Diagnosing Alzheimer's the Bayesian way

Alzheimer's Disease is one the most debilitating diseases, but how do we diagnose it accurately? Researchers have been trying to answer this question by building generative models to describe how patient biomarkers, such as MRI scans, psychological tests, and lab tests relate over time to the underlying brain deterioration that's present in Alzheimer's Disease. In this notebook we show how we translated these models to the Bayesian framework in Stan and how this allowed for several model improvements that can ultimately improve our understanding of Alzheimer's and help physicians in diagnosis. In particular, we describe how we hierarchically model patient disease trajectories to obtain stable estimates for patients who lack data. We describe how fitting in Stan yields uncertainties on these disease trajectories, and why that is important for weighing the pros and cons of risky treatment. Lastly, we describe a new method for Bayesian modeling of these monotonic disease trajectories in Stan using I-Splines.