Paper:
Disease Trajectory Maps
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. Longitudinal 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 longitudinal EHR data. 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 longitudinal data. 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.

Review:
In short, the main contribution of the paper is a framework for learning a low-dimensional representation of time series data.   In this work, the authors propose a probabilistic model that learns a low-dimensional representation of univariate time-series data. The authors learn the model using a stochastic variational inference algorithm tailored to their application, which allows the model to scale to large datasets. Applied to a real world dataset of patients with a complex autoimmune disease, the model appears to learn clinically meaningful representations of disease trajectories.  
Overall, this is an important and interesting problem. Increasingly, researchers in ML and healthcare are studying methods for learning from longitudinal (time series) data (as opposed to more traditional approaches that consider only snapshot data). The work is well motivated, and clearly presented. Moreover, the authors include experiments on real data pertaining to patients with a complex chronic disease. Evaluation is two-fold. First look at clusters obtained by clustering low-dimensional representation, and then test relationship between low-dimensional representation and outcome. However, I do have a few concerns regarding this evaluation:   *The authors state that the median number of observations is 2 for TSS data and 3 for PFVC data. This is somewhat concerning given that the proposed model is primarily meant to model trajectories. If half of the patients have only two or fewer measurements, is this really a trajectory? Have the authors experimented with other datasets, or perhaps simulated data?  *Another related concern, is whether it makes sense clinically to compare patients who have 2 measurements with patients who have 22 measurements? Are these even clinically comparable? How does the number of measurements vary across clusters?  *In this particular example, it seems like we could characterize PFVC and TSS trajectories based on extent of changes in measurements and when they occur. Do we really need DTMs to help us identify declining trajectories vs. recovering trajectories? Again, I can see that while these trajectories are relatively simple, there may be disease processes with more complex trajectories to which the proposed method could be applied. Simulations may help show this.   *Quantitative evaluation only sheds so much light on the ability of the low dimensional representation to identify important clinical subgroups. In order to quantitatively evaluate clusters, why not look at outcome purity within each cluster? This idea is somewhat explored in the last figure of the paper, but could be interesting to show the frequency of outcomes within each of the clusters in Figures 1 & 2.  *In the introduction DTM is described as a method for modeling the trajectory of a single clinical marker. How do the clusters captured by PFVC and TSS compare? Can the proposed method capture trends in multivariate trajectories?