Topology-Based Query Framework for Longitudinal Omics Trajectories
1 Abstract 1.1 Background Many longitudinal omics studies contain only a small number of repeated measurements collected before, during, or after an intervention. Existing approaches, including mixed-effects models and generalized additive models, estimate temporal effects but do not generally provide a discrete representation of trajectory topology that can be queried directly across experimental groups. 1.2 Methods We developed LongOmicsTraj, an open-source R package for topology-based representation and querying of short longitudinal omics trajectories. The framework encodes the direction of change between adjacent visits as up, down, or flat, with the ordered sequence defining an Ordinal Trajectory State (OTS). LongOmicsTraj operates downstream of trajectory estimation and can therefore be applied to empirical summaries or model-derived visit-level estimates, including those from linear mixed-effects models, generalized additive models, and polynomial regression, following a maSigPro-style time-course formulation [1]. OTS labels provide a common representation for topology-based querying, cross-group comparison, and evaluation of higherlevel representations such as trajectory clusters. We evaluated the framework using controlled simulations and bronchial biopsy transcriptomic data from the GLUCOLD corticosteroid intervention study (GEO accession GSE36221), measured at baseline, 6 months, and 30 months. The biological analysis compared continued inhaled corticosteroid (ICS) treatment, ICS withdrawal after 6 months, and placebo. 1.3 Results In simulations, LongOmicsTraj recovered predefined stable, monotonic, transient, rebound, and oscillatory trajectories with high accuracy when longitudinal signal was sufficiently clear, with performance declining under high-noise conditions and depending partly on the upstream estimator. In GLUCOLD, comparator-aware topology queries reduced 20,358 measured transcripts to 168 genes showing a corticosteroid response that was maintained during continued treatment, reversed following withdrawal, and was not reproduced under placebo. The selected genes included established corticosteroid-response genes and were enriched for immune-cell migration, chemotaxis, cell adhesion, and extracellular-matrix organisation. Topology-aware evaluation of FlexMix trajectory clusters additionally revealed substantial within-cluster temporal heterogeneity, with topology purities of approximately 46% to 60%. 1.4 Conclusions LongOmicsTraj provides a compact, directly queryable representation of temporal direction and order in short longitudinal omics studies. It complements existing longitudinal estimation and clustering methods by making trajectory structure explicit, enabling structured cross-group queries and quantification of temporal heterogeneity within trajectory clusters.