Disease progression modeling of Alzheimer's disease based on variational probability principal component analysis

Alzheimer's disease (AD) is a neurodegenerative disorder and the leading cause of dementia. Early diagnosis and monitoring of disease progression are crucial for effective intervention. This study presents a novel disease progression model based on Variational Probabilistic Principal Component Analysis (VPPCA), which uses a Bayesian framework for dimensionality reduction and uncertainty quantification. By analyzing 1,021 amyloid-positive patients from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database, we extracted 25 features, including CSF (ABETA, TAU, PTAU), PET (FDG, AV45), and MRI volumetrics, along with cognitive and functional assessments. VPPCA compresses these multi-modal biomarkers into a single first principal component score (VPPCA1), which serves as a measure of disease progression. To ensure biological grounding and avoid circularity, we demonstrated that a VPPCA1 model using only non-cognitive features (CSF, PET, MRI, demographics) correlates strongly with cognitive decline (r = 0.658 with ADAS-Cog13), confirming that it captures genuine pathological progression rather than simply reflecting cognitive assessments. Block-wise feature ablation revealed that multi-modal integration is essential, with cognitive features showing the highest importance (0.1064), though all modalities contribute complementarily. In classification tasks, VPPCA exhibited strong performance with ROC-AUC values of 0.990 (CN vs Dementia), 0.774 (CN vs MCI), and 0.785 (MCI vs Dementia). A Bayesian hierarchical longitudinal model effectively captured patient-specific progression trajectories, offering personalized predictions of future disease states. VPPCA outperforms Probabilistic PCA (PPCA) by providing uncertainty quantification, with patient-specific confidence levels (σ = 0.086-0.136), which correlate with data quality, enabling automatic risk stratification. This work demonstrates that VPPCA offers a robust, biologically-grounded framework for modeling AD progression, providing actionable uncertainty quantification that improves clinical decision support and facilitates personalized care.