Topological Summaries of Tumor Images Improve Prediction of Disease Free Survival in Glioblastoma Multiforme

In this paper we propose a novel statistic, the smooth Euler characteristic transform (SECT). The SECT is designed to integrate shape information into standard statistical models. More specifically, the SECT allows us to represent shapes as a collection of vectors with little to no loss in information. As a result, detailed shape information can be combined with biomarkers such as gene expression in standard statistical frameworks, such as linear mixed models. We illustrate the utility of the SECT in radiogenomics by predicting disease free survival in glioblastoma multiforme patients based on the shape of their tumor as assayed by magnetic resonance imaging. We show that the SECT features outperform gene expression, volumetric features, and morphometric features in predicting disease free survival.

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