Mixture of multivariate t linear mixed models for multi-outcome longitudinal data with heterogeneity

The issues of model-based clustering and classification of longitudinal data have received increasing attention in recent years. In this paper, we propose a finite mixture of multivariate t linear mixed-effects model (FM-MtLMM) for analyzing longitudinally measured multi-outcome data arisen from more than one heterogeneous sub-population. The motivation behind this work comes from a cohort study of patients with primary biliary cirrhosis, where the interest is in classifying new patients into two or more prognostic groups on the basis of their longitudinally observed bilirubin and albumin levels. The proposed FM-MtLMM offers robustness and flexibility to accommodate fat tails or atypical observations contained in one or several of the groups. An efficient alternating expectation conditional maximization (AECM) algorithm is employed for the computation of maximum likelihood estimates of parameters. The calculation of standard errors is effected by an information-based method. Practical techniques for clustering of multivariate longitudinal data, estimation of random effects, and classification of future patients are also provided. The methodology is illustrated by analyzing Mayo Clinic Primary Biliary Cirrhosis sequential (PBCseq) data and a simulation study.