Shape invariant mixture model for clustering non-linear longitudinal growth trajectories

In longitudinal studies, it is often of great interest to cluster individual trajectories based on repeated measurements taken over time. Non-linear growth trajectories are often seen in practice, and the individual data can also be measured sparsely, and at irregular time points, which may complicate the modeling process. Motivated by a study of pregnant women hormone profiles, we proposed a shape invariant growth mixture model for clustering non-linear growth trajectories. Bayesian inference via Monte Carlo Markov Chain was employed to estimate the parameters of interest. We compared our model to the commonly used growth mixture model and functional clustering approach by simulation studies. Results from analyzing the real data and simulated data were presented and discussed.