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A Novel Multi-view Mixture Model Framework for Longitudinal Clustering with Application to ANCA-Associated Vasculitis

Shen Jia, David Selby, Mark A Little, Tin Lok James Ng

Abstract

Effectively modeling irregularly sampled longitudinal data is essential for understanding disease progression and improving risk prediction. We propose a two-view mixture model that integrates static baseline covariates and longitudinal biomarker trajectories within a unified probabilistic clustering framework. Temporal patterns are modeled using Neural Ordinary Differential Equations. Model training uses an EM algorithm with a sparsity-inducing log-penalty for interpretable subgroup discovery. Application of the model to an Irish cohort of ANCA-associated vasculitis patients reveals subgroups with heterogeneous serum creatinine trajectories and variation in end-stage kidney disease outcomes.

A Novel Multi-view Mixture Model Framework for Longitudinal Clustering with Application to ANCA-Associated Vasculitis

Abstract

Effectively modeling irregularly sampled longitudinal data is essential for understanding disease progression and improving risk prediction. We propose a two-view mixture model that integrates static baseline covariates and longitudinal biomarker trajectories within a unified probabilistic clustering framework. Temporal patterns are modeled using Neural Ordinary Differential Equations. Model training uses an EM algorithm with a sparsity-inducing log-penalty for interpretable subgroup discovery. Application of the model to an Irish cohort of ANCA-associated vasculitis patients reveals subgroups with heterogeneous serum creatinine trajectories and variation in end-stage kidney disease outcomes.

Paper Structure

This paper contains 23 sections, 40 equations, 4 figures, 11 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Neural Ordinary Differential Equation
  4. Neural ODE for Longitudinal Data
  5. Multi-view Mixture Model
  6. EM Algorithm
  7. Sparsity Inducing Log Penalty
  8. Methodology
  9. Model Specification
  10. EM Algorithm
  11. Model Selection
  12. Simulation Studies
  13. Simulation Design
  14. Simulation 1
  15. Simulation 2
  16. ...and 8 more sections

Figures (4)

  • Figure 1: EM Algorithm for the Two-View Mixture Model with Sparsity-Inducing Log Penalty
  • Figure 2: Explanatory Data Analysis
  • Figure 3: Latent Cluster for creatinine covering from 180 days to 3 years (2 clusters)
  • Figure 4: Mean latent representations of each cluster across the dimensions of the combined and observed continuous latent space under the 2-cluster configuration