# Modeling Disease Trajectories

My next project will (with high probability) involve modeling “disease trajectories” in some form. Though a concrete problem definition is still a few months away, I ran into some interesting recent work in this space that I will be reading soon. This post simply lists and quotes content from these papers that I found interesting. I will append to this post as I come across more.

## Disease Trajectory Maps

*Peter Schulam, Raman Arora. NIPS ‘16.*

Peter approaches this space from the application point of view, and has a bunch of other papers in this domain since 2015:

- Integrative Analysis using Coupled Latent Variable Models for Individualizing Prognoses. JMLR ‘16.
- A Framework for Individualizing Predictions of Disease Trajectories by Exploiting Multi-Resolution Structure. NIPS ‘15.
- Clustering Longitudinal Clinical Marker Trajectories from Electronic Health Data: Applications to Phenotyping and Endotype Discovery. AAAI ‘15.

His coauthor Suchi Saria is also active in this space. He links to an exciting commentary on predictive analytics in healthcare.

The crux of NIPS ‘16 is the following:

[…] we propose the Disease Trajectory Map (DTM), a novel probabilistic model that learns low-dimensional representations of sparse and irregularly sampled longitudinal data.

“Sparse and irregularly sampled longitudinal data” is essentially point process data.

I usually find representation-learning papers short on the evaluation front, simply because the evaluation ill-defined. A useful proxy is to use the learned representation in a machine learning task with ground truth, such as classification. The evaluation presented in this paper is does not do this and is unfamiliar to me, but I think the gist is that DTM’s corraborate what is already known medically, as shown via some hypothesis and association tests.

It still appears to be a primarily exploratory technique, potentially useful as input to classifiers further down the learning pipeline. The usual skepticism of the lack statistical guarantees and robustness apply.

## Patient Flow Prediction via Discriminative Learning of Mutually-Correcting Processes

*Hongteng Xu, Weichang Wu, Shamim Nemati, and Hongyuan Zha. TKDE ‘16*

Hongteng approaches this space from the theoretical point of view. He has a bunch of earlier work on point processes with his advisor (and prolific point process expert) Hongyuan Zha.

This paper specifically is not about how diseases evolve, but on how patients move between different care units (CUs) in a medical facility.

In this paper, we focus on an important problem of predicting the so-called “patient flow” from longitudinal electronic health records (EHRs). […] jointly predicting patients’ destination CUs and duration days.

## Longitudinal Mixed Membership Trajectory Models for Disability Survey Data

*Daniel Manrique-Vallier. Annals of Applied Statistics, ‘14.*

This is pretty far removed from disease trajectory modeling, but has a nice survey that I want to peruse later. The paper essentially combines “Latent Trajectory Models”, which jointly model trajectories and clusters, and mixed memborship models, which permit soft-assignments of data points to clusters. It is easy to see its applicability to disease trajectories.