Omics data at scale: methods for feature selection and feature set testing

Abstract

This thesis develops novel statistical methodologies to address key challenges in the analysis of high-dimensional omics data, characterized by complex, multi-layered molecular measurements. Conventional feature and pathway analyses often suffer from heuristic selection procedures, limited flexibility, and compromised error control. The first contribution, Active Volcano Plots, provides a statistically rigorous alternative to ad hoc “double filtering,” enabling valid post hoc inference under interactive thresholding through lower bounds on the True Discovery Proportion (TDP) derived from All-Resolutions Inference. The second, Simultaneous Enrichment Analysis (SEA), introduces a unified framework for large-scale feature set testing that accommodates both self-contained and competitive hypotheses while ensuring strong Family-Wise Error Rate (FWER) control and providing complementary TDP-based inference. The third method, OCEAN, extends SEA to multi-omics contexts by testing two-way feature sets across molecular layers, allowing inference on marginal and joint signals under structured dependency while maintaining FWER control. Finally, SLaPMEG integrates latent process mixed models with global testing for longitudinal omics data, accounting for within-subject correlation and time-varying effects. All methods are validated through theory, simulations, and applications to real datasets (e.g., Duchenne muscular dystrophy, cancer), and implemented in open-source R packages, enhancing reproducibility, flexibility, and interpretability in complex omics analyses.