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

Hongtao Hao, Joseph L. Austerweil

TL;DR

The paper introduces the Joint Progression Model (JPM) to address mixed-pathology progression in neurodegenerative diseases by reframing single-disease trajectories as partial rankings and placing a probabilistic, energy-based prior over joint progressions. It formalizes four ranking-based variants (Pairwise Preferences, Generalized Bradley–Terry, Plackett–Luce, and a BT-informed Mallows) and develops generative and inferential algorithms to recover aggregate progression from cross-sectional data, integrating with an existing Event-Based Model likelihood. Through extensive synthetic experiments, JPM demonstrates up to ~21% improvements in ordering accuracy over SA-EBM and shows variant-specific strengths, with the Mallows variant offering controllable sharpness. Real-data analysis on NACC aligns Mallows and SA-EBM with established literature on AD and VaD progression, while providing practical guidance on variant selection based on input ranking characteristics. Overall, JPM provides a principled, flexible framework for joint disease progression, enabling better understanding and simulation of mixed-pathology dynamics.

Abstract

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.

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

TL;DR

The paper introduces the Joint Progression Model (JPM) to address mixed-pathology progression in neurodegenerative diseases by reframing single-disease trajectories as partial rankings and placing a probabilistic, energy-based prior over joint progressions. It formalizes four ranking-based variants (Pairwise Preferences, Generalized Bradley–Terry, Plackett–Luce, and a BT-informed Mallows) and develops generative and inferential algorithms to recover aggregate progression from cross-sectional data, integrating with an existing Event-Based Model likelihood. Through extensive synthetic experiments, JPM demonstrates up to ~21% improvements in ordering accuracy over SA-EBM and shows variant-specific strengths, with the Mallows variant offering controllable sharpness. Real-data analysis on NACC aligns Mallows and SA-EBM with established literature on AD and VaD progression, while providing practical guidance on variant selection based on input ranking characteristics. Overall, JPM provides a principled, flexible framework for joint disease progression, enabling better understanding and simulation of mixed-pathology dynamics.

Abstract

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.

Paper Structure

This paper contains 45 sections, 25 equations, 26 figures, 13 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. JPM theory and algorithms
  4. Problem statement
  5. Variant 1: Pairwise Preferences (PP)
  6. Variant 2: Generalized Bradley--Terry (BT)
  7. Variant 3: Plackett--Luce (PL)
  8. Variant 4: BT-informed Mallow's Model
  9. Generative and inference algorithms
  10. Theoretical analysis
  11. Q1: Model calibration
  12. Q2: Characterizing the Generation of Aggregate Rankings
  13. Q3: Which Generative Variant to Choose?
  14. Synthetic experiments & results
  15. Synthetic data generation
  16. ...and 30 more sections

Figures (26)

  • Figure 1: Distribution of calibration by generative and inference JPM variant
  • Figure 2: Separation and sharpness of different JPM variants
  • Figure 3: Correlation between sharpness and input partial ranking characteristics when the aggregate rankings are generated with the BT variant
  • Figure 4: Correlation between sharpness and input partial ranking characteristics when the aggregate rankings are generated with the PL variant
  • Figure 5: Correlation between sharpness and input partial ranking characteristics when the aggregate rankings are generated with the PP variant
  • ...and 21 more figures