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

TL;DR

This paper introduces a novel method using variational autoencoders and mixed-effects regression to analyze disjoint longitudinal data in rare disease studies, enabling treatment effect assessment despite changing measurement instruments.

Contribution

It develops a joint latent space modeling approach with a new statistical testing method for analyzing disjoint longitudinal data in small sample rare disease trials.

Findings

Successfully aligned motor performance data from different instruments.

Quantified treatment switch effects in spinal muscular atrophy.

Demonstrated potential for modeling small, disjoint datasets.

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.