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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 the use of measurement instruments changes 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\u2010effects regression. We tackle this by mapping observations of each instrument to an aligned low\u2010dimensional 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\u2010effects 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\u2010effects 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\u2010effects 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.<\/jats:p>","DOI":"10.1002\/sim.70701","type":"journal-article","created":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T08:55:48Z","timestamp":1787216148000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Using Latent Representations to Link Disjoint Longitudinal Data for Mixed\u2010Effects Regression"],"prefix":"10.1002","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-6775-2377","authenticated-orcid":false,"given":"Clemens","family":"Sch\u00e4chter","sequence":"first","affiliation":[{"name":"Institute of Medical Biometry and Statistics (IMBI), Medical Faculty and Medical Center University of Freiburg  Freiburg Germany"},{"name":"Freiburg Center for Data Analysis, Modeling and AI University of Freiburg  Freiburg 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