A Mixed-Effects Model with Time Reparametrization for Longitudinal Univariate Manifold-Valued Data

Area of Science:

• Neuroscience
• Biostatistics
• Medical Imaging

Background:

• Longitudinal data analysis is crucial for understanding neurodegenerative diseases like Alzheimer's.
• Traditional mixed-effects models may not fully capture individual variations in disease progression and onset.
• Implicit reference times in models can complicate the interpretation of Alzheimer's disease trajectories.

Purpose of the Study:

• To propose a novel generative statistical model for longitudinal data in the context of Alzheimer's disease.
• To estimate an average disease progression model, incorporating subject-specific time shifts and acceleration factors.
• To provide a more accurate and individualized approach to modeling neurodegenerative disease progression.

Main Methods:

• Development of a generative statistical model within a univariate Riemannian manifold setting.
• Estimation of subject-specific time shifts to account for variability in age at disease onset.
• Estimation of subject-specific acceleration factors to account for variability in disease progression speed.

Main Results:

• The proposed model successfully analyzes longitudinal data, including neuropsychological scores and cortical thickness measurements.
• Individualized time shifts and acceleration factors allow for affine reparametrization of the average disease progression.
• The model effectively distinguishes between individuals with slow versus fast disease progression and early versus late onset.

Conclusions:

• The novel generative statistical model offers a robust framework for analyzing Alzheimer's disease progression.
• Accounting for individual time shifts and acceleration factors enhances the precision of disease progression modeling.
• This approach facilitates better identification of patient subgroups based on disease trajectory characteristics.