Extended correlation functions for spatial analysis of multiplex imaging data

Imaging platforms for generating highly multiplexed histological images are being continually developed and improved. Significant improvements have also been made in the accuracy of methods for automated cell segmentation and classification. However, less attention has focussed on the quantification and analysis of the resulting point clouds which describe the spatial coordinates of individual cells. We focus here on a particular spatial statistical method, the cross-pair correlation function (cross-PCF), which can identify positive and negative spatial correlation between cells across a range of length scales. However, limitations of the cross-PCF hinder its widespread application to multiplexed histology. For example, it can only consider relations between pairs of cells, and cells must be classified using discrete categorical labels (rather than labelling continuous labels such as stain intensity). In this paper, we present three extensions to the cross-PCF which address these limitations and permit more detailed analysis of multiplex images: Topographical Correlation Maps (TCMs) can visualise local clustering and exclusion between cells; Neighbourhood Correlation Functions (NCFs) can identify colocalisation of two or more cell types; and weighted-PCFs (wPCFs) describe spatial correlation between points with continuous (rather than discrete) labels. We apply the extended PCFs to synthetic and biological datasets in order to demonstrate the insight that they can generate. Impact statementThis paper introduces three methods for performing spatial analysis on multiplex digital pathology images. We apply the methods to synthetic datasets and regions of interest from a murine colorectal carcinoma, in order to illustrate their relative strengths and weaknesses. We note that these methods have wider application to marked point pattern data from other sources.