waveome: a toolkit for longitudinal omics analysis using Gaussian processes

Identifying meaningful associations from small-sample longitudinal data is challenging, especially in low signal-to-noise environments where the Gaussian likelihood assumption does not hold. We introduce two methods to algorithmically perform variable selection with sparse, irregularly sampled, longitudinal count data with over-dispersion to characterize nonlinear relationships between omics measurements and covariates of interest using Gaussian processes. The first is an additive non-greedy search-based method, while the second is a penalization approach using Horseshoe priors on kernel hyperparameters. In simulation studies, both methods outperform conventional statistical models in terms of distributional fit and exhibit a trade-off in feature selection. Applying the penalized variant to a real-world Crohns disease cohort, we recover well-established biomarkers, such as short-chain fatty acids, secondary bile acids, and specific lipid species, and uncover novel candidates for cross-sectional and temporal disease severity. Both methods are implemented in an open-source Python library, waveome, offering a robust set of tools for longitudinal biomarker discovery.