Multivariate skew-normal at linear mixed models for multi-outcome longitudinal data

More than one series of longitudinal data frequently encountered in biomedical, psychological and clinical research are routinely analyzed under a multivariate linear mixed model framework with underlying multivariate normality assumptions for the random effects and within-subject errors. However, such normality assumption might not offer robust inference if the data, even after being transformed, particularly exhibit skewness. In this paper, we propose a multivariate skew-normal linear mixed model constructed by assuming a multivariate skew-normal distribution for the random effects and a multivariate normal distribution for the random errors. A damped exponential correlation structure is adopted to address the within-subject autocorrelation possibly existing among irregularly observed measures. We present an efficient alternating expectation-conditional maximization (AECM) algorithm for maximum likelihood estimation of parameters. The techniques for estimation of random effects and prediction of future outcomes are discussed. Our proposed model is motivated by, and used for, the analysis of AIDS clinical trials in which we investigate the ‘association-of-the-evolutions’ and the ‘evolution-of-the-association’ of HIV-1 RNA copies and CD4⁺T cell counts during antiviral therapies.