Background The spatial architecture of immune cells in the tumor microenvironment (TME) has been shown to have crucial clinical implications, correlating with disease prognosis and treatment response. The rapid expansion of single-cell, spatial technologies, such as multiplexed spatial proteomics imaging, probe the TME to reveal cell phenotypes and their arrangements. However, few statistical methods are available to test for an association between the spatial distribution of cells and continuous, binary, or survival clinical outcomes.

Methods We develop a new topological approach, termed TopKAT, to test for an association between spatially-resolved, single-cell images of TMEs and patient-level outcomes. TopKAT first characterizes the geometry of immune cell arrangements in each image by examining the evolution of shapes within a network of cells connected at increasing distances apart. Then, geometric similarities between images are compared to similarities in the sample-level outcomes. If images exhibiting similar topological structure among the cells tend to have similar outcomes, TopKAT reflects this association in a small p-value.

Results We examined the power and false positive control of TopKAT using simulated single-cell data for continuous, binary, and survival outcomes. We found that TopKAT can offer more power and better control false positives over alternative analytical methods, particularly when the images exhibit large open spaces within the spatial distribution of cells. We then applied TopKAT to two studies in triple negative breast cancer to identify prognostic and clinically-relevant geometric cell structures. In the first study, samples were identified as exhibiting either ‘compartmentalization’ between immune and tumor cells, where immune and tumor cells resided in distinct regions within the TME, or ‘mixing’ between immune and tumor cells, where the cells colocalized. We found that TopKAT recapitulated these classifications and found these geometric distinctions were associated with survival. In the second study, we found that the geometric structure of immune cells in the TME was predictive of treatment response in patients receiving neoadjuvant chemotherapy and immunotherapy.

Conclusions TopKAT is a novel topological approach for studying the associations between the spatial arrangement of cells in spatially-resolved, single-cell images of tumor biopsies with patient-level clinical outcomes.