Abstract

Repeated measurements are common in many fields, where random vari

ables are observed repeatedly across different subjects. Such data have an underlying

hierarchical structure, and it is of interest to learn covariance/correlation at different levels. Most existing methods for sparse covariance/correlation matrix estimation

assume independent samples. Ignoring the underlying hierarchical structure and correlation within the subject may lead to erroneous scientific conclusions. In this paper,

we propose to distinguish between the between-subject covariance structure and the

within-subject covariance structure.

In the presence of repeated measurement, this

leads to the problem of sparse and positive-definite estimation of between-subject and

within-subject covariance matrices. Our estimators are solutions to convex optimization problems that can be solved efficiently. We establish estimation error rates for the

proposed estimators and demonstrate their favorable performance through theoretical

analysis and comprehensive simulation studies. We further apply our methods to construct between-subject and within-subject covariance graphs of clinical variables from

hemodialysis patients.

Information

Preprint No.SS-2024-0279
Manuscript IDSS-2024-0279
Complete AuthorsSunpeng Duan, Guo Yu, Juntao Duan, Yuedong Wang
Corresponding AuthorsGuo Yu
Emailsguoyu@ucsb.edu

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Acknowledgments

We thank Fresenius Medical Care North America for providing de-identified data

and Dr. Hanjie Zhang for discussing real data analysis. We also thank the editor,

associate editor, and two referees for constructive comments that substantially

improved an earlier draft. We have no conflicts of interest to declare.

The R codes that support and reproduce the finding of this study are openly

hosted on the Github repository: https://github.com/sunpeng52/GGM. The

hemodialysis data are available on the COVID RADx Data Hub. This research

was partially supported by the NIH grant R01DK130067.

Supplementary Materials

The online Supplementary Material includes proofs of the theoretical results,

computational details, and additional data analyses.

Supplementary materials are available for download.