Abstract

Multiplexed spatial proteomics platforms yield high-resolution images of spatial expression of proteins from tissue samples. Images undergo a complex pre-processing pipeline to identify individual cells (termed segmentation) and to predict the cell phenotypes. It is common to conduct downstream analysis on the resulting predicted cells. However, cell segmentation and phenotyping are prone to error and this approach neglects the measured protein levels. Further, new research suggests topological analysis of spatial proteomics may yield more power than alternative approaches. We propose a method, TOASTER, that circumvents reliance on segmentation and phenotyping and instead tests the association between continuous spatial protein expression and a patient-level response variable. TOASTER uses topological data analysis to first characterize the presence of topological features in univariate and bivariate spatial protein expression. We propose three methods for associating our topological characterization of each image with an outcome using either a functional data analytic approach, a gridwise testing approach, or using kernel association testing. Simulations demonstrate that our approach improves power and controls type I error, even in the presence of gaps or tears in the image. We demonstrate our approach on a study in triple-negative breast cancer to reveal topological features of protein expression associated with immunotherapy response.