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

Abstract

Objectives 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 settles for defining simple spatial groupings of patients using clustering analyses or dimension reduction. Our goal is to see if topological data analysis (TDA), a relatively new unsupervised technique, is able to obtain a more complete understanding of patient space. Methods TDA is optimized to detect "holes" in data, such as the insides of circles (loops) or the insides of spheres (voids). We apply TDA to a space of 266 previously untreated patients with Chronic Lymphocytic Leukemia (CLL). We use the "daisy" distance metric defined by Kaufman and Rouseeuw to compute distances between clinical records. We describe novel computational and graphical methods to interpret the structures detected by TDA. Results Using TDA, we find clear evidence of the existence of both loops and voids in the CLL data. The most persistent loop and the most persistent void can be interpreted using three dichotomized, prognostically important factors in CLL: _IGHV_ somatic mutation status, beta-2 microglobulin, and Rai stage. Conclusion We applied a cutting-edge analysis tool, TDA, to better define the "space of patients" in CLL clinical data. Patient space turns out to be richer and more complex than current models imply. TDA could become a powerful tool in the biomedical informatician's arsenal for interpreting high-dimensional data. It may provide novel insights into biological processes and improve our understanding of clinical and biological data sets.