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

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 use 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 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 2-fold. 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. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.多形性胶质母细胞瘤（Glioblastoma multiforme, GBM）是一类侵袭性人类脑癌，在癌症生物学领域正被广泛研究。该肿瘤进展迅速，且获取分子数据的相对时间成本较高，使得图像等易得数据类型成为指导患者临床干预的重要资源。本研究旨在利用GBM患者的医学图像信息开展统计分析。为此，我们设计了一种全新的统计量——光滑欧拉特征变换（smooth Euler characteristic transform, SECT），用于量化肿瘤的磁共振图像。得益于其明确的内积结构，相较于此前提出的其他拓扑汇总统计量，SECT可适用于更广泛的函数型与非参数建模场景。在对一组GBM患者队列进行分析后，我们发现SECT对临床结局的预测性能优于现有肿瘤形态量化指标与常用分子检测手段。具体而言，我们证实仅使用SECT特征即可解释的GBM患者生存数据方差，高于基因表达、体积特征及形态计量特征所能解释的部分。本研究的核心结论可归纳为两点：其一，医学图像蕴含宝贵信息，可在临床预后及其他医疗决策中发挥重要作用；其二，SECT是可用于医学影像信息学更广范围研究的可靠工具。本文的补充材料（包含复现本研究所需实验材料的标准化说明）可作为在线补充资源获取。