A Principled Statistical Framework for Analyzing Spatial Patterns in Spatially Resolved Multi-Omics

<jats:title>Abstract</jats:title> <jats:p> Emerging spatial multi-omics technologies enable the profiling of molecular variation within its tissue context, yet existing methods for identifying spatially variable features lack principled approaches to experimental design and cross-sample inference. Here, we present STORM, a principled <jats:bold>S</jats:bold> tatistical <jats:bold>TO</jats:bold> ol for spatially <jats:bold>R</jats:bold> esolved <jats:bold>M</jats:bold> ulti-omics, for rigorously analyzing spatial patterns in spatial multi-omics research. STORM incorporates a robust and efficient nonparametric test that quantifies local deviations in molecular feature measurements to detect spatial dependence across transcriptomic and proteomic data. It further estimates an interpretable spatial effect size, supports power calculations for both spatial locations and biological replicates, and enables formal group-level comparisons. In several simulated and experimental spatial multi-omics case studies, STORM demonstrates reliable performance in detecting spatial structures while offering quantitative support for study design decisions. Overall, STORM provides a principled statistical framework that unifies spatial hypothesis testing, effect size estimation, power analysis, and experimental design for spatial multi-omics data. </jats:p>