Graphical models for mean and covariance of multivariate longitudinal data.

ABSTRACT

Joint mean-covariance modeling of multivariate longitudinal data helps to understand the relative changes among multiple longitudinally measured and correlated outcomes. A key challenge in the analysis of multivariate longitudinal data is the complex covariance structure. This is due to the contemporaneous and cross-temporal associations between multiple longitudinal outcomes. Graphical and data-driven tools that can aid in visualizing the dependence patterns among multiple longitudinal outcomes are not readily available. In this work, we show the role of graphical techniques profile plots, and multivariate regressograms, in developing mean and covariance models for multivariate longitudinal data. We introduce an R package MLGM (Multivariate Longitudinal Graphical Models) to facilitate visualization and modeling mean and covariance patterns. Through two real studies, microarray data from the T-cell activation study and Mayo Clinic's primary biliary cirrhosis of the liver study, we show the key features of MLGM. We evaluate the finite sample performance of the proposed mean-covariance estimation approach through simulations.