A Permutation-Based Test for Spatial Colocalization in Heterogeneous Tissue Samples

Thomas M. Menino Convention & Exhibition Center 

Spatial proteomics reveals immune cell organization, offering key insights into immune function and disease mechanism. Standard approaches assessing colocalization between cell types assume spatial homogeneity across samples. In real tissues, however, cell density patterns can vary substantially from patient to patient; if this heterogeneity is not incorporated, the resulting inference can be biased.
We propose a permutation-based, multi-scale test built on the Ripley's K function. For each sample and target cell-type pair, we compute Kcross curve over distances r (neighborhood radii) and average across samples to obtain an observed group-level curve. To preserve patient heterogeneity, we permute all cell-type labels within each sample. Each permutation yields one group-level permuted curve (averaged across samples); the set of permuted curves forms the empirical null for the group-level curve. We compute permutation p-values at each r by comparing observed curve to the null, then use the Cauchy combination test for a single global p-value. The procedure controls Type I error in both homogeneous and heterogeneous simulations, and identifies meaningful colocalization in TNBC tissue

Spatial Proteomics

Ripley's K-function

Cell-Type Colocalization

Permutation-based Inference 

Section on Statistics in Imaging