基於Mapper演算法的拓撲學引導乳癌患者存活分析

摘要

本研究應用拓樸數據分析（TDA）中的數學工具「Mapper演算法」，分析超過1,000名TCGA-BRCA患者的基因表現數據，以找出與存活相關的隱藏分子模式。位於網絡高風險區域附近的患者，其存活率顯著較差；高度增殖的基因表現模式整體與較差的預後相關，但治療可縮小不同增殖組別之間的存活差距。進一步分析發現，部分患者的存活結果與其臨床預期行為不一致，其中包括一群基底樣（Basal-like）亞型患者，其預後意外地良好，且與一組獨特、對治療反應較佳的基因標記相關，揭示了傳統分類方法未能辨識的分子程式。透過對未見過的患者進行訓練與測試的驗證結果顯示，在調整年齡、腫瘤分期與治療等因素後，由拓樸結構推導出的風險分組仍與存活率顯著相關，證明基因表現數據的幾何結構中，蘊含超越傳統乳癌分類方法的臨床意義與預後資訊。

English

This study applied a mathematical tool from Topological Data Analysis (TDA), called the Mapper algorithm, to gene expression data from more than 1,000 TCGA-BRCA patients to identify hidden molecular patterns associated with survival. Patients located near high-risk regions of the network showed significantly poorer survival, and highly proliferative gene expression patterns were associated with worse outcomes overall, although treatment narrowed this survival gap across proliferation groups. The analysis further uncovered patients whose survival outcomes were inconsistent with their expected clinical behavior, including a subgroup of Basal-like patients with unexpectedly favorable outcomes linked to a distinct, more treatment-responsive gene signature, revealing molecular programs missed by traditional classification methods. Validation through training and testing on unseen patients confirmed that topology-derived risk groups remained significantly associated with survival after adjusting for age, tumor stage, and treatment, demonstrating that the geometric structure of gene expression data contains clinically meaningful prognostic information beyond traditional breast cancer classification methods.

基於Mapper演算法的拓撲學引導乳癌患者存活分析

Topology-Informed Survival Analysis of Breast Cancer Patients Using the Mapper Algorithm

摘要

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