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

<p>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.</p

An Activity Index for Raw Accelerometry Data and Its Comparison with Other Activity Metrics - Fig 6

<p>The “receiver operating characteristic” (ROC) curves of Activity Index (AI), activity count (AC), AC with Low Frequency Extension (LFE) and Euclidean Norm Minus One (ENMO) to predict whether metabolic equivalents (MET) is smaller or greater than 3 (A) and 1.5 (B), and whether MET is bigger than 1.5 but smaller than 3 (C). The ROC curves for AI, AC and ENMO are solid, dashed and dotted, respectively, while AC with and without LFE are rendered in purple and orange. The corresponding area under the curve (AUC) of each ROC curve is given in the legend section.</p

A general framework for accelerometer-related studies.

<p>The left panel illustrates two general data types: raw data and summary measures. The right panel shows 4 common research interests. The mid panel contains 6 common analysis pathways between the data and the research interests.</p

The “receiver operating characteristic” (ROC) curves for distinguishing four pairs of activity types, using Activity Index (AI, solid curves) or activity count (AC, dashed curves in different color for AC with and without Low Frequency Extension (LFE)) or Euclidean Norm Minus One (ENMO, dotted curves), respectively.

<p>The corresponding area under the curve (AUC) of each ROC curve is given in the legend section.</p

An Activity Index for Raw Accelerometry Data and Its Comparison with Other Activity Metrics - Fig 5

<p>Scatterplots of metabolic equivalents (METs) versus Activity Index (AI) (A), activity count (AC) (B), AC with Low Frequency Extension (LFE) (C) and Euclidean Norm Minus One (ENMO) (D). MET is on <i>x</i>-axis for all four plots, while AI, AC, AC (LFE) and ENMO are on the <i>y</i>-axis in (A), (B), (C) and (D), respectively. Each point in the figure represents a participant's median METs during a certain activity (rendered in different colors) versus the median AI, AC or ENMO while he/she was performing the same activity.</p

Comparison of the boxplots of Activity Index (AI), activity count (AC), AC with Low Frequency Extention (LFE) and Euclidean Norm Minus One (ENMO) during different types of activities.

<p>Outliers outside of the upper and lower whiskers are omitted. Each type of summary metric from all the participants were pooled together and plotted according to the type of activity.</p

Summary Statistics of AI, AC, AC (LFE), and ENMO of each activity.

<p>Summary Statistics of AI, AC, AC (LFE), and ENMO of each activity.</p