developed the model using longitudinal data from the Alzheimer's Disease Neuroimaging Initiative. We illustrate the patterns of biomarker rates of change and the model performance to predict the time to conversion from MCI to dementia.