A robust, scalable K-statistic for quantifying immune cell clustering in spatial proteomics data

Spatial summary statistics based on point process theory are widely used to quantify the spatial organization of cell populations in single-cell spatial proteomics data. Among these, Ripley's K is a popular metric for assessing whether cells are spatially clustered or are randomly dispersed. However, the key assumption of spatial homogeneity is frequently violated in spatial proteomics data, leading to overestimates of cell clustering and colocalization. To address this, we propose a novel method, termed KAMP (K adjustment by Analytical Moments of the Permutation distribution), for quantifying the spatial organization of cells in spatial proteomics samples. KAMP leverages background cells in each sample along with a new closed-form representation of the first and second moments of the permutation null distribution of Ripley's K. Our method is robust to inhomogeneity, computationally efficient even in large datasets, and provides approximate p-values to test spatial clustering and colocalization. Methodological developments are motivated by a spatial proteomics study of women with ovarian cancer; in the subset with sufficient B cells and macrophages, KAMP provides exploratory, scale-specific evidence linking B cell-macrophage colocalization with overall patient survival. Notably, we also find evidence that using K without correcting for sample inhomogeneity may bias hazard ratio estimates in downstream analyses.