Patients are complex and heterogeneous; clinical data sets are complicated by noise, missing data, and the presence of mixed-type data. Using such data sets requires understanding the high-dimensional “space of patients”, composed of all measurements that define all relevant phenotypes. The current state-of-the-art merely defines spatial groupings of patients using cluster analyses. Our goal is to apply topological data analysis (TDA), a new unsupervised technique, to obtain a more complete understanding of patient space. We applied TDA to a space of 266 previously untreated patients with Chronic Lymphocytic Leukemia (CLL), using the “daisy” metric to compute distances between clinical records. We found clear evidence for both loops and voids in the CLL data. To interpret these structures, we developed novel computational and graphical methods. The most persistent loop and the most persistent void can be explained using three dichotomized, prognostically important factors in CLL:IGHVsomatic mutation status, beta-2 microglobulin, and Rai stage. In conclusion, patient space turns out to be richer and more complex than current models suggest. TDA could become a powerful tool in a researcher’s arsenal for interpreting high-dimensional data by providing novel insights into biological processes and improving our understanding of clinical and biological data sets.
患者群体具有复杂性与异质性；临床数据集则因噪声、缺失数据及混合类型数据的存在而更显复杂。运用此类数据集需深入理解由所有相关表型定义指标构成的高维“患者空间”。当前最先进的方法仅通过聚类分析界定患者空间分组。本研究旨在应用拓扑数据分析这一新型无监督技术，以更全面地解析患者空间。我们采用“daisy”度量计算临床记录间距离，对266例初治慢性淋巴细胞白血病患者的空间进行拓扑数据分析。研究发现CLL数据中明确存在环状结构与空洞结构。为阐释这些拓扑特征，我们开发了创新的计算与图形化分析方法。其中最具持续性的环状结构与空洞结构可通过CLL三种重要的二分化预后因素得到解释：IGHV体细胞突变状态、β2微球蛋白及Rai分期。结论表明，患者空间比现有模型所揭示的更为丰富和复杂。拓扑数据分析通过为生物过程提供新颖见解并深化我们对临床与生物学数据集的理解，有望成为研究人员解析高维数据的强大工具。
Topological Structures in the Space of Treatment-Naïve Patients with Chronic Lymphocytic Leukemia
肿瘤(癌症)患者之家