# Joint Progression Modeling (JPM): A Probabilistic Framework for Mixed-Pathology Progression

arXiv: https://arxiv.org/abs/2512.03475 · HTML: https://mlsanity.com/paper/2512.03475/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 52 references that are in the map.
- First posted on arXiv 3 Dec 2025.

## Builds on (most cited first, 2 of 2)

- [On A Mallows-type Model For (Ranked) Choices](https://mlsanity.com/paper/2207.01783/) (2022)
- [Unscrambling disease progression at scale: fast inference of event permutations with optimal transport](https://mlsanity.com/paper/2410.14388/) (2024)

## Abstract (arXiv)

Event-based models (EBMs) infer disease progression from cross-sectional data, and standard EBMs assume a single underlying disease per individual. In contrast, mixed pathologies are common in neurodegeneration. We introduce the Joint Progression Model (JPM), a probabilistic framework that treats single-disease trajectories as partial rankings and builds a prior over joint progressions. We study several JPM variants (Pairwise, Bradley-Terry, Plackett-Luce, and Mallows) and analyze three properties: (i) calibration -- whether lower model energy predicts smaller distance to the ground truth ordering; (ii) separation -- the degree to which sampled rankings are distinguishable from random permutations; and (iii) sharpness -- the stability of sampled aggregate rankings. All variants are calibrated, and all achieve near-perfect separation; sharpness varies by variant and is well-predicted by simple features of the input partial rankings (number and length of rankings, conflict, and overlap). In synthetic experiments, JPM improves ordering accuracy by roughly 21 percent over a strong EBM baseline (SA-EBM) that treats the joint disease as a single condition. Finally, using NACC, we find that the Mallows variant of JPM and the baseline model (SA-EBM) have results that are more consistent with prior literature on the possible disease progression of the mixed pathology of AD and VaD.