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

arXiv: https://arxiv.org/abs/2510.25531 · HTML: https://mlsanity.com/paper/2510.25531/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 69 references that are in the map.
- First posted on arXiv 29 Oct 2025.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Unsupervised Domain Adaptation by Backpropagation](https://mlsanity.com/paper/1409.7495/) (2014)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Learning Transferable Features with Deep Adaptation Networks](https://mlsanity.com/paper/1502.02791/) (2015)
- [Adversarial Discriminative Domain Adaptation](https://mlsanity.com/paper/1702.05464/) (2017)
- [Domain Adaptation for Medical Image Analysis: A Survey](https://mlsanity.com/paper/2102.09508/) (2021)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [GP-VAE: Deep Probabilistic Time Series Imputation](https://mlsanity.com/paper/1907.04155/) (2019)
- [Handling Incomplete Heterogeneous Data using VAEs](https://mlsanity.com/paper/1807.03653/) (2018)
- [Controlling the false discovery rate via knockoffs](https://mlsanity.com/paper/1404.5609/) (2014)
- [Exact post-selection inference, with application to the lasso](https://mlsanity.com/paper/1311.6238/) (2013)
- [Transfer Learning for Domain Adaptation in MRI: Application in Brain Lesion Segmentation](https://mlsanity.com/paper/1702.07841/) (2017)
- [Aggregation of Multiple Knockoffs](https://mlsanity.com/paper/2002.09269/) (2020)
- [Deep dynamic modeling with just two time points: Can we still allow for individual trajectories?](https://mlsanity.com/paper/2012.00634/) (2020)
- [ICE-NODE: Integration of Clinical Embeddings with Neural Ordinary Differential Equations](https://mlsanity.com/paper/2207.01873/) (2022)
- [Investigating a domain adaptation approach for integrating different measurement instruments in a longitudinal clinical registry](https://mlsanity.com/paper/2312.00616/) (2023)
- [DALSA: Domain Adaptation for Supervised Learning From Sparsely Annotated MR Images](https://mlsanity.com/paper/2403.07434/) (2024)
- [Latent mixed-effect models for high-dimensional longitudinal data](https://mlsanity.com/paper/2409.11008/) (2024)
- [A statistical approach to latent dynamic modeling with differential equations](https://mlsanity.com/paper/2311.16286/) (2023)

## Built on by (most cited first, 1 of 1)

- [Large language models as synthetic clinical experts to inform longitudinal rare-disease modeling](https://mlsanity.com/paper/2608.16507/) (2026)

## Abstract (arXiv)

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.