Topological Structures in the Space of Treatment-Naïve Patients with Chronic Lymphocytic Leukemia
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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 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.
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The black arrow highlights the longest barcode.
It might be easier to see if the longest barcode was in a different color or had a dashed line overlayed on top of it.
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e green and light blue clusters are on one side, and the other colors(especially the dark blue and magenta) are on the other side of the hole.
It's hard to tell exactly which part of the structure is being referenced (at least for me). It might be helpful to add an annotation like a circle to show which area is being discussed.
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