Graph of graphs analysis for multiplexed data with application to imaging mass cytometry

Imaging Mass Cytometry (IMC) combines laser ablation and mass spectrometry to quantitate metal-conjugated primary antibodies incubated in intact tumor tissue slides. This strategy allows spatially-resolved multiplexing of dozens of simultaneous protein targets with 1μm resolution. Each slide is a spatial assay consisting of high-dimensional multivariate observations (m-dimensional feature space) collected at different spatial positions and capturing data from a single biological sample or even representative spots from multiple samples when using tissue microarrays. Often, each of these spatial assays could be characterized by several regions of interest (ROIs). To extract meaningful information from the multi-dimensional observations recorded at different ROIs across different assays, we propose to analyze such datasets using a two-step graph-based approach. We first construct for each ROI a graph representing the interactions between the m covariates and compute an m dimensional vector characterizing the steady state distribution among features. We then use all these m-dimensional vectors to construct a graph between the ROIs from all assays. This second graph is subjected to a nonlinear dimension reduction analysis, retrieving the intrinsic geometric representation of the ROIs. Such a representation provides the foundation for efficient and accurate organization of the different ROIs that correlates with their phenotypes. Theoretically, we show that when the ROIs have a particular bi-modal distribution, the new representation gives rise to a better distinction between the two modalities compared to the maximum a posteriori (MAP) estimator. We applied our method to predict the sensitivity to PD-1 axis blockers treatment of lung cancer subjects based on IMC data, achieving 97.3% average accuracy on two IMC datasets. This serves as empirical evidence that the graph of graphs approach enables us to integrate multiple ROIs and the intra-relationships between the features at each ROI, giving rise to an informative representation that is strongly associated with the phenotypic state of the entire image.Author summary: We propose a two-step graph-based analyses for high-dimensional multiplexed datasets characterizing ROIs and their inter-relationships. The first step consists of extracting the steady state distribution of the random walk on the graph, which captures the mutual relations between the covariates of each ROI. The second step employs a nonlinear dimensionality reduction on the steady state distributions to construct a map that unravels the intrinsic geometric structure of the ROIs. We theoretically show that when the ROIs have a two-class structure, our method accentuates the distinction between the classes. Particularly, in a setting with Gaussian distribution it outperforms the MAP estimator, implying that the mutual relations between the covariates within the ROIs and spatial coordinates are well captured by the steady state distributions. We apply our method to imaging mass cytometry (IMC). Our analysis provides a representation that facilitates prediction of the sensitivity to PD-1 axis blockers treatment of lung cancer subjects. Particularly, our approach achieves state of the art results with average accuracy of 97.3% on two IMC datasets.