Hierarchical Bayesian inference to model continuous phenotypical progression in Alzheimer's Disease.

Throughout an organism's lifespan, a multitude of biological systems transition through complex biophysical processes. These processes serve as indicators of the underlying biological states. Inferring these latent unobserved states is a key problem in modern biology and neuroscience. Unfortunately, in many experimental setups, we can at best obtain snapshots of the system at different times for different individuals, and one major challenge is the one of reconciling those measurements. This formalism is particularly relevant in the study of Alzheimer's Disease (AD) progression, in which we observe in brain donors the aggregation of pathological proteins but the underlying disease state is unknown. The progression of AD can be modeled by assigning a latent score - termed pseudotime - to each pathological state, creating a pseudotemporal ordering of donors based on their pathological burden. This paper proposes a hierarchical Bayesian framework to model AD progression using detailed quantification of multiple AD pathological proteins from the Seattle AD Brain Cell Atlas consortium (SEA-AD). Inspired by biophysical models, we model pathological burden as an exponential process. Theoretical properties of the model are studied, by using linearization to reveal convergence and identifiability properties. We provide Markov chain Monte Carlo estimation algorithms, and show the effectiveness of our approach with multiple simulation studies across data conditions. Applying the methodology to SEA-AD brain data, we infer pseudotime for each donor and order them by pathological burden. Finally, we analyze the information within each pathological feature and utilize it to refine the model by focusing on the most informative pathologies. This lays the groundwork for suggesting future experimental design approaches.