multiTEMPTED: Joint Dimensionality Reduction of Longitudinal Multi-omic Data with Modality-Specific Temporal Dynamics

Longitudinal multi-omic studies profile multiple molecular layers, such as microbiome composition, metabolomics, lipidomics, and proteomics, repeatedly over time. These layers reflect shared subject-level biological processes yet each may exhibit its own temporal dynamics. Most existing methods either integrate multiple omics modalities cross-sectionally or model a single modality longitudinally. The few methods that handle longitudinal multi-omic data assume a shared temporal trajectory across all modalities, limiting their ability to capture modality-specific dynamics, and can be computationally prohibitive at the scale of modern cohort studies. We introduce multiTEMPTED, an extension of the temporal tensor decomposition framework to M>=1 simultaneous omic modalities. The method jointly estimates subject components shared across modalities, modality-specific feature loadings identifying the contributing molecular features, and modality-specific temporal trajectories, while accommodating arbitrary, unaligned sampling schedules across subjects and modalities without imputation. In the MOMS-PI pregnancy cohort, joint analysis of the vaginal microbiome and cervicovaginal cytokines yields clearer separation between preterm and term birth outcomes than microbiome data alone, implicates Lactobacillus-dominant communities as protective, and identifies diverging cytokine trajectories in women who subsequently deliver preterm. In an exercise study profiling four plasma omics modalities, the leading unsupervised subject component from multiTEMPTED is strongly associated with sex, whereas the leading components from MEFISTO show no discernible association with known study phenotypes and appear numerically degenerate. In simulation experiments, multiTEMPTED accurately recovers the underlying component structure across a range of noise levels, outperforms MEFISTO in multiple settings, and runs several orders of magnitude faster. multiTEMPTED is implemented in the open-source R package multi.tempted (https://github.com/loulind/multi.tempted).