Semiparametric Bayesian latent trajectory models

Latent trajectory models (LTMs) characterize longitudinal data using a finite mixture of curves. We address uncertainty in the number of latent classes and in the form of the class-specific curves using a semiparametric Bayesian approach. A mixture of functional Dirichlet processes (FDP) is used to characterize the distribution of longitudinal trajectories. The FDP is defined by replacing the atoms in the stick-breaking representation of a Dirichlet process with random functions. Based on the FDP, subjects are automatically clustered into an unknown number of groups based on their latent trajectories. To allow joint nonparametric modeling with a multivariate response, we generalize the FDP to a class of joint FDPs (JFDP). The proposed approach allows the response distribution to be unknown and varying with trajectory class. An MCMC algorithm is developed for posterior computation. The methods are motivated by an epidemiologic study of water quality and pregnancy outcomes.