  Medical researchers are coming to appreciate that many diseases are in fact
complex, heterogeneous syndromes composed of subpopulations that express
different variants of a related complication. Time series data extracted from
individual electronic health records (EHR) offer an exciting new way to study
subtle differences in the way these diseases progress over time. In this paper,
we focus on answering two questions that can be asked using these databases of
time series. First, we want to understand whether there are individuals with
similar disease trajectories and whether there are a small number of degrees of
freedom that account for differences in trajectories across the population.
Second, we want to understand how important clinical outcomes are associated
with disease trajectories. To answer these questions, we propose the Disease
Trajectory Map (DTM), a novel probabilistic model that learns low-dimensional
representations of sparse and irregularly sampled time series. We propose a
stochastic variational inference algorithm for learning the DTM that allows the
model to scale to large modern medical datasets. To demonstrate the DTM, we
analyze data collected on patients with the complex autoimmune disease,
scleroderma. We find that DTM learns meaningful representations of disease
trajectories and that the representations are significantly associated with
important clinical outcomes.
