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Digital pathology enables computational analysis algorithms to be applied at scale to histological images. An example is the identification of immune cells within solid tumours. Image analysis algorithms can extract precise cell locations from immunohistochemistry slides, but the resulting spatial coordinates, or point patterns, can be difficult to interpret. Since localisation of immune cells within tumours may reflect their functional status and correlates with patient prognosis, novel descriptors of their spatial distributions are of biological and clinical interest. A range of spatial statistics have been used to analyse such point patterns but, individually, these approaches only partially describe complex immune cell distributions. In this study, we apply three spatial statistics to locations of CD68+ macrophages within human head and neck tumours, and show that images grouped semi-quantitatively by a pathologist share similar statistics. We generate a synthetic dataset which emulates human samples and use it to demonstrate that combining multiple spatial statistics with a maximum likelihood approach better predicts human classifications than any single statistic. We can also estimate the error associated with our classifications. Importantly, this methodology is adaptable and can be extended to other histological investigations or applied to point patterns outside of histology.

Original publication




Journal article


Scientific reports

Publication Date





Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK.


Macrophages, Humans, Head and Neck Neoplasms, Antigens, CD, Antigens, Differentiation, Myelomonocytic, Likelihood Functions, Cohort Studies, Algorithms, Squamous Cell Carcinoma of Head and Neck