2025 Theses Doctoral

Statistical and Machine Learning Methods for Neurodegenerative Disease Modeling

Cai, Zexi

Neurodegenerative disorders pose significant challenges, including slow progression, a lack of sensitive biomarkers, and considerable heterogeneity among patients. This dissertation addresses these issues by developing novel statistical models for predicting and modeling disease progression.

The first part of the thesis tackled the significant challenge of predicting disease progression in the absence of true disease state labels. This work integrates two mainstream machine learning approaches, i.e., generative and discriminative models, to enhance the prediction accuracy of disease progression. The model captures complex disease progression transitions, handles high-dimensional variables, and provides more accurate predictions of future disease states. Subsequent sections model disease trajectories using ordinary differential equations (ODEs). These two works account for the heterogeneity in disease progression rates across individuals, modeled through longitudinal registration associated with each individual's baseline characteristics.

The second part of this work focuses on curative treatments, where the effect is modeled as a change in the ODE parameters that reflect the progression rate, with variational inference employed to approximate the posterior distribution of the unknown initial conditions. The registration function is linked with baseline characteristics via a flexible neural network architecture.

The third part addresses palliative interventions through covariate-dependent shifts in trajectories. We use a spline-based approach to approximate the latent trajectory, and impose penalization on the difference of the spline-induced gradient and the ODE model. The longitudinal registration is modeled as a flexible parametric form of the baseline covariates, and a coordinate gradient ascent algorithm is proposed for the parameter estimation. By leveraging distinct techniques in the two works, the dynamic model offers more accurate estimations of disease progression and allows for individualized disease dynamics, which is crucial for optimizing treatment strategies and improving patient outcomes.