Multilevel Matrix-Variate Analysis and its Application to Accelerometry-Measured Physical Activity in Clinical Populations

ABSTRACT

The number of studies where the primary measurement is a matrix is exploding. In response to this, we propose a statistical framework for modeling populations of repeatedly observed matrix-variate measurements. The 2D structure is handled via a matrix-variate distribution with decomposable row/column-specific covariance matrices and a linear mixed effect framework is used to model the multilevel design. The proposed framework flexibly expands to accommodate many common crossed and nested designs and introduces two important concepts: the between-subject distance and intraclass correlation coefficient, both defined for matrix-variate data. The computational feasibility and performance of the approach is shown in extensive simulation studies. The method is motivated by and applied to a study that monitored physical activity of individuals diagnosed with congestive heart failure (CHF) over a 4- to 9-month period. The long-term patterns of physical activity are studied and compared in two CHF subgroups: with and without adverse clinical events. Supplementary materials for this article, that include de-identified accelerometry and clinical data, are available online.

KEYWORDS:

• Actigraphy
• Principal component analysis
• Separable covariance

Supplementary Material

• chfData.zip Contains de-identified raw accelerometry data and covariates including age, gender, BMI, event week, and event type. This file can also can be downloaded via https://www.dropbox.com/s/34q3x6xtkiq5x6w/chfData.zip?dl=0.

• Appendix Appendix containing derivations of BLUPs for calculating the principal scores, description, and derivations of projection method.

Acknowledgment

The authors gratefully acknowledge Ciprian Crainiceanu’s help on the article.