Unscrambling disease progression at scale: fast inference of event permutations with optimal transport

TL;DR

This paper introduces a novel optimal transport-based method for fast, scalable inference of disease progression event sequences, enabling detailed modeling of neurodegenerative and age-related conditions with high accuracy and interpretability.

Contribution

It presents a new approach leveraging optimal transport for permutation inference, achieving 1000x faster results and handling more features than existing methods.

Findings

Significantly faster inference than state-of-the-art methods.

Demonstrated robustness to noise in simulated data.

Successfully applied to real-world Alzheimer's and macular degeneration datasets.

Abstract

Disease progression models infer group-level temporal trajectories of change in patients' features as a chronic degenerative condition plays out. They provide unique insight into disease biology and staging systems with individual-level clinical utility. Discrete models consider disease progression as a latent permutation of events, where each event corresponds to a feature becoming measurably abnormal. However, permutation inference using traditional maximum likelihood approaches becomes prohibitive due to combinatoric explosion, severely limiting model dimensionality and utility. Here we leverage ideas from optimal transport to model disease progression as a latent permutation matrix of events belonging to the Birkhoff polytope, facilitating fast inference via optimisation of the variational lower bound. This enables a factor of 1000 times faster inference than the current state of the art and, correspondingly, supports models with several orders of magnitude more features than the current state of the art can consider. Experiments demonstrate the increase in speed, accuracy and robustness to noise in simulation. Further experiments with real-world imaging data from two separate datasets, one from Alzheimer's disease patients, the other age-related macular degeneration, showcase, for the first time, pixel-level disease progression events in the brain and eye, respectively. Our method is low compute, interpretable and applicable to any progressive condition and data modality, giving it broad potential clinical utility.