# A comparison of methods for clustering longitudinal data with slowly changing trends

Longitudinal clustering provides a detailed yet comprehensible description of time profiles among subjects. With several approaches that are commonly used for this purpose, it remains unclear under which conditions a method is preferred over another method. We investigated the performance of five methods using Monte Carlo simulations on synthetic datasets, representing various scenarios involving polynomial time profiles. The performance was evaluated on two aspects: The agreement of the group assignment to the simulated reference, as measured by the split-join distance, and the trend estimation error, as measured by a weighted minimum of the mean squared error (WMMSE). Growth mixture modeling (GMM) was found to achieve the best overall performance, followed closely by a two-step approach using growth curve modeling and *k*-means (GCKM). Considering the model similarities between GMM and GCKM, the latter is preferred for large datasets for its computational efficiency. Longitudinal *k*-means (KML) and group-based trajectory modeling were found to have practically identical solutions in the case that the group trajectory model of the latter method is correctly specified. Both methods performed less than GMM and GCKM in most settings.