Detecting clinically relevant topological structures in multiplexed spatial proteomics using TopKAT

Multiplexed spatial proteomics profiling platforms expose the intricate geometric structure of cells in the tumor microenvironment (TME). The spatial arrangement of cells has been shown to have important clinical implications, correlating with disease prognosis and treatment response. These datasets require new statistical methods to test whether cell-level images are associated with patient-level outcomes. We propose the topological kernel association test (TopKAT), which combines persistent homology with kernel testing to determine whether geometric structures created by cells predict continuous, binary, or survival outcomes. TopKAT quantifies the topological structure of cells in each image using persistence diagrams and compares the similarities between persistence diagrams on the basis of the number and lifespan of the detected homologies among cells. We show that TopKAT can be more powerful than existing approaches, particularly when cells arise along the boundary of a ring and demonstrate its utility in breast cancer and colorectal cancer applications.