Cluster analysis for longitudinal data and its application in the detection of adiposity trajectories

The identification of latent profile trajectories in longitudinal studies represents an important challenge for specialists since they could provide insights to better understand their problem of interest. The majority of the statistical methodologies for cluster analysis for longitudinal data are based on growth curve or mixed-effects models, and often incorporate covariates for a better adjustment. In particular, for Bayesian nonparametric methods, Dirichlet process mixture models are widely used together. We propose a clustering methodology for longitudinal data based on mixture models generated by a discrete random probability measure whose weights are decreasingly ordered by construction. Additionally, data is modeled without making use of covariates and assuming independence across time for individual measurements. Our approach also provides a straightforward procedure to merge some estimated groups, since it could happen that there are many of them, to be easily explained by experts. Our results suggest that, at least for a first analysis, this framework is enough to effectively detect groups in the data; further exploration of each group could incorporate extra information. We apply our methodology for detecting adiposity trajectories in Mexican children in a secondary analysis of the "Prenatal Omega-3 fatty acid Supplementation and Child Growth and Development" study (POSGRAD) cohort.