Cluster analysis of longitudinal profiles with subgroups

In this paper, we cluster profiles of longitudinal data using a penalized regression method. The uniqueness of our approach is that we allow individual variation of longitudinal patterns for each subject. Specifically, we utilize a pairwise-grouping penalization on the parameters corresponding to the nonparametric B-spline models, and thereby 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 subjects could have different time points of measurements. 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 asymptotically. In addition, we show that our method outperforms the existing competitive approaches in our simulation studies and real data example.