Topological Structures in the Space of Treatment-Naive Patients With Chronic Lymphocytic Leukemia

Abstract

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: IGHV somatic 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 researchers arsenal for interpreting high-dimensional data by providing novel insights into biological processes and improving our understanding of clinical and biological data sets. Simple SummaryClinical data sets incorporate continuous data like blood pressure or sodium levels, categorical data like cancer grade or stage, and binary data like sex or marital status. Measurements on an individual patient define a point in a high-dimensional space; data from many patients defines a "point cloud". The "shape" of the point cloud influences experimental design by describing patient variability. Topological data analysis (TDA) is a mathematical technique for understanding the shape of point clouds by finding "holes" that correspond to combinations of patient characteristics that are never observed. TDA results are stratified by dimension. Zero-dimensional features define patient subtypes. One-dimensional features ("loops") are analogs of the inside of a circle or a donut hole. Two-dimensional features ("voids") are analogs of the inside of a balloon. Here, we apply TDA to a clinical data set of previously untreated patients with Chronic Lymphocytic Leukemia to find loops and voids.