Joint Modeling and Clustering Paired Generalized Longitudinal Trajectories With Application to Cocaine Abuse Treatment Data

In a cocaine dependence treatment study, we have paired binary longitudinal trajectories that record the cocaine use patterns of each patient before and after a treatment. To better understand the drug-using behaviors among the patients, we propose a general framework based on functional data analysis to jointly model and cluster these paired non-Gaussian longitudinal trajectories. Our approach assumes that the response variables follow distributions from the exponential family, with the canonical parameters determined by some latent Gaussian processes. To reduce the dimensionality of the latent processes, we express them by a truncated Karhunen-Lóeve (KL) expansion allowing the mean and covariance functions to be different across clusters. We further represent the mean and eigenfunctions functions by flexible spline bases, and determine the orders of the truncated KL expansions using data-driven methods. By treating the cluster membership as a missing value, we cluster the cocaine use trajectories by a likelihood-based approach. The cluster membership and parameter estimates are jointly estimated by a Monte Carlo EM algorithm with Gibbs sampling steps. We discover subgroups of patients with distinct behaviors in terms of overall probability to use, binge verses periodic use pattern, etc. The joint modeling approach also sheds new lights on relating relapse behavior to baseline pattern in each subgroup. Supplementary materials for this article are available online.