Cluster analysis of longitudinal profiles with subgroups

In this paper, we cluster profiles of longitudinal data using a penalized regression method. Specifically, we allow heterogeneous variation of longitudinal patterns for each subject, and utilize a pairwise-grouping penalization on coefficients of the nonparametric B-spline models to form subgroups. Consequently, we identify clusters based on different patterns of the predicted longitudinal curves. One advantage of the proposed method is that there is no need to pre-specify the number of clusters; instead the number of clusters is selected automatically through a model selection criterion. Our method is also applicable for unbalanced data where different subjects could have measurements at different time points. To implement the proposed method, we develop an alternating direction method of multipliers (ADMM) algorithm which has the desirable convergence property. In theory, we establish the consistency properties for approximated nonparametric function estimation and subgrouping memberships. In addition, we show that our method outperforms the existing competitive approaches in our simulation studies and real data example.