Detecting Clinically Relevant Topological Structures in Multiplexed Spatial Proteomics Imaging Using TopKAT

Novel multiplexed spatial proteomics imaging platforms expose the spatial architecture of cells in the tumor microenvironment (TME). The diverse cell population in the TME, including its spatial context, has been shown to have important clinical implications, correlating with disease prognosis and treatment response. The accelerating implementation of spatial proteomic technologies motivates new statistical models to test if cell-level images associate with patient-level endpoints. Few existing methods can robustly characterize the geometry of the spatial arrangement of cells and also yield both a valid and powerful test for association with patient-level outcomes. We propose a topology-based approach that combines persistent homology with kernel testing to determine if topological structures created by cells predict continuous, binary, or survival clinical endpoints. We term our method TopKAT (Topological Kernel Association Test) and show that it can be more powerful than statistical tests grounded in the spatial point process model, particularly when cells arise along the boundary of a ring. We demonstrate the properties of TopKAT through simulation studies and apply it to two studies of triple negative breast cancer where we show that TopKAT recovers clinically relevant topological structures in the spatial distribution of immune and tumor cells.