September 2023 Using persistent homology topological features to characterize medical images: Case studies on lung and brain cancers
Chul Moon, Qiwei Li, Guanghua Xiao
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Ann. Appl. Stat. 17(3): 2192-2211 (September 2023). DOI: 10.1214/22-AOAS1714

Abstract

Tumor shape is a key factor that affects tumor growth and metastasis. This paper proposes a topological feature computed by persistent homology to characterize tumor progression from digital pathology and radiology images and examines its effect on the time-to-event data. The proposed topological features are invariant to scale-preserving transformation and can summarize various tumor shape patterns. The topological features are represented in functional space and used as functional predictors in a functional Cox proportional hazards model. The proposed model enables interpretable inference about the association between topological shape features and survival risks. Two case studies are conducted using consecutive 133 lung cancer and 77 brain tumor patients. The results of both studies show that the topological features predict survival prognosis after adjusting clinical variables, and the predicted high-risk groups have worse survival outcomes than the low-risk groups. Also, the topological shape features found to be positively associated with survival hazards are irregular and heterogeneous shape patterns which are known to be related to tumor progression.

Citation

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Chul Moon. Qiwei Li. Guanghua Xiao. "Using persistent homology topological features to characterize medical images: Case studies on lung and brain cancers." Ann. Appl. Stat. 17 (3) 2192 - 2211, September 2023. https://doi.org/10.1214/22-AOAS1714

Information

Received: 1 September 2021; Revised: 1 October 2022; Published: September 2023
First available in Project Euclid: 7 September 2023

MathSciNet: MR4637663
Digital Object Identifier: 10.1214/22-AOAS1714

Keywords: Cox proportional hazards model , Functional data analysis , Survival analysis , topological data analysis , tumor shape

Rights: Copyright © 2023 Institute of Mathematical Statistics

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Vol.17 • No. 3 • September 2023
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