Predicting Clinical Outcomes in Glioblastoma: An Application of Topological and Functional Data Analysis

TL;DR

This paper introduces the smooth Euler characteristic transform (SECT), a novel topological statistic for MRI analysis of glioblastoma, demonstrating its superior predictive power for patient outcomes over traditional molecular and shape features.

Contribution

The paper develops SECT, a new topological data analysis method that effectively quantifies tumor shapes in MRI images for clinical outcome prediction.

Findings

SECT outperforms existing shape quantifications in predicting survival.

SECT explains more variance in outcomes than gene expression and volumetric features.

Images contain valuable prognostic information beyond molecular data.

Abstract

Glioblastoma multiforme (GBM) is an aggressive form of human brain cancer that is under active study in the field of cancer biology. Its rapid progression and the relative time cost of obtaining molecular data make other readily-available forms of data, such as images, an important resource for actionable measures in patients. Our goal is to utilize information given by medical images taken from GBM patients in statistical settings. To do this, we design a novel statistic---the smooth Euler characteristic transform (SECT)---that quantifies magnetic resonance images (MRIs) of tumors. Due to its well-defined inner product structure, the SECT can be used in a wider range of functional and nonparametric modeling approaches than other previously proposed topological summary statistics. When applied to a cohort of GBM patients, we find that the SECT is a better predictor of clinical outcomes than both existing tumor shape quantifications and common molecular assays. Specifically, we demonstrate that SECT features alone explain more of the variance in GBM patient survival than gene expression, volumetric features, and morphometric features. The main takeaways from our findings are thus twofold. First, they suggest that images contain valuable information that can play an important role in clinical prognosis and other medical decisions. Second, they show that the SECT is a viable tool for the broader study of medical imaging informatics.