An important endpoint variable in a cocaine rehabilitation study is the time to first relapse of a patient after the treatment. We propose a joint modeling approach based on functional data analysis to study the relationship between the baseline longitudinal cocaine-use pattern and the interval censored time to first relapse. For the baseline cocaine-use pattern, we consider both self-reported cocaine-use amount trajectories and dichotomized use trajectories. Variations within the generalized longitudinal trajectories are modeled through a latent Gaussian process, which is characterized by a few leading functional principal components. The association between the baseline longitudinal trajectories and the time to first relapse is built upon the latent principal component scores. The mean and the eigenfunctions of the latent Gaussian process as well as the hazard function of time to first relapse are modeled nonparametrically using penalized splines, and the parameters in the joint model are estimated by a Monte Carlo EM algorithm based on Metropolis–Hastings steps. An Akaike information criterion (AIC) based on effective degrees of freedom is proposed to choose the tuning parameters, and a modified empirical information is proposed to estimate the variance–covariance matrix of the estimators.
"Joint modeling of longitudinal drug using pattern and time to first relapse in cocaine dependence treatment data." Ann. Appl. Stat. 9 (3) 1621 - 1642, September 2015. https://doi.org/10.1214/15-AOAS852