Using latent representations to link disjoint longitudinal data for mixed-effects regression

2025-10-29

AI Summary

Longitudinal studies of rare diseases often suffer from small sample sizes and instrument changes during treatment, resulting in sparse, non-comparable measurements that hinder conventional mixed-effects regression. To address this, we propose a novel framework coupling variational autoencoders with mixed-effects regression—enabling, for the first time, unified low-dimensional latent trajectory modeling across heterogeneous measurement instruments. The framework supports multi-source data integration and statistical inference of treatment-switching effects. It permits hypothesis testing on joint model parameters and provides interpretable back-projection of latent effects onto original clinical outcome scales. Evaluated on real-world spinal muscular atrophy data, the method successfully integrates multiple clinical rating scales and precisely quantifies the long-term efficacy of treatment switching, demonstrating both effectiveness and robustness in modeling discontinuous longitudinal data under small-sample conditions.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Mixture of Experts (MoE)
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Many rare diseases offer limited established treatment options, leading patients to switch therapies when new medications emerge. To analyze the impact of such treatment switches within the low sample size limitations of rare disease trials, it is important to use all available data sources. This, however, is complicated when usage of measurement instruments change during the observation period, for example when instruments are adapted to specific age ranges. The resulting disjoint longitudinal data trajectories, complicate the application of traditional modeling approaches like mixed-effects regression. We tackle this by mapping observations of each instrument to a aligned low-dimensional temporal trajectory, enabling longitudinal modeling across instruments. Specifically, we employ a set of variational autoencoder architectures to embed item values into a shared latent space for each time point. Temporal disease dynamics and treatment switch effects are then captured through a mixed-effects regression model applied to latent representations. To enable statistical inference, we present a novel statistical testing approach that accounts for the joint parameter estimation of mixed-effects regression and variational autoencoders. The methodology is applied to quantify the impact of treatment switches for patients with spinal muscular atrophy. Here, our approach aligns motor performance items from different measurement instruments for mixed-effects regression and maps estimated effects back to the observed item level to quantify the treatment switch effect. Our approach allows for model selection as well as for assessing effects of treatment switching. The results highlight the potential of modeling in joint latent representations for addressing small data challenges.

Problem

• Linking disjoint longitudinal data from different measurement instruments
• Modeling treatment switch effects in rare diseases with small samples
• Aligning heterogeneous clinical data using shared latent representations

Innovation

• Mapping instrument observations to aligned latent trajectories
• Using variational autoencoders for shared latent space embedding
• Applying mixed-effects regression on latent representations