Interdisciplinary Approaches to Automated Obstructive Sleep Apnea Diagnosis Through High-Dimensional Multiple Scaled Data Analysis

  • Giseon HeoEmail author
  • Kathryn Leonard
  • Xu Wang
  • Yi Zhou
Part of the Association for Women in Mathematics Series book series (AWMS, volume 17)


Obstructive sleep apnea (OSA) is a wide-spread condition that results in debilitating consequences including death. Diagnosis is a lengthy and expensive process because OSA is a multifactorial disorder, making it necessary to study many different types of data, including DNA sequences, multiple time series, metabolites, airflow in airway, and shape analysis of airway and patients’ faces. OSA data are an example of complex and multi-dimensional data for which analysis and interpretation can be challenging, requiring sophisticated analytic techniques. It may be no longer effective to independently apply methods from a specific discipline such as statistics, mathematics, or computing science. In this article, combining the analyses of three datasets from independent OSA studies, we illustrate the complementary nature of the techniques. Specifically, we apply techniques in statistics, machine learning, geometry, and computational topology to derive automated analytic tools for each data type. Taken together, these techniques provide a sophisticated diagnostic tool. A novel geometric OSA severity index (GSI) is developed using methods from computational geometry. This index measures the volume of the airway obstruction in OSA patients. The lower the GSI value is, the more severe the airway obstruction is. Persistent homology is employed to extract the importance information from 28-dimensional polysomnography (PSG) data. Random forests and principal component analysis are used and compared to identify important variables in the PSG, while logistic regression and random forest are used and compared to verify the prediction power of the identified variables. The results indicate that persistent homology can accurately extract importance information from PSG, and the identified important variables are meaningful for predicting obstructive apnea–hypopnea index (ahi). Cluster analysis is used to identify the pattern of the survey information, and the importance of responses to individual questions in survey questionnaires is also identified by random forest. The results from all three independent studies are very meaningful in clinical studies and can be used as guidance for clinical practitioners.



The authors would like to thank the Institute for Computational and Experimental Research Mathematics, the National Science Foundation (NSF-HRD 1500481), and the Association for Women in Mathematics for support, financial, and otherwise, of this collaboration. We thank the National Sleep Research Resource for their permission to use the dataset. We would like to thank the National Sciences and Engineering Research Council of Canada, Seed Grant from Women and Children’s Health Research Institute, University of Alberta, and Biomedical Research Award from American Association of Orthodontists Foundation. We would like to thank Facundo Mémoli for discussion on persistent homology.


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Copyright information

© The Author(s) and the Association for Women in Mathematics 2019

Authors and Affiliations

  1. 1.School of DentistryUniversity of AlbertaEdmontonCanada
  2. 2.Department of Computer ScienceOccidental CollegeLos AngelesUSA
  3. 3.Department of MathematicsWilfrid Laurier UniversityWaterlooCanada
  4. 4.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada

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