  In this work, we consider the problem of predicting the course of a
progressive disease, such as cancer or Alzheimer's. Progressive diseases often
start with mild symptoms that might precede a diagnosis, and each patient
follows their own trajectory. Patient trajectories exhibit wild variability,
which can be associated with many factors such as genotype, age, or sex. An
additional layer of complexity is that, in real life, the amount and type of
data available for each patient can differ significantly. For example, for one
patient we might have no prior history, whereas for another patient we might
have detailed clinical assessments obtained at multiple prior time-points. This
paper presents a probabilistic model that can handle multiple modalities
(including images and clinical assessments) and variable patient histories with
irregular timings and missing entries, to predict clinical scores at future
time-points. We use a sigmoidal function to model latent disease progression,
which gives rise to clinical observations in our generative model. We
implemented an approximate Bayesian inference strategy on the proposed model to
estimate the parameters on data from a large population of subjects.
Furthermore, the Bayesian framework enables the model to automatically
fine-tune its predictions based on historical observations that might be
available on the test subject. We applied our method to a longitudinal
Alzheimer's disease dataset with more than 3000 subjects [23] and present a
detailed empirical analysis of prediction performance under different
scenarios, with comparisons against several benchmarks. We also demonstrate how
the proposed model can be interrogated to glean insights about temporal
dynamics in Alzheimer's disease.
