Statistical modeling and inference for Jack's Alzheimer's disease biomarker cascade with practical and computational...

Alzheimer's Disease (AD) research increasingly recognizes the importance of characterizing the joint and relative dynamics of biomarker trajectories during the preclinical phase. Jack's model stands as the most well-known theoretical framework of these processes. While it offers conceptual guidance on modeling, it is not a directly implementable model for observed data. Key challenges include: (i) biomarker measurements are often noisy, depend on individual characteristics, and often exhibit complex temporal and cross-sectional correlations; (ii) data are sampled sparsely and may cover only a limited window of disease progression; and (iii) the temporal scale of the disease may not be synchronized across individuals. To address these challenges, we introduce a multivariate (for the multiple biomarkers), sparse (for the longitudinal sampling mechanism), nonlinear (for the hypothesized S-shape of biomarker evolution) latent variable model that accounts for complex correlation structures and individual factors. Crucially, we identify and address substantial practical and computational issues due to the noisy, sparse, and limited longitudinal data. Our contribution includes using a penalized likelihood to address estimates being close to the boundary due to degenerate cases, implementing a Gaussian Quadrature Newton-Raphson algorithm for efficient estimation under flexible correlation structures, and proposing a practical solution for potentially incomplete biomarker trajectories. We evaluate the finite-sample performance of the proposed method through simulations designed to mimic real-world data. We then apply the model to 2 longitudinal AD cohorts, BIOCARD and ADNI, to estimate biomarker trajectories across imaging, cerebrospinal fluid, and cognitive domains. These applications provide insights into the temporal dynamics of AD biomarkers, supporting improvements in preclinical diagnosis and guiding future research.