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Ghosal R, Varma VR, Volfson D, Hillel I, Urbanek J, Hausdorff JM, Watts A, Zipunnikov V. Distributional data analysis via quantile functions and its application to modeling digital biomarkers of gait in Alzheimer's Disease. Biostatistics 2023; 24:539-561. [PMID: 36519565 PMCID: PMC10544806 DOI: 10.1093/biostatistics/kxab041] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2021] [Revised: 09/10/2021] [Accepted: 10/19/2021] [Indexed: 07/20/2023] Open
Abstract
With the advent of continuous health monitoring with wearable devices, users now generate their unique streams of continuous data such as minute-level step counts or heartbeats. Summarizing these streams via scalar summaries often ignores the distributional nature of wearable data and almost unavoidably leads to the loss of critical information. We propose to capture the distributional nature of wearable data via user-specific quantile functions (QF) and use these QFs as predictors in scalar-on-quantile-function-regression (SOQFR). As an alternative approach, we also propose to represent QFs via user-specific L-moments, robust rank-based analogs of traditional moments, and use L-moments as predictors in SOQFR (SOQFR-L). These two approaches provide two mutually consistent interpretations: in terms of quantile levels by SOQFR and in terms of L-moments by SOQFR-L. We also demonstrate how to deal with multi-modal distributional data via Joint and Individual Variation Explained using L-moments. The proposed methods are illustrated in a study of association of digital gait biomarkers with cognitive function in Alzheimers disease. Our analysis shows that the proposed methods demonstrate higher predictive performance and attain much stronger associations with clinical cognitive scales compared to simple distributional summaries.
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Affiliation(s)
- Rahul Ghosal
- Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD, USA
| | - Vijay R Varma
- National Institute on Aging (NIA), National Institutes of Health (NIH), Baltimore, MD, USA
| | - Dmitri Volfson
- Neuroscience Analytics, Computational Biology, Takeda, Cambridge, MA, USA
| | - Inbar Hillel
- Center for the Study of Movement, Cognition and Mobility, Neurological Institute, Tel Aviv Sourasky Medical Center, Tel Aviv, Israel
| | - Jacek Urbanek
- Department of Medicine, Johns Hopkins University School of Medicine, Baltimore, MD, USA
| | - Jeffrey M Hausdorff
- Center for the Study of Movement, Cognition and Mobility, Neurological Institute, Tel Aviv Sourasky Medical Center, Tel Aviv, Israel, Department of Physical Therapy, Sackler Faculty of Medicine, and Sagol School of Neuroscience, Tel Aviv University, Tel Aviv, Israel, and Rush Alzheimer’s Disease Center and Department of Orthopedic Surgery, Rush University Medical Center, Chicago, IL, USA
| | - Amber Watts
- Department of Psychology, University of Kansas, Lawrence, KS, USA
| | - Vadim Zipunnikov
- Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD, USA
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Shape-constrained estimation in functional regression with Bernstein polynomials. Comput Stat Data Anal 2023. [DOI: 10.1016/j.csda.2022.107614] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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